%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN180-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 01:47:15 PM UTC 2026
% Result : Unsatisfiable 14.18s 2.05s
% Output : Proof 14.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN180-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n011.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 15:37:45 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.18/2.05 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 14.18/2.05
% 14.18/2.05 % SZS status Unsatisfiable
% 14.18/2.05
% 14.18/2.06 % SZS output start Proof
% 14.18/2.06 Axiom 1 (axiom_1): s0(d) = true.
% 14.18/2.06 Axiom 2 (axiom_28): k0(e) = true.
% 14.18/2.06 Axiom 3 (axiom_14): p0(b, X) = true.
% 14.18/2.06 Axiom 4 (axiom_17): q0(X, d) = true.
% 14.18/2.06 Axiom 5 (axiom_19): m0(X, d, Y) = true.
% 14.18/2.06 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 14.18/2.06 Axiom 7 (rule_236): ifeq(n2(X), true, m3(X, X, X), true) = true.
% 14.18/2.06 Axiom 8 (rule_137): ifeq(p1(X, Y, Z), true, n2(Z), true) = true.
% 14.18/2.06 Axiom 9 (rule_085): ifeq(p0(X, Y), true, p1(Y, Y, Y), true) = true.
% 14.18/2.06 Axiom 10 (rule_194): ifeq(k2(X, Y), true, k3(Y, Y, X), true) = true.
% 14.18/2.06 Axiom 11 (rule_129): ifeq(q1(X, Y, Y), true, k2(Y, Y), true) = true.
% 14.18/2.06 Axiom 12 (rule_122): ifeq(m0(X, Y, X), true, q1(X, X, X), true) = true.
% 14.18/2.06 Axiom 13 (rule_177): ifeq(p1(X, X, X), true, ifeq(k0(Y), true, q2(X, Y, Y), true), true) = true.
% 14.18/2.06 Axiom 14 (rule_107): ifeq(m0(e, d, X), true, ifeq(m0(X, d, X), true, q1(e, X, X), true), true) = true.
% 14.18/2.06 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.
% 14.18/2.06 Axiom 16 (rule_295): ifeq(m3(X, Y, X), true, ifeq(k3(Z, Z, W), true, ifeq(q2(X, V, W), true, q4(W, V), true), true), true) = true.
% 14.18/2.06 Axiom 17 (rule_187): ifeq(q2(X, X, X), true, ifeq(r1(X), true, ifeq(k0(X), true, ifeq(m0(Y, Z, W), true, q2(W, X, W), true), true), true), true) = true.
% 14.18/2.06
% 14.18/2.06 Goal 1 (prove_this): q4(a, e) = true.
% 14.18/2.06 Proof:
% 14.18/2.06 q4(a, e)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(true, true, q4(a, e), true)
% 14.18/2.06 = { by axiom 17 (rule_187) R->L }
% 14.18/2.06 ifeq(ifeq(q2(e, e, e), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(true, true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 2 (axiom_28) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(k0(e), true, q2(e, e, e), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(true, true, ifeq(k0(e), true, q2(e, e, e), true), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 9 (rule_085) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(ifeq(p0(b, e), true, p1(e, e, e), true), true, ifeq(k0(e), true, q2(e, e, e), true), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 3 (axiom_14) }
% 14.18/2.06 ifeq(ifeq(ifeq(ifeq(true, true, p1(e, e, e), true), true, ifeq(k0(e), true, q2(e, e, e), true), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(ifeq(ifeq(p1(e, e, e), true, ifeq(k0(e), true, q2(e, e, e), true), true), true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 13 (rule_177) }
% 14.18/2.06 ifeq(ifeq(true, true, ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(ifeq(r1(e), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(true, true, r1(e), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 4 (axiom_17) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(q0(e, d), true, r1(e), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(true, true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 12 (rule_122) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(ifeq(m0(d, d, d), true, q1(d, d, d), true), true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 5 (axiom_19) }
% 14.18/2.06 ifeq(ifeq(ifeq(ifeq(true, true, q1(d, d, d), true), true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(e, d), true, r1(e), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(e, d), true, ifeq(true, true, r1(e), true), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 1 (axiom_1) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(e, d), true, ifeq(s0(d), true, r1(e), true), true), true), true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 15 (rule_124) }
% 14.18/2.06 ifeq(ifeq(true, true, ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(ifeq(k0(e), true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 2 (axiom_28) }
% 14.18/2.06 ifeq(ifeq(true, true, ifeq(m0(X, d, a), true, q2(a, e, a), true), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(ifeq(m0(X, d, a), true, q2(a, e, a), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 5 (axiom_19) }
% 14.18/2.06 ifeq(ifeq(true, true, q2(a, e, a), true), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(q2(a, e, a), true, q4(a, e), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(true, true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 7 (rule_236) R->L }
% 14.18/2.06 ifeq(ifeq(n2(a), true, m3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(true, true, n2(a), true), true, m3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 9 (rule_085) R->L }
% 14.18/2.06 ifeq(ifeq(ifeq(ifeq(p0(b, a), true, p1(a, a, a), true), true, n2(a), true), true, m3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 3 (axiom_14) }
% 14.18/2.06 ifeq(ifeq(ifeq(ifeq(true, true, p1(a, a, a), true), true, n2(a), true), true, m3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(ifeq(ifeq(p1(a, a, a), true, n2(a), true), true, m3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 8 (rule_137) }
% 14.18/2.06 ifeq(ifeq(true, true, m3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.06 ifeq(m3(a, a, a), true, ifeq(q2(a, e, a), true, q4(a, e), true), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(m3(a, a, a), true, ifeq(true, true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.06 = { by axiom 10 (rule_194) R->L }
% 14.18/2.06 ifeq(m3(a, a, a), true, ifeq(ifeq(k2(a, a), true, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.06 = { by axiom 6 (ifeq_axiom) R->L }
% 14.18/2.06 ifeq(m3(a, a, a), true, ifeq(ifeq(ifeq(true, true, k2(a, a), true), true, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.06 = { by axiom 14 (rule_107) R->L }
% 14.18/2.06 ifeq(m3(a, a, a), true, ifeq(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, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.06 = { by axiom 5 (axiom_19) }
% 14.18/2.07 ifeq(m3(a, a, a), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(m0(a, d, a), true, q1(e, a, a), true), true), true, k2(a, a), true), true, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.07 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.07 ifeq(m3(a, a, a), true, ifeq(ifeq(ifeq(ifeq(m0(a, d, a), true, q1(e, a, a), true), true, k2(a, a), true), true, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.07 = { by axiom 5 (axiom_19) }
% 14.18/2.07 ifeq(m3(a, a, a), true, ifeq(ifeq(ifeq(ifeq(true, true, q1(e, a, a), true), true, k2(a, a), true), true, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.07 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.07 ifeq(m3(a, a, a), true, ifeq(ifeq(ifeq(q1(e, a, a), true, k2(a, a), true), true, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.07 = { by axiom 11 (rule_129) }
% 14.18/2.07 ifeq(m3(a, a, a), true, ifeq(ifeq(true, true, k3(a, a, a), true), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.07 = { by axiom 6 (ifeq_axiom) }
% 14.18/2.07 ifeq(m3(a, a, a), true, ifeq(k3(a, a, a), true, ifeq(q2(a, e, a), true, q4(a, e), true), true), true)
% 14.18/2.07 = { by axiom 16 (rule_295) }
% 14.18/2.07 true
% 14.18/2.07 % SZS output end Proof
% 14.18/2.07
% 14.18/2.07 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------