%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL117-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 09:37:30 AM UTC 2026
% Result : Unsatisfiable 6.49s 1.09s
% Output : Proof 6.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL117-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.16 % Computer : n026.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Mon Sep 28 21:42:56 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.49/1.09 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 6.49/1.09
% 6.49/1.09 % SZS status Unsatisfiable
% 6.49/1.09
% 6.49/1.09 % SZS output start Proof
% 6.49/1.09 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 6.49/1.09 Axiom 2 (cls_conjecture_0): c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 6.49/1.09 Axiom 3 (cls_conjecture_1): c_in(c_Pair(v_x, v_x_H, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 6.49/1.09 Axiom 4 (cls_conjecture_2): c_in(c_Pair(v_ya, v_y_Ha, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 6.49/1.09 Axiom 5 (cls_Comb_Oparcontract_Ointros__3_0): c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, X), Y), Z), c_Comb_Ocomb_Oop_A_D_D(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_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true.
% 6.49/1.09 Axiom 6 (cls_Comb_Oparcontract_Ointros__4_0): ifeq(c_in(c_Pair(X, Y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(c_in(c_Pair(Z, W, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, 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, W), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true) = true.
% 6.49/1.09
% 6.49/1.09 Goal 1 (cls_conjecture_3): tuple(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), X, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) = tuple(true, true).
% 6.49/1.09 The goal is true when:
% 6.49/1.09 X = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w))
% 6.49/1.09
% 6.49/1.09 Proof:
% 6.49/1.09 tuple(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 6.49/1.09 tuple(ifeq(true, true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 6 (cls_Comb_Oparcontract_Ointros__4_0) R->L }
% 6.49/1.09 tuple(ifeq(ifeq(c_in(c_Pair(v_ya, v_y_Ha, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 2 (cls_conjecture_0) }
% 6.49/1.09 tuple(ifeq(ifeq(c_in(c_Pair(v_ya, v_y_Ha, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(true, true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 1 (ifeq_axiom) }
% 6.49/1.09 tuple(ifeq(ifeq(c_in(c_Pair(v_ya, v_y_Ha, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 4 (cls_conjecture_2) }
% 6.49/1.09 tuple(ifeq(ifeq(true, true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 1 (ifeq_axiom) }
% 6.49/1.09 tuple(ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 6.49/1.09 tuple(ifeq(true, true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 6 (cls_Comb_Oparcontract_Ointros__4_0) R->L }
% 6.49/1.09 tuple(ifeq(ifeq(c_in(c_Pair(v_x, v_x_H, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, 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_x_H, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 2 (cls_conjecture_0) }
% 6.49/1.09 tuple(ifeq(ifeq(c_in(c_Pair(v_x, v_x_H, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, 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_x_H, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 1 (ifeq_axiom) }
% 6.49/1.09 tuple(ifeq(ifeq(c_in(c_Pair(v_x, v_x_H, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, 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_x_H, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 3 (cls_conjecture_1) }
% 6.49/1.09 tuple(ifeq(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_x_H, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 1 (ifeq_axiom) }
% 6.49/1.09 tuple(ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, ifeq(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_z)), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), true), true), c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 6 (cls_Comb_Oparcontract_Ointros__4_0) }
% 6.49/1.09 tuple(true, c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_x_H), v_y_Ha), v_w), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H, v_w), c_Comb_Ocomb_Oop_A_D_D(v_y_Ha, v_w)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 6.49/1.09 = { by axiom 5 (cls_Comb_Oparcontract_Ointros__3_0) }
% 6.49/1.09 tuple(true, true)
% 6.49/1.09 % SZS output end Proof
% 6.49/1.09
% 6.49/1.09 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------