%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN110-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 11.61s 1.75s
% Output : Proof 11.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN110-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n002.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Mon Sep 28 15:37:07 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.61/1.75 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 11.61/1.75
% 11.61/1.75 % SZS status Unsatisfiable
% 11.61/1.75
% 11.61/1.75 % SZS output start Proof
% 11.61/1.75 Axiom 1 (axiom_24): l0(c) = true.
% 11.61/1.75 Axiom 2 (axiom_33): q0(d, c) = true.
% 11.61/1.75 Axiom 3 (axiom_37): n0(b, a) = true.
% 11.61/1.75 Axiom 4 (axiom_19): m0(X, d, Y) = true.
% 11.61/1.76 Axiom 5 (axiom_12): m0(a, X, a) = true.
% 11.61/1.76 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 11.61/1.76 Axiom 7 (rule_001): ifeq(n0(X, Y), true, k1(Y), true) = true.
% 11.61/1.76 Axiom 8 (rule_020): ifeq(l0(c), true, m1(c, c, c), true) = true.
% 11.61/1.76 Axiom 9 (rule_129): ifeq(q1(X, Y, Y), true, k2(Y, Y), true) = true.
% 11.61/1.76 Axiom 10 (rule_107): ifeq(m0(e, d, X), true, ifeq(m0(X, d, X), true, q1(e, X, X), true), true) = true.
% 11.61/1.76 Axiom 11 (rule_127): ifeq(k2(X, Y), true, ifeq(m1(Z, Y, W), true, ifeq(k1(X), true, k2(W, Y), true), true), true) = true.
% 11.61/1.76 Axiom 12 (rule_024): ifeq(m1(X, c, X), true, ifeq(m0(a, Y, a), true, ifeq(q0(Z, X), true, m1(Z, a, X), true), true), true) = true.
% 11.61/1.76
% 11.61/1.76 Goal 1 (prove_this): k2(c, a) = true.
% 11.61/1.76 Proof:
% 11.61/1.76 k2(c, a)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) R->L }
% 11.61/1.76 ifeq(true, true, k2(c, a), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) R->L }
% 11.61/1.76 ifeq(true, true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 9 (rule_129) R->L }
% 11.61/1.76 ifeq(ifeq(q1(e, a, a), true, k2(a, a), true), true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) R->L }
% 11.61/1.76 ifeq(ifeq(ifeq(true, true, q1(e, a, a), true), true, k2(a, a), true), true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 4 (axiom_19) R->L }
% 11.61/1.76 ifeq(ifeq(ifeq(m0(a, d, a), true, q1(e, a, a), true), true, k2(a, a), true), true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) R->L }
% 11.61/1.76 ifeq(ifeq(ifeq(true, true, ifeq(m0(a, d, a), true, q1(e, a, a), true), true), true, k2(a, a), true), true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 4 (axiom_19) R->L }
% 11.61/1.76 ifeq(ifeq(ifeq(m0(e, d, a), true, ifeq(m0(a, d, a), true, q1(e, a, a), true), true), true, k2(a, a), true), true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 10 (rule_107) }
% 11.61/1.76 ifeq(ifeq(true, true, k2(a, a), true), true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(true, true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 7 (rule_001) R->L }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(n0(b, a), true, k1(a), true), true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 3 (axiom_37) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(true, true, k1(a), true), true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(k1(a), true, k2(c, a), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) R->L }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(true, true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 12 (rule_024) R->L }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(m1(c, c, c), true, ifeq(m0(a, X, a), true, ifeq(q0(d, c), true, m1(d, a, c), true), true), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 5 (axiom_12) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(m1(c, c, c), true, ifeq(true, true, ifeq(q0(d, c), true, m1(d, a, c), true), true), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(m1(c, c, c), true, ifeq(q0(d, c), true, m1(d, a, c), true), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 2 (axiom_33) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(m1(c, c, c), true, ifeq(true, true, m1(d, a, c), true), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) R->L }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(ifeq(true, true, m1(c, c, c), true), true, ifeq(true, true, m1(d, a, c), true), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 1 (axiom_24) R->L }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(ifeq(l0(c), true, m1(c, c, c), true), true, ifeq(true, true, m1(d, a, c), true), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 8 (rule_020) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(true, true, ifeq(true, true, m1(d, a, c), true), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(ifeq(true, true, m1(d, a, c), true), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 6 (ifeq_axiom) }
% 11.61/1.76 ifeq(k2(a, a), true, ifeq(m1(d, a, c), true, ifeq(k1(a), true, k2(c, a), true), true), true)
% 11.61/1.76 = { by axiom 11 (rule_127) }
% 11.61/1.76 true
% 11.61/1.76 % SZS output end Proof
% 11.61/1.76
% 11.61/1.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------