%---------------- SGGS v1.0 (IJCAR 2020 submission) ----------------%

------ Parsing...successful


------ Proving...
use I-
not ground preserving

Gamma_0: (extend-no-conflict)
  0: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]

Gamma_1: (extend-no-conflict)
  0: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]
  1: [c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),
tc_prod(X1,X1))]

Gamma_2: (extend-conflict)
  0: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]
  1: [c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),
tc_prod(X1,X1))]
  2: [~(c_in(c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))], ~(
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))

Gamma_3: (move)
  0: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]
  1: [~(c_in(c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))], ~(
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))
  2: [c_in(c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),
tc_prod(X1,X1))]

Gamma_4: (right-split)
  0: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]
  1: [~(c_in(c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))], ~(
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))
  2: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x | [c_in(
c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))]
  3: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))]
  4: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(v_r,X0),tc_prod(X0,X0))]
  5: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(v_r,X1),tc_prod(X1,X1))]
  6: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r | [c_in(
c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(X0,t_a),tc_prod(t_a,t_a))]
  7: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a))]
  8: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(X1,X0),tc_prod(X0,X0))]
  9: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1))]

Gamma_5: (resolve)
  0: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]
  1: [~(c_in(c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))], ~(
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))
  2: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x | [~(
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))]
  3: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))]
  4: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(v_r,X0),tc_prod(X0,X0))]
  5: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(v_r,X1),tc_prod(X1,X1))]
  6: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r | [c_in(
c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(X0,t_a),tc_prod(t_a,t_a))]
  7: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a))]
  8: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(X1,X0),tc_prod(X0,X0))]
  9: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1))]

Gamma_6: (extend-conflict)
  0: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]
  1: [~(c_in(c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))], ~(
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))
  2: [~(c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))]
  3: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))]
  4: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(v_r,X0),tc_prod(X0,X0))]
  5: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(v_r,X1),tc_prod(X1,X1))]
  6: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r | [c_in(
c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(X0,t_a),tc_prod(t_a,t_a))]
  7: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a))]
  8: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(X1,X0),tc_prod(X0,X0))]
  9: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1))]

Gamma_7: (move)
  0: [~(c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))]
  1: [c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),
tc_prod(t_a,t_a))]
  2: [~(c_in(c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))], ~(
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))
  3: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))]
  4: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(v_r,X0),tc_prod(X0,X0))]
  5: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(v_r,X1),tc_prod(X1,X1))]
  6: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r | [c_in(
c_Pair(v_x,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(X0,t_a),tc_prod(t_a,t_a))]
  7: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(X1,t_a),tc_prod(t_a,t_a))]
  8: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a | [c_in(
c_Pair(v_x,v_x,X0,X0),c_Transitive__Closure_Ortrancl(X1,X0),tc_prod(X0,X0))]
  9: top(X1) != t_a & top(X1) != t_a & top(X1) != t_a & top(X2) != v_r & top(X1) != t_a & top(X1) != t_a & top(X0) != v_x & top(X0) != v_x | [c_in(
c_Pair(X0,X0,X1,X1),c_Transitive__Closure_Ortrancl(X2,X1),tc_prod(X1,X1))]

Gamma_8: (resolve)
  0: [~(c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)))]
  1: []

SZS status Unsatisfiable