%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:24:08 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.29s
% Output : Proof 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO633-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 17:59:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.29 Command-line arguments: --no-flatten-goal
% 0.23/0.29
% 0.23/0.29 % SZS status Unsatisfiable
% 0.23/0.29
% 1.23/0.40 % SZS output start Proof
% 1.23/0.40 Axiom 1 (clause_6_04): E(f(X), s(s(s(s(0))))) = true.
% 1.23/0.40 Axiom 2 (clause_8_05): E(f(X), s(s(s(s(s(0)))))) = true.
% 1.23/0.40 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.23/0.40 Axiom 4 (clause_1_10): ifeq(E(f(X), s(s(s(s(s(0)))))), true, ifeq(E(f(Y), s(s(s(s(0))))), true, E(f(X), s(s(s(0)))), true), true) = true.
% 1.23/0.40 Axiom 5 (clause_4_12): ifeq(E(f(X), s(s(s(0)))), true, ifeq(E(f(Y), s(s(s(s(s(0)))))), true, ifeq(E(f(Z), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(s(0))), true), true), true) = true.
% 1.23/0.40 Axiom 6 (clause_12_09): ifeq(E(f(X), s(s(0))), true, ifeq(E(f(Y), s(s(s(0)))), true, ifeq(E(f(Z), s(s(s(s(s(0)))))), true, ifeq(E(f(W), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(0)), true), true), true), true) = true.
% 1.23/0.41 Axiom 7 (clause_2_07): ifeq(E(f(X), s(s(s(s(s(0)))))), true, ifeq(E(f(Y), s(0)), true, ifeq(E(f(Z), s(s(s(0)))), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(V), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true) = true.
% 1.23/0.41
% 1.23/0.41 Goal 1 (clause_5_03): tuple(E(f(X), s(s(0))), E(f(Y), s(s(s(s(0))))), E(f(Z), s(s(s(0)))), E(f(W), s(0)), E(f(V), 0), E(f(U), s(s(s(s(s(0))))))) = tuple(true, true, true, true, true, true).
% 1.23/0.41 The goal is true when:
% 1.23/0.41 X = AP(s(s(s(s(s(s(0)))))), Y5)
% 1.23/0.41 Y = T5
% 1.23/0.41 Z = V5
% 1.23/0.41 W = AP(s(s(s(s(s(s(0)))))), X4)
% 1.23/0.41 V = AP(s(s(s(s(s(s(0)))))), U)
% 1.23/0.41 U = W5
% 1.23/0.41
% 1.23/0.41 Proof:
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), E(f(T5), s(s(s(s(0))))), E(f(V5), s(s(s(0)))), E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), E(f(W5), s(s(s(s(s(0)))))))
% 1.23/0.41 = { by axiom 1 (clause_6_04) }
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true, E(f(V5), s(s(s(0)))), E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), E(f(W5), s(s(s(s(s(0)))))))
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true, ifeq(true, true, E(f(V5), s(s(s(0)))), true), E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), E(f(W5), s(s(s(s(s(0)))))))
% 1.23/0.41 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true, ifeq(E(f(U5), s(s(s(s(0))))), true, E(f(V5), s(s(s(0)))), true), E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), E(f(W5), s(s(s(s(s(0)))))))
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true, ifeq(true, true, ifeq(E(f(U5), s(s(s(s(0))))), true, E(f(V5), s(s(s(0)))), true), true), E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), E(f(W5), s(s(s(s(s(0)))))))
% 1.23/0.41 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true, ifeq(E(f(V5), s(s(s(s(s(0)))))), true, ifeq(E(f(U5), s(s(s(s(0))))), true, E(f(V5), s(s(s(0)))), true), true), E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), E(f(W5), s(s(s(s(s(0)))))))
% 1.23/0.41 = { by axiom 4 (clause_1_10) }
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), E(f(W5), s(s(s(s(s(0)))))))
% 1.23/0.41 = { by axiom 2 (clause_8_05) }
% 1.23/0.41 tuple(E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.41 tuple(ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(ifeq(true, true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.41 tuple(ifeq(E(f(S4), s(s(s(s(s(0)))))), true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(ifeq(true, true, ifeq(E(f(S4), s(s(s(s(s(0)))))), true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 4 (clause_1_10) R->L }
% 1.23/0.41 tuple(ifeq(ifeq(E(f(T4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z5), s(s(s(s(0))))), true, E(f(T4), s(s(s(0)))), true), true), true, ifeq(E(f(S4), s(s(s(s(s(0)))))), true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 2 (clause_8_05) }
% 1.23/0.41 tuple(ifeq(ifeq(true, true, ifeq(E(f(Z5), s(s(s(s(0))))), true, E(f(T4), s(s(s(0)))), true), true), true, ifeq(E(f(S4), s(s(s(s(s(0)))))), true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.41 tuple(ifeq(ifeq(E(f(Z5), s(s(s(s(0))))), true, E(f(T4), s(s(s(0)))), true), true, ifeq(E(f(S4), s(s(s(s(s(0)))))), true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 1 (clause_6_04) }
% 1.23/0.41 tuple(ifeq(ifeq(true, true, E(f(T4), s(s(s(0)))), true), true, ifeq(E(f(S4), s(s(s(s(s(0)))))), true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.41 tuple(ifeq(E(f(T4), s(s(s(0)))), true, ifeq(E(f(S4), s(s(s(s(s(0)))))), true, ifeq(E(f(X5), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y5)), s(s(0))), true), true), true), true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 5 (clause_4_12) }
