%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL124-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.08s 0.14s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL124-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 21:41:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.14 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.08/0.14
% 0.08/0.14 % SZS status Unsatisfiable
% 0.08/0.14
% 0.08/0.14 % SZS output start Proof
% 0.08/0.15 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.15 Axiom 2 (cls_Comb_Ocontract_OK_0): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, X), Y), X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.08/0.15 Axiom 3 (cls_conjecture_0): ifeq(c_in(c_Pair(X, Y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(c_in(c_Pair(X, Z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(Z, v_x(X, Z, Y), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true) = true.
% 0.08/0.15
% 0.08/0.15 Goal 1 (cls_Comb_OI__contract__E_0): c_in(c_Pair(c_Comb_OI, X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.08/0.15 The goal is true when:
% 0.08/0.15 X = v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI)
% 0.08/0.15
% 0.08/0.15 Proof:
% 0.08/0.15 c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.08/0.15 = { by axiom 1 (ifeq_axiom) R->L }
% 0.08/0.15 ifeq(true, true, c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.08/0.15 = { by axiom 2 (cls_Comb_Ocontract_OK_0) R->L }
% 0.08/0.15 ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.08/0.15 = { by axiom 1 (ifeq_axiom) R->L }
% 0.08/0.15 ifeq(true, true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true)
% 0.08/0.15 = { by axiom 2 (cls_Comb_Ocontract_OK_0) R->L }
% 0.08/0.15 ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_OI, v_x(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, c_Comb_OI), X), c_Comb_OI, c_Comb_OI), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true)
% 0.08/0.15 = { by axiom 3 (cls_conjecture_0) }
% 0.08/0.15 true
% 0.08/0.15 % SZS output end Proof
% 0.08/0.15
% 0.08/0.15 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------