%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:37:31 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.32s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n026.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:44:11 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.32 Command-line arguments: --no-flatten-goal
% 0.19/0.32
% 0.19/0.32 % SZS status Unsatisfiable
% 0.19/0.32
% 0.19/0.34 % SZS output start Proof
% 0.19/0.34 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.34 Axiom 2 (cls_conjecture_1): c_in(c_Pair(v_y, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true.
% 0.19/0.34 Axiom 3 (cls_conjecture_2): c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true.
% 0.19/0.34 Axiom 4 (cls_Transitive__Closure_Or__into__rtrancl_0): ifeq(c_in(X, Y, tc_prod(Z, Z)), true, c_in(X, c_Transitive__Closure_Ortrancl(Y, Z), tc_prod(Z, Z)), true) = true.
% 0.19/0.34 Axiom 5 (cls_conjecture_4): ifeq(c_in(c_Pair(v_x, X, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_y, v_xaa(X), t_a, t_a), v_r, tc_prod(t_a, t_a)), true) = true.
% 0.19/0.34 Axiom 6 (cls_conjecture_3): ifeq(c_in(c_Pair(v_x, X, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(X, v_xaa(X), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true) = true.
% 0.19/0.34 Axiom 7 (cls_conjecture_7): ifeq(c_in(c_Pair(X, Y, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_in(c_Pair(X, Z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(Z, v_xa(X, Y, Z), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true) = true.
% 0.19/0.34 Axiom 8 (cls_conjecture_6): ifeq(c_in(c_Pair(X, Y, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_in(c_Pair(X, Z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(Z, v_xa(X, Z, Y), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true) = true.
% 0.19/0.34 Axiom 9 (cls_Transitive__Closure_Ortrancl__trans_0): ifeq(c_in(c_Pair(X, Y, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, ifeq(c_in(c_Pair(Y, V, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true, c_in(c_Pair(X, V, Z, Z), c_Transitive__Closure_Ortrancl(W, Z), tc_prod(Z, Z)), true), true) = true.
% 0.19/0.34
% 0.19/0.34 Goal 1 (cls_conjecture_5): tuple(c_in(c_Pair(v_z, X, t_a, t_a), v_r, tc_prod(t_a, t_a)), c_in(c_Pair(v_xb, X, t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a))) = tuple(true, true).
% 0.19/0.34 The goal is true when:
% 0.19/0.34 X = v_xa(v_y, v_z, v_xaa(v_xb))
% 0.19/0.34
% 0.19/0.34 Proof:
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)))
% 0.19/0.34 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(true, true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 4 (cls_Transitive__Closure_Or__into__rtrancl_0) R->L }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(ifeq(true, true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 5 (cls_conjecture_4) R->L }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(ifeq(ifeq(c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 3 (cls_conjecture_2) }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(ifeq(ifeq(true, true, c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 1 (ifeq_axiom) }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(ifeq(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(ifeq(true, true, ifeq(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 2 (cls_conjecture_1) R->L }
% 0.19/0.34 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(ifeq(c_in(c_Pair(v_y, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true), true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.34 = { by axiom 7 (cls_conjecture_7) }
% 0.19/0.35 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(true, true, c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.35 = { by axiom 1 (ifeq_axiom) }
% 0.19/0.35 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true))
% 0.19/0.35 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.35 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(true, true, ifeq(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true))
% 0.19/0.35 = { by axiom 6 (cls_conjecture_3) R->L }
% 0.19/0.35 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xb, v_xaa(v_xb), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, ifeq(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true))
% 0.19/0.35 = { by axiom 3 (cls_conjecture_2) }
% 0.19/0.35 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(ifeq(true, true, c_in(c_Pair(v_xb, v_xaa(v_xb), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true, ifeq(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true))
% 0.19/0.35 = { by axiom 1 (ifeq_axiom) }
% 0.19/0.35 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), ifeq(c_in(c_Pair(v_xb, v_xaa(v_xb), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true, ifeq(c_in(c_Pair(v_xaa(v_xb), v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true, c_in(c_Pair(v_xb, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), c_Transitive__Closure_Ortrancl(v_r, t_a), tc_prod(t_a, t_a)), true), true))
% 0.19/0.35 = { by axiom 9 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.19/0.35 tuple(c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true)
% 0.19/0.35 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.35 tuple(ifeq(true, true, c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true)
% 0.19/0.35 = { by axiom 5 (cls_conjecture_4) R->L }
% 0.19/0.35 tuple(ifeq(ifeq(c_in(c_Pair(v_x, v_xb, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true)
% 0.19/0.35 = { by axiom 3 (cls_conjecture_2) }
% 0.19/0.35 tuple(ifeq(ifeq(true, true, c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true, c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true)
% 0.19/0.35 = { by axiom 1 (ifeq_axiom) }
% 0.19/0.35 tuple(ifeq(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true)
% 0.19/0.35 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.35 tuple(ifeq(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(true, true, c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true), true)
% 0.19/0.35 = { by axiom 2 (cls_conjecture_1) R->L }
% 0.19/0.35 tuple(ifeq(c_in(c_Pair(v_y, v_xaa(v_xb), t_a, t_a), v_r, tc_prod(t_a, t_a)), true, ifeq(c_in(c_Pair(v_y, v_z, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, c_in(c_Pair(v_z, v_xa(v_y, v_z, v_xaa(v_xb)), t_a, t_a), v_r, tc_prod(t_a, t_a)), true), true), true)
% 0.19/0.35 = { by axiom 8 (cls_conjecture_6) }
% 0.19/0.35 tuple(true, true)
% 0.19/0.35 % SZS output end Proof
% 0.19/0.35
% 0.19/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------