% 1.23/0.41 tuple(true, true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 5 (clause_4_12) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(E(f(V4), s(s(s(0)))), true, ifeq(E(f(W4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(ifeq(true, true, E(f(V4), s(s(s(0)))), true), true, ifeq(E(f(W4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(ifeq(E(f(U4), s(s(s(s(0))))), true, E(f(V4), s(s(s(0)))), true), true, ifeq(E(f(W4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(ifeq(true, true, ifeq(E(f(U4), s(s(s(s(0))))), true, E(f(V4), s(s(s(0)))), true), true), true, ifeq(E(f(W4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(ifeq(E(f(V4), s(s(s(s(s(0)))))), true, ifeq(E(f(U4), s(s(s(s(0))))), true, E(f(V4), s(s(s(0)))), true), true), true, ifeq(E(f(W4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 4 (clause_1_10) }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(true, true, ifeq(E(f(W4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(E(f(W4), s(s(s(s(s(0)))))), true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 2 (clause_8_05) }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(true, true, ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(E(f(Z4), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 1 (clause_6_04) }
% 1.23/0.41 tuple(true, true, true, ifeq(ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.41 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(true, true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.41 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(E(f(T3), s(s(s(s(s(0)))))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(true, true, ifeq(E(f(T3), s(s(s(s(s(0)))))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.42 = { by axiom 4 (clause_1_10) R->L }
% 1.23/0.42 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(ifeq(E(f(U3), s(s(s(s(s(0)))))), true, ifeq(E(f(Y4), s(s(s(s(0))))), true, E(f(U3), s(s(s(0)))), true), true), true, ifeq(E(f(T3), s(s(s(s(s(0)))))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.42 = { by axiom 2 (clause_8_05) }
% 1.23/0.42 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(ifeq(true, true, ifeq(E(f(Y4), s(s(s(s(0))))), true, E(f(U3), s(s(s(0)))), true), true), true, ifeq(E(f(T3), s(s(s(s(s(0)))))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(ifeq(E(f(Y4), s(s(s(s(0))))), true, E(f(U3), s(s(s(0)))), true), true, ifeq(E(f(T3), s(s(s(s(s(0)))))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.42 = { by axiom 1 (clause_6_04) }
% 1.23/0.42 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(ifeq(true, true, E(f(U3), s(s(s(0)))), true), true, ifeq(E(f(T3), s(s(s(s(s(0)))))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V3)), s(s(0))), true, ifeq(E(f(U3), s(s(s(0)))), true, ifeq(E(f(T3), s(s(s(s(s(0)))))), true, ifeq(E(f(S3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), X4)), s(0)), true), true), true), true), E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.42 = { by axiom 6 (clause_12_09) }
% 1.23/0.42 tuple(true, true, true, true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 6 (clause_12_09) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(E(f(Z3), s(s(s(0)))), true, ifeq(E(f(Y3), s(s(s(s(s(0)))))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(ifeq(true, true, E(f(Z3), s(s(s(0)))), true), true, ifeq(E(f(Y3), s(s(s(s(s(0)))))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(ifeq(E(f(W3), s(s(s(s(0))))), true, E(f(Z3), s(s(s(0)))), true), true, ifeq(E(f(Y3), s(s(s(s(s(0)))))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(ifeq(true, true, ifeq(E(f(W3), s(s(s(s(0))))), true, E(f(Z3), s(s(s(0)))), true), true), true, ifeq(E(f(Y3), s(s(s(s(s(0)))))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(ifeq(E(f(Z3), s(s(s(s(s(0)))))), true, ifeq(E(f(W3), s(s(s(s(0))))), true, E(f(Z3), s(s(s(0)))), true), true), true, ifeq(E(f(Y3), s(s(s(s(s(0)))))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 4 (clause_1_10) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(true, true, ifeq(E(f(Y3), s(s(s(s(s(0)))))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(E(f(Y3), s(s(s(s(s(0)))))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 2 (clause_8_05) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(true, true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(E(f(X3), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 1 (clause_6_04) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(true, true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(E(f(V2), s(s(s(s(s(0)))))), true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(true, true, ifeq(E(f(V2), s(s(s(s(s(0)))))), true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 