%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN144-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:47:10 PM UTC 2026
% Result : Unsatisfiable 7.52s 1.29s
% Output : Proof 7.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN144-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n005.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 15:36:46 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.52/1.29 Command-line arguments: --no-flatten-goal
% 7.52/1.29
% 7.52/1.29 % SZS status Unsatisfiable
% 7.52/1.29
% 7.52/1.30 % SZS output start Proof
% 7.52/1.30 Axiom 1 (axiom_13): r0(e) = true.
% 7.52/1.30 Axiom 2 (axiom_28): k0(e) = true.
% 7.52/1.30 Axiom 3 (axiom_20): l0(a) = true.
% 7.52/1.30 Axiom 4 (axiom_15): n0(a, b) = true.
% 7.52/1.30 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 7.52/1.30 Axiom 6 (rule_001): ifeq(n0(X, Y), true, k1(Y), true) = true.
% 7.52/1.30 Axiom 7 (rule_176): ifeq(m1(X, Y, X), true, p2(Y, X, Y), true) = true.
% 7.52/1.30 Axiom 8 (rule_267): ifeq(p2(X, Y, Z), true, r3(X, Z, X), true) = true.
% 7.52/1.30 Axiom 9 (rule_021): ifeq(k0(X), true, ifeq(l0(Y), true, m1(Y, X, Y), true), true) = true.
% 7.52/1.30 Axiom 10 (rule_303): ifeq(p4(X, Y, Z), true, ifeq(r0(X), true, m5(X, Z), true), true) = true.
% 7.52/1.30 Axiom 11 (rule_285): ifeq(r3(X, Y, X), true, ifeq(r0(Y), true, p4(Y, Y, X), true), true) = true.
% 7.52/1.30 Axiom 12 (rule_155): ifeq(p2(e, X, Y), true, ifeq(k1(Z), true, p2(X, Y, Y), true), true) = true.
% 7.52/1.30
% 7.52/1.30 Goal 1 (prove_this): m5(e, a) = true.
% 7.52/1.30 Proof:
% 7.52/1.30 m5(e, a)
% 7.52/1.30 = { by axiom 5 (ifeq_axiom) R->L }
% 7.52/1.30 ifeq(true, true, m5(e, a), true)
% 7.52/1.30 = { by axiom 1 (axiom_13) R->L }
% 7.52/1.30 ifeq(r0(e), true, m5(e, a), true)
% 7.52/1.30 = { by axiom 5 (ifeq_axiom) R->L }
% 7.52/1.30 ifeq(true, true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.30 = { by axiom 11 (rule_285) R->L }
% 7.52/1.30 ifeq(ifeq(r3(a, e, a), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.30 = { by axiom 5 (ifeq_axiom) R->L }
% 7.52/1.30 ifeq(ifeq(ifeq(true, true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.30 = { by axiom 12 (rule_155) R->L }
% 7.52/1.30 ifeq(ifeq(ifeq(ifeq(p2(e, a, e), true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.30 = { by axiom 5 (ifeq_axiom) R->L }
% 7.52/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p2(e, a, e), true), true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.30 = { by axiom 9 (rule_021) R->L }
% 7.52/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(k0(e), true, ifeq(l0(a), true, m1(a, e, a), true), true), true, p2(e, a, e), true), true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.30 = { by axiom 2 (axiom_28) }
% 7.52/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(l0(a), true, m1(a, e, a), true), true), true, p2(e, a, e), true), true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.30 = { by axiom 5 (ifeq_axiom) }
% 7.52/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, m1(a, e, a), true), true, p2(e, a, e), true), true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 3 (axiom_20) }
% 7.52/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, m1(a, e, a), true), true, p2(e, a, e), true), true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 5 (ifeq_axiom) }
% 7.52/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(m1(a, e, a), true, p2(e, a, e), true), true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 7 (rule_176) }
% 7.52/1.31 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(k1(b), true, p2(a, e, e), true), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 5 (ifeq_axiom) }
% 7.52/1.31 ifeq(ifeq(ifeq(ifeq(k1(b), true, p2(a, e, e), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 5 (ifeq_axiom) R->L }
% 7.52/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, k1(b), true), true, p2(a, e, e), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 4 (axiom_15) R->L }
% 7.52/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(n0(a, b), true, k1(b), true), true, p2(a, e, e), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 6 (rule_001) }
% 7.52/1.31 ifeq(ifeq(ifeq(ifeq(true, true, p2(a, e, e), true), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 5 (ifeq_axiom) }
% 7.52/1.31 ifeq(ifeq(ifeq(p2(a, e, e), true, r3(a, e, a), true), true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 8 (rule_267) }
% 7.52/1.31 ifeq(ifeq(true, true, ifeq(r0(e), true, p4(e, e, a), true), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 5 (ifeq_axiom) }
% 7.52/1.31 ifeq(ifeq(r0(e), true, p4(e, e, a), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 1 (axiom_13) }
% 7.52/1.31 ifeq(ifeq(true, true, p4(e, e, a), true), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 5 (ifeq_axiom) }
% 7.52/1.31 ifeq(p4(e, e, a), true, ifeq(r0(e), true, m5(e, a), true), true)
% 7.52/1.31 = { by axiom 10 (rule_303) }
% 7.52/1.31 true
% 7.52/1.31 % SZS output end Proof
% 7.52/1.31
% 7.52/1.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------