%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN179-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 01:47:15 PM UTC 2026
% Result : Unsatisfiable 8.51s 1.35s
% Output : Proof 8.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN179-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n004.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 15:37:36 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.51/1.35 Command-line arguments: --no-flatten-goal
% 8.51/1.35
% 8.51/1.35 % SZS status Unsatisfiable
% 8.51/1.35
% 8.51/1.37 % SZS output start Proof
% 8.51/1.37 Axiom 1 (axiom_13): r0(e) = true.
% 8.51/1.37 Axiom 2 (axiom_28): k0(e) = true.
% 8.51/1.37 Axiom 3 (axiom_20): l0(a) = true.
% 8.51/1.37 Axiom 4 (axiom_1): s0(d) = true.
% 8.51/1.37 Axiom 5 (axiom_3): n0(d, e) = true.
% 8.51/1.37 Axiom 6 (axiom_17): q0(X, d) = true.
% 8.51/1.37 Axiom 7 (axiom_19): m0(X, d, Y) = true.
% 8.51/1.37 Axiom 8 (axiom_12): m0(a, X, a) = true.
% 8.51/1.37 Axiom 9 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 8.51/1.37 Axiom 10 (rule_088): ifeq(l0(a), true, p1(a, a, a), true) = true.
% 8.51/1.37 Axiom 11 (rule_181): ifeq(p1(X, X, X), true, q2(X, X, X), true) = true.
% 8.51/1.37 Axiom 12 (rule_122): ifeq(m0(X, Y, X), true, q1(X, X, X), true) = true.
% 8.51/1.37 Axiom 13 (rule_090): ifeq(k0(e), true, ifeq(r0(e), true, p1(e, e, e), true), true) = true.
% 8.51/1.37 Axiom 14 (rule_145): ifeq(p1(X, Y, e), true, ifeq(r0(e), true, p2(e, X, Y), true), true) = true.
% 8.51/1.37 Axiom 15 (rule_256): ifeq(q3(X, Y), true, ifeq(p2(X, Y, Y), true, q3(Y, Y), true), true) = true.
% 8.51/1.37 Axiom 16 (rule_255): ifeq(q2(X, Y, Z), true, ifeq(n0(X, Y), true, q3(Y, Z), true), true) = true.
% 8.51/1.37 Axiom 17 (rule_082): ifeq(p1(X, Y, Z), true, ifeq(m0(X, Y, Z), true, p1(Y, W, X), true), true) = true.
% 8.51/1.37 Axiom 18 (rule_124): ifeq(q1(d, X, d), true, ifeq(q0(Y, X), true, ifeq(s0(d), true, r1(Y), true), true), true) = true.
% 8.51/1.37 Axiom 19 (rule_187): ifeq(q2(X, X, X), true, ifeq(r1(X), true, ifeq(k0(X), true, ifeq(m0(Y, Z, W), true, q2(W, X, W), true), true), true), true) = true.
% 8.51/1.37
% 8.51/1.37 Goal 1 (prove_this): q3(d, X) = true.
% 8.51/1.37 The goal is true when:
% 8.51/1.37 X = d
% 8.51/1.37
% 8.51/1.37 Proof:
% 8.51/1.37 q3(d, d)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(true, true, q3(d, d), true)
% 8.51/1.37 = { by axiom 14 (rule_145) R->L }
% 8.51/1.37 ifeq(ifeq(p1(d, d, e), true, ifeq(r0(e), true, p2(e, d, d), true), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 1 (axiom_13) }
% 8.51/1.37 ifeq(ifeq(p1(d, d, e), true, ifeq(true, true, p2(e, d, d), true), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(p1(d, d, e), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(true, true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 17 (rule_082) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(p1(a, e, a), true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(a, e, a), true), true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 8 (axiom_12) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(m0(a, a, a), true, p1(a, e, a), true), true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(m0(a, a, a), true, p1(a, e, a), true), true), true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 10 (rule_088) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, p1(a, a, a), true), true, ifeq(m0(a, a, a), true, p1(a, e, a), true), true), true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 3 (axiom_20) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(a, a, a), true), true, ifeq(m0(a, a, a), true, p1(a, e, a), true), true), true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(p1(a, a, a), true, ifeq(m0(a, a, a), true, p1(a, e, a), true), true), true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 17 (rule_082) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(m0(a, e, a), true, p1(e, d, a), true), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(m0(a, e, a), true, p1(e, d, a), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 8 (axiom_12) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(true, true, p1(e, d, a), true), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(ifeq(p1(e, d, a), true, p1(d, d, e), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(p1(e, d, a), true, ifeq(true, true, p1(d, d, e), true), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 7 (axiom_19) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(p1(e, d, a), true, ifeq(m0(e, d, a), true, p1(d, d, e), true), true), true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 17 (rule_082) }
% 8.51/1.37 ifeq(ifeq(true, true, p2(e, d, d), true), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(p2(e, d, d), true, q3(d, d), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(true, true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 16 (rule_255) R->L }
% 8.51/1.37 ifeq(ifeq(q2(d, e, d), true, ifeq(n0(d, e), true, q3(e, d), true), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 5 (axiom_3) }
% 8.51/1.37 ifeq(ifeq(q2(d, e, d), true, ifeq(true, true, q3(e, d), true), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(q2(d, e, d), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(true, true, q2(d, e, d), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 7 (axiom_19) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(m0(X, d, d), true, q2(d, e, d), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(true, true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 2 (axiom_28) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(true, true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 18 (rule_124) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(e, d), true, ifeq(s0(d), true, r1(e), true), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 4 (axiom_1) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(e, d), true, ifeq(true, true, r1(e), true), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, q1(d, d, d), true), true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 7 (axiom_19) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(m0(d, d, d), true, q1(d, d, d), true), true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 12 (rule_122) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(q0(e, d), true, r1(e), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 6 (axiom_17) }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(true, true, r1(e), true), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.37 ifeq(ifeq(ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(true, true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 11 (rule_181) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(p1(e, e, e), true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.37 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.37 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(e, e, e), true), true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 1 (axiom_13) R->L }
% 8.51/1.38 ifeq(ifeq(ifeq(ifeq(ifeq(r0(e), true, p1(e, e, e), true), true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 9 (ifeq_axiom) R->L }
% 8.51/1.38 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(r0(e), true, p1(e, e, e), true), true), true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 2 (axiom_28) R->L }
% 8.51/1.38 ifeq(ifeq(ifeq(ifeq(ifeq(k0(e), true, ifeq(r0(e), true, p1(e, e, e), true), true), true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 13 (rule_090) }
% 8.51/1.38 ifeq(ifeq(ifeq(ifeq(true, true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.38 ifeq(ifeq(ifeq(q2(e, e, e), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, d), true, q2(d, e, d), true), true), true), true), true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 19 (rule_187) }
% 8.51/1.38 ifeq(ifeq(true, true, q3(e, d), true), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 9 (ifeq_axiom) }
% 8.51/1.38 ifeq(q3(e, d), true, ifeq(p2(e, d, d), true, q3(d, d), true), true)
% 8.51/1.38 = { by axiom 15 (rule_256) }
% 8.51/1.38 true
% 8.51/1.38 % SZS output end Proof
% 8.51/1.38
% 8.51/1.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------