%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL102-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 09:37:27 AM UTC 2026
% Result : Unsatisfiable 0.46s 0.29s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL102-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n018.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:39:55 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.29 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
% 0.46/0.29
% 0.46/0.29 % SZS status Unsatisfiable
% 0.46/0.29
% 0.46/0.29 % SZS output start Proof
% 0.46/0.29 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.46/0.29 Axiom 2 (cls_conjecture_1): c_in(c_Pair(v_y, v_za, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.46/0.29 Axiom 3 (cls_conjecture_2): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.46/0.29 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.
% 0.46/0.29 Axiom 5 (cls_Comb_Ocontract_OAp1_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, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X, Z), c_Comb_Ocomb_Oop_A_D_D(Y, Z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true) = true.
% 0.46/0.29 Axiom 6 (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.
% 0.46/0.29
% 0.46/0.29 Goal 1 (cls_conjecture_3): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 0.46/0.29 Proof:
% 0.46/0.29 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.46/0.29 = { by axiom 1 (ifeq_axiom) R->L }
% 0.46/0.29 ifeq(true, true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.46/0.29 = { by axiom 4 (cls_Transitive__Closure_Or__into__rtrancl_0) R->L }
% 0.46/0.29 ifeq(ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.46/0.29 = { by axiom 1 (ifeq_axiom) R->L }
% 0.46/0.29 ifeq(ifeq(ifeq(true, true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.46/0.29 = { by axiom 2 (cls_conjecture_1) R->L }
% 0.46/0.29 ifeq(ifeq(ifeq(c_in(c_Pair(v_y, v_za, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Ocontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.46/0.29 = { by axiom 5 (cls_Comb_Ocontract_OAp1_0) }
% 0.46/0.29 ifeq(ifeq(true, true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.46/0.29 = { by axiom 1 (ifeq_axiom) }
% 0.46/0.29 ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true)
% 0.46/0.29 = { by axiom 1 (ifeq_axiom) R->L }
% 0.46/0.29 ifeq(true, true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true)
% 0.46/0.29 = { by axiom 3 (cls_conjecture_2) R->L }
% 0.46/0.29 ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_za, v_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Transitive__Closure_Ortrancl(c_Comb_Ocontract, tc_Comb_Ocomb), tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true)
% 0.46/0.29 = { by axiom 6 (cls_Transitive__Closure_Ortrancl__trans_0) }
% 0.46/0.29 true
% 0.46/0.29 % SZS output end Proof
% 0.46/0.29
% 0.46/0.29 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------