%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN138-1 : 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 15.53s 2.28s
% Output : Proof 15.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN138-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:36:31 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.53/2.28 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
% 15.53/2.28
% 15.53/2.28 % SZS status Unsatisfiable
% 15.53/2.29
% 15.53/2.29 % SZS output start Proof
% 15.53/2.29 Axiom 1 (axiom_1): s0(d) = true.
% 15.53/2.29 Axiom 2 (axiom_24): l0(c) = true.
% 15.53/2.29 Axiom 3 (axiom_28): k0(e) = true.
% 15.53/2.29 Axiom 4 (axiom_17): q0(X, d) = true.
% 15.53/2.29 Axiom 5 (axiom_30): n0(e, e) = true.
% 15.53/2.29 Axiom 6 (axiom_19): m0(X, d, Y) = true.
% 15.53/2.29 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 15.53/2.29 Axiom 8 (rule_001): ifeq(n0(X, Y), true, k1(Y), true) = true.
% 15.53/2.29 Axiom 9 (rule_129): ifeq(q1(X, Y, Y), true, k2(Y, Y), true) = true.
% 15.53/2.29 Axiom 10 (rule_122): ifeq(m0(X, Y, X), true, q1(X, X, X), true) = true.
% 15.53/2.29 Axiom 11 (rule_188): ifeq(r1(X), true, ifeq(l0(X), true, r2(X), true), true) = true.
% 15.53/2.29 Axiom 12 (rule_021): ifeq(k0(X), true, ifeq(l0(Y), true, m1(Y, X, Y), true), true) = true.
% 15.53/2.29 Axiom 13 (rule_231): ifeq(r2(X), true, ifeq(k2(c, Y), true, m3(X, Y, X), true), true) = true.
% 15.53/2.29 Axiom 14 (rule_107): ifeq(m0(e, d, X), true, ifeq(m0(X, d, X), true, q1(e, X, X), true), true) = true.
% 15.53/2.29 Axiom 15 (rule_124): ifeq(q1(d, X, d), true, ifeq(q0(Y, X), true, ifeq(s0(d), true, r1(Y), true), true), true) = true.
% 15.53/2.29 Axiom 16 (rule_127): ifeq(k2(X, Y), true, ifeq(m1(Z, Y, W), true, ifeq(k1(X), true, k2(W, Y), true), true), true) = true.
% 15.53/2.29
% 15.53/2.29 Goal 1 (prove_this): m3(c, e, c) = true.
% 15.53/2.29 Proof:
% 15.53/2.29 m3(c, e, c)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(true, true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 16 (rule_127) R->L }
% 15.53/2.29 ifeq(ifeq(k2(e, e), true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(true, true, k2(e, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 14 (rule_107) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(ifeq(m0(e, d, e), true, ifeq(m0(e, d, e), true, q1(e, e, e), true), true), true, k2(e, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 6 (axiom_19) }
% 15.53/2.29 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(m0(e, d, e), true, q1(e, e, e), true), true), true, k2(e, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(ifeq(ifeq(ifeq(m0(e, d, e), true, q1(e, e, e), true), true, k2(e, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 6 (axiom_19) }
% 15.53/2.29 ifeq(ifeq(ifeq(ifeq(true, true, q1(e, e, e), true), true, k2(e, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(ifeq(ifeq(q1(e, e, e), true, k2(e, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 9 (rule_129) }
% 15.53/2.29 ifeq(ifeq(true, true, ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(ifeq(m1(c, e, c), true, ifeq(k1(e), true, k2(c, e), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(true, true, m1(c, e, c), true), true, ifeq(k1(e), true, k2(c, e), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 2 (axiom_24) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(l0(c), true, m1(c, e, c), true), true, ifeq(k1(e), true, k2(c, e), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(true, true, ifeq(l0(c), true, m1(c, e, c), true), true), true, ifeq(k1(e), true, k2(c, e), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 3 (axiom_28) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(k0(e), true, ifeq(l0(c), true, m1(c, e, c), true), true), true, ifeq(k1(e), true, k2(c, e), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 12 (rule_021) }
% 15.53/2.29 ifeq(ifeq(true, true, ifeq(k1(e), true, k2(c, e), true), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(ifeq(k1(e), true, k2(c, e), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(true, true, k1(e), true), true, k2(c, e), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 5 (axiom_30) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(n0(e, e), true, k1(e), true), true, k2(c, e), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 8 (rule_001) }
% 15.53/2.29 ifeq(ifeq(true, true, k2(c, e), true), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(k2(c, e), true, m3(c, e, c), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(true, true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 11 (rule_188) R->L }
% 15.53/2.29 ifeq(ifeq(r1(c), true, ifeq(l0(c), true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 2 (axiom_24) }
% 15.53/2.29 ifeq(ifeq(r1(c), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(true, true, r1(c), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 4 (axiom_17) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(q0(c, d), true, r1(c), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(true, true, ifeq(q0(c, d), true, r1(c), true), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 10 (rule_122) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(ifeq(m0(d, d, d), true, q1(d, d, d), true), true, ifeq(q0(c, d), true, r1(c), true), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 6 (axiom_19) }
% 15.53/2.29 ifeq(ifeq(ifeq(ifeq(true, true, q1(d, d, d), true), true, ifeq(q0(c, d), true, r1(c), true), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(c, d), true, r1(c), true), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(c, d), true, ifeq(true, true, r1(c), true), true), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 1 (axiom_1) R->L }
% 15.53/2.29 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(c, d), true, ifeq(s0(d), true, r1(c), true), true), true), true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 15 (rule_124) }
% 15.53/2.29 ifeq(ifeq(true, true, ifeq(true, true, r2(c), true), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(ifeq(true, true, r2(c), true), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 7 (ifeq_axiom) }
% 15.53/2.29 ifeq(r2(c), true, ifeq(k2(c, e), true, m3(c, e, c), true), true)
% 15.53/2.29 = { by axiom 13 (rule_231) }
% 15.53/2.29 true
% 15.53/2.29 % SZS output end Proof
% 15.53/2.29
% 15.53/2.29 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------