%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN155-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:47:12 PM UTC 2026
% Result : Unsatisfiable 3.69s 0.70s
% Output : Proof 3.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN155-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n001.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 15:43:03 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.69/0.70 Command-line arguments: --no-flatten-goal
% 3.69/0.70
% 3.69/0.70 % SZS status Unsatisfiable
% 3.69/0.70
% 3.69/0.71 % SZS output start Proof
% 3.69/0.71 Axiom 1 (axiom_13): r0(e) = true.
% 3.69/0.71 Axiom 2 (axiom_34): n0(c, d) = true.
% 3.69/0.71 Axiom 3 (axiom_30): n0(e, e) = true.
% 3.69/0.71 Axiom 4 (axiom_18): p0(c, b) = true.
% 3.69/0.71 Axiom 5 (axiom_14): p0(b, X) = true.
% 3.69/0.71 Axiom 6 (axiom_27): m0(e, b, c) = true.
% 3.69/0.71 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.69/0.71 Axiom 8 (rule_012): ifeq(r0(e), true, m1(e, e, e), true) = true.
% 3.69/0.71 Axiom 9 (rule_236): ifeq(n2(X), true, m3(X, X, X), true) = true.
% 3.69/0.71 Axiom 10 (rule_137): ifeq(p1(X, Y, Z), true, n2(Z), true) = true.
% 3.69/0.71 Axiom 11 (rule_240): ifeq(p2(X, Y, Z), true, n3(Z), true) = true.
% 3.69/0.71 Axiom 12 (rule_186): ifeq(l1(X, Y), true, q2(Y, Y, X), true) = true.
% 3.69/0.71 Axiom 13 (rule_085): ifeq(p0(X, Y), true, p1(Y, Y, Y), true) = true.
% 3.69/0.71 Axiom 14 (rule_150): ifeq(m1(X, X, Y), true, p2(Y, Y, Y), true) = true.
% 3.69/0.71 Axiom 15 (rule_284): ifeq(k4(X), true, ifeq(m3(Y, Y, Y), true, n4(Y, Y), true), true) = true.
% 3.69/0.71 Axiom 16 (rule_255): ifeq(q2(X, Y, Z), true, ifeq(n0(X, Y), true, q3(Y, Z), true), true) = true.
% 3.69/0.71 Axiom 17 (rule_274): ifeq(q3(e, b), true, ifeq(n3(e), true, ifeq(n0(c, d), true, k4(c), true), true), true) = true.
% 3.69/0.71 Axiom 18 (rule_003): ifeq(p0(X, Y), true, ifeq(r0(Z), true, ifeq(m0(W, Y, X), true, l1(Y, W), true), true), true) = true.
% 3.69/0.71
% 3.69/0.71 Goal 1 (prove_this): n4(X, a) = true.
% 3.69/0.71 The goal is true when:
% 3.69/0.71 X = a
% 3.69/0.71
% 3.69/0.71 Proof:
% 3.69/0.71 n4(a, a)
% 3.69/0.71 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.71 ifeq(true, true, n4(a, a), true)
% 3.69/0.71 = { by axiom 9 (rule_236) R->L }
% 3.69/0.71 ifeq(ifeq(n2(a), true, m3(a, a, a), true), true, n4(a, a), true)
% 3.69/0.71 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.71 ifeq(ifeq(ifeq(true, true, n2(a), true), true, m3(a, a, a), true), true, n4(a, a), true)
% 3.69/0.71 = { by axiom 13 (rule_085) R->L }
% 3.69/0.71 ifeq(ifeq(ifeq(ifeq(p0(b, a), true, p1(a, a, a), true), true, n2(a), true), true, m3(a, a, a), true), true, n4(a, a), true)
% 3.69/0.71 = { by axiom 5 (axiom_14) }
% 3.69/0.71 ifeq(ifeq(ifeq(ifeq(true, true, p1(a, a, a), true), true, n2(a), true), true, m3(a, a, a), true), true, n4(a, a), true)
% 3.69/0.71 = { by axiom 7 (ifeq_axiom) }
% 3.69/0.71 ifeq(ifeq(ifeq(p1(a, a, a), true, n2(a), true), true, m3(a, a, a), true), true, n4(a, a), true)
% 3.69/0.71 = { by axiom 10 (rule_137) }
% 3.69/0.71 ifeq(ifeq(true, true, m3(a, a, a), true), true, n4(a, a), true)
% 3.69/0.71 = { by axiom 7 (ifeq_axiom) }
% 3.69/0.71 ifeq(m3(a, a, a), true, n4(a, a), true)
% 3.69/0.71 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.71 ifeq(true, true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.71 = { by axiom 17 (rule_274) R->L }
% 3.69/0.71 ifeq(ifeq(q3(e, b), true, ifeq(n3(e), true, ifeq(n0(c, d), true, k4(c), true), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 2 (axiom_34) }
% 3.69/0.72 ifeq(ifeq(q3(e, b), true, ifeq(n3(e), true, ifeq(true, true, k4(c), true), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) }
% 3.69/0.72 ifeq(ifeq(q3(e, b), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(true, true, q3(e, b), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 3 (axiom_30) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(n0(e, e), true, q3(e, b), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(true, true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 12 (rule_186) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(l1(b, e), true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, l1(b, e), true), true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 1 (axiom_13) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(r0(e), true, l1(b, e), true), true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(r0(e), true, ifeq(true, true, l1(b, e), true), true), true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(r0(e), true, ifeq(true, true, l1(b, e), true), true), true), true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 4 (axiom_18) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(p0(c, b), true, ifeq(r0(e), true, ifeq(true, true, l1(b, e), true), true), true), true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 6 (axiom_27) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(p0(c, b), true, ifeq(r0(e), true, ifeq(m0(e, b, c), true, l1(b, e), true), true), true), true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 18 (rule_003) }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(true, true, q2(e, e, b), true), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) }
% 3.69/0.72 ifeq(ifeq(ifeq(q2(e, e, b), true, ifeq(n0(e, e), true, q3(e, b), true), true), true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 16 (rule_255) }
% 3.69/0.72 ifeq(ifeq(true, true, ifeq(n3(e), true, k4(c), true), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) }
% 3.69/0.72 ifeq(ifeq(n3(e), true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(true, true, n3(e), true), true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 14 (rule_150) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(m1(e, e, e), true, p2(e, e, e), true), true, n3(e), true), true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, m1(e, e, e), true), true, p2(e, e, e), true), true, n3(e), true), true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 1 (axiom_13) R->L }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(ifeq(r0(e), true, m1(e, e, e), true), true, p2(e, e, e), true), true, n3(e), true), true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 8 (rule_012) }
% 3.69/0.72 ifeq(ifeq(ifeq(ifeq(true, true, p2(e, e, e), true), true, n3(e), true), true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) }
% 3.69/0.72 ifeq(ifeq(ifeq(p2(e, e, e), true, n3(e), true), true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 11 (rule_240) }
% 3.69/0.72 ifeq(ifeq(true, true, k4(c), true), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 7 (ifeq_axiom) }
% 3.69/0.72 ifeq(k4(c), true, ifeq(m3(a, a, a), true, n4(a, a), true), true)
% 3.69/0.72 = { by axiom 15 (rule_284) }
% 3.69/0.72 true
% 3.69/0.72 % SZS output end Proof
% 3.69/0.72
% 3.69/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------