%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN109-1 : TPTP v9.3.1. Released v1.1.0.
% 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 01:47:06 PM UTC 2026
% Result : Unsatisfiable 9.27s 1.46s
% Output : Proof 9.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN109-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n026.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 15:37:11 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.27/1.46 Command-line arguments: --no-flatten-goal
% 9.27/1.46
% 9.27/1.46 % SZS status Unsatisfiable
% 9.27/1.46
% 9.27/1.46 % SZS output start Proof
% 9.27/1.46 Axiom 1 (axiom_5): s0(b) = true.
% 9.27/1.46 Axiom 2 (axiom_26): n0(d, c) = true.
% 9.27/1.46 Axiom 3 (axiom_14): p0(b, X) = true.
% 9.27/1.46 Axiom 4 (axiom_19): m0(X, d, Y) = true.
% 9.27/1.46 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 9.27/1.46 Axiom 6 (rule_001): ifeq(n0(X, Y), true, k1(Y), true) = true.
% 9.27/1.46 Axiom 7 (rule_129): ifeq(q1(X, Y, Y), true, k2(Y, Y), true) = true.
% 9.27/1.46 Axiom 8 (rule_029): ifeq(p0(X, Y), true, ifeq(s0(X), true, m1(X, Y, X), true), true) = true.
% 9.27/1.46 Axiom 9 (rule_107): ifeq(m0(e, d, X), true, ifeq(m0(X, d, X), true, q1(e, X, X), true), true) = true.
% 9.27/1.46 Axiom 10 (rule_127): ifeq(k2(X, Y), true, ifeq(m1(Z, Y, W), true, ifeq(k1(X), true, k2(W, Y), true), true), true) = true.
% 9.27/1.46
% 9.27/1.46 Goal 1 (prove_this): k2(b, c) = true.
% 9.27/1.46 Proof:
% 9.27/1.46 k2(b, c)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) R->L }
% 9.27/1.46 ifeq(true, true, k2(b, c), true)
% 9.27/1.46 = { by axiom 6 (rule_001) R->L }
% 9.27/1.46 ifeq(ifeq(n0(d, c), true, k1(c), true), true, k2(b, c), true)
% 9.27/1.46 = { by axiom 2 (axiom_26) }
% 9.27/1.46 ifeq(ifeq(true, true, k1(c), true), true, k2(b, c), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) }
% 9.27/1.46 ifeq(k1(c), true, k2(b, c), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) R->L }
% 9.27/1.46 ifeq(true, true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 7 (rule_129) R->L }
% 9.27/1.46 ifeq(ifeq(q1(e, c, c), true, k2(c, c), true), true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) R->L }
% 9.27/1.46 ifeq(ifeq(ifeq(true, true, q1(e, c, c), true), true, k2(c, c), true), true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 4 (axiom_19) R->L }
% 9.27/1.46 ifeq(ifeq(ifeq(m0(c, d, c), true, q1(e, c, c), true), true, k2(c, c), true), true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) R->L }
% 9.27/1.46 ifeq(ifeq(ifeq(true, true, ifeq(m0(c, d, c), true, q1(e, c, c), true), true), true, k2(c, c), true), true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 4 (axiom_19) R->L }
% 9.27/1.46 ifeq(ifeq(ifeq(m0(e, d, c), true, ifeq(m0(c, d, c), true, q1(e, c, c), true), true), true, k2(c, c), true), true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 9 (rule_107) }
% 9.27/1.46 ifeq(ifeq(true, true, k2(c, c), true), true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) }
% 9.27/1.46 ifeq(k2(c, c), true, ifeq(k1(c), true, k2(b, c), true), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) R->L }
% 9.27/1.46 ifeq(k2(c, c), true, ifeq(true, true, ifeq(k1(c), true, k2(b, c), true), true), true)
% 9.27/1.46 = { by axiom 8 (rule_029) R->L }
% 9.27/1.46 ifeq(k2(c, c), true, ifeq(ifeq(p0(b, c), true, ifeq(s0(b), true, m1(b, c, b), true), true), true, ifeq(k1(c), true, k2(b, c), true), true), true)
% 9.27/1.46 = { by axiom 1 (axiom_5) }
% 9.27/1.46 ifeq(k2(c, c), true, ifeq(ifeq(p0(b, c), true, ifeq(true, true, m1(b, c, b), true), true), true, ifeq(k1(c), true, k2(b, c), true), true), true)
% 9.27/1.46 = { by axiom 3 (axiom_14) }
% 9.27/1.46 ifeq(k2(c, c), true, ifeq(ifeq(true, true, ifeq(true, true, m1(b, c, b), true), true), true, ifeq(k1(c), true, k2(b, c), true), true), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) }
% 9.27/1.46 ifeq(k2(c, c), true, ifeq(ifeq(true, true, m1(b, c, b), true), true, ifeq(k1(c), true, k2(b, c), true), true), true)
% 9.27/1.46 = { by axiom 5 (ifeq_axiom) }
% 9.27/1.46 ifeq(k2(c, c), true, ifeq(m1(b, c, b), true, ifeq(k1(c), true, k2(b, c), true), true), true)
% 9.27/1.46 = { by axiom 10 (rule_127) }
% 9.27/1.46 true
% 9.27/1.46 % SZS output end Proof
% 9.27/1.46
% 9.27/1.46 RESULT: Unsatisfiable (the axioms are contradictory).
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