4 (clause_1_10) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(ifeq(E(f(W2), s(s(s(s(s(0)))))), true, ifeq(E(f(S2), s(s(s(s(0))))), true, E(f(W2), s(s(s(0)))), true), true), true, ifeq(E(f(V2), s(s(s(s(s(0)))))), true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 2 (clause_8_05) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(E(f(S2), s(s(s(s(0))))), true, E(f(W2), s(s(s(0)))), true), true), true, ifeq(E(f(V2), s(s(s(s(s(0)))))), true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(ifeq(E(f(S2), s(s(s(s(0))))), true, E(f(W2), s(s(s(0)))), true), true, ifeq(E(f(V2), s(s(s(s(s(0)))))), true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 1 (clause_6_04) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(ifeq(true, true, E(f(W2), s(s(s(0)))), true), true, ifeq(E(f(V2), s(s(s(s(s(0)))))), true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(ifeq(E(f(W2), s(s(s(0)))), true, ifeq(E(f(V2), s(s(s(s(s(0)))))), true, ifeq(E(f(U2), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), T2)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 5 (clause_4_12) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.42 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.42 = { by axiom 5 (clause_4_12) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(E(f(Y2), s(s(s(0)))), true, ifeq(E(f(X2), s(s(s(s(s(0)))))), true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(ifeq(true, true, E(f(Y2), s(s(s(0)))), true), true, ifeq(E(f(X2), s(s(s(s(s(0)))))), true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.42 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.42 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(ifeq(E(f(Z2), s(s(s(s(0))))), true, E(f(Y2), s(s(s(0)))), true), true, ifeq(E(f(X2), s(s(s(s(s(0)))))), true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(ifeq(true, true, ifeq(E(f(Z2), s(s(s(s(0))))), true, E(f(Y2), s(s(s(0)))), true), true), true, ifeq(E(f(X2), s(s(s(s(s(0)))))), true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(ifeq(E(f(Y2), s(s(s(s(s(0)))))), true, ifeq(E(f(Z2), s(s(s(s(0))))), true, E(f(Y2), s(s(s(0)))), true), true), true, ifeq(E(f(X2), s(s(s(s(s(0)))))), true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 4 (clause_1_10) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(true, true, ifeq(E(f(X2), s(s(s(s(s(0)))))), true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(E(f(X2), s(s(s(s(s(0)))))), true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 2 (clause_8_05) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(true, true, ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(E(f(S), s(s(s(s(0))))), true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 1 (clause_6_04) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(true, true, E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true)
% 1.23/0.43 = { by axiom 1 (clause_6_04) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(true, true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true)
% 1.23/0.43 = { by axiom 4 (clause_1_10) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(E(f(Z), s(s(s(s(s(0)))))), true, ifeq(E(f(T), s(s(s(s(0))))), true, E(f(Z), s(s(s(0)))), true), true), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true)
% 1.23/0.43 = { by axiom 2 (clause_8_05) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(true, true, ifeq(E(f(T), s(s(s(s(0))))), true, E(f(Z), s(s(s(0)))), true), true), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(E(f(T), s(s(s(s(0))))), true, E(f(Z), s(s(s(0)))), true), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true)
% 1.23/0.43 = { by axiom 1 (clause_6_04) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(ifeq(true, true, E(f(Z), s(s(s(0)))), true), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(E(f(Z), s(s(s(0)))), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true)
% 1.23/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(true, true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(E(f(Z), s(s(s(0)))), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true), true)
% 1.23/0.43 = { by axiom 2 (clause_8_05) R->L }
% 1.23/0.43 tuple(true, true, true, true, ifeq(E(f(X), s(s(s(s(s(0)))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), Y)), s(0)), true, ifeq(E(f(Z), s(s(s(0)))), true, ifeq(E(f(W), s(s(s(s(0))))), true, ifeq(E(f(AP(s(s(s(s(s(s(0)))))), V)), s(s(0))), true, E(f(AP(s(s(s(s(s(s(0)))))), U)), 0), true), true), true), true), true), true)
% 1.23/0.43 = { by axiom 7 (clause_2_07) }
% 1.23/0.43 tuple(true, true, true, true, true, true)
% 1.23/0.43 % SZS output end Proof
% 1.23/0.43
% 1.23/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------