%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN273-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 01:47:26 PM UTC 2026
% Result : Unsatisfiable 18.34s 2.72s
% Output : Proof 18.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN273-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.29 % Computer : n014.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Mon Sep 28 15:40:05 UTC 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.34/2.72 Command-line arguments: --no-flatten-goal
% 18.34/2.72
% 18.34/2.72 % SZS status Unsatisfiable
% 18.34/2.72
% 18.34/2.74 % SZS output start Proof
% 18.34/2.74 Axiom 1 (axiom_28): k0(e) = true.
% 18.34/2.74 Axiom 2 (axiom_24): l0(c) = true.
% 18.34/2.74 Axiom 3 (axiom_5): s0(b) = true.
% 18.34/2.74 Axiom 4 (axiom_15): n0(a, b) = true.
% 18.34/2.74 Axiom 5 (axiom_3): n0(d, e) = true.
% 18.34/2.75 Axiom 6 (axiom_14): p0(b, X) = true.
% 18.34/2.75 Axiom 7 (axiom_19): m0(X, d, Y) = true.
% 18.34/2.75 Axiom 8 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 18.34/2.75 Axiom 9 (rule_001): ifeq(n0(X, Y), true, k1(Y), true) = true.
% 18.34/2.75 Axiom 10 (rule_194): ifeq(k2(X, Y), true, k3(Y, Y, X), true) = true.
% 18.34/2.75 Axiom 11 (rule_129): ifeq(q1(X, Y, Y), true, k2(Y, Y), true) = true.
% 18.34/2.75 Axiom 12 (rule_287): ifeq(k3(X, X, Y), true, p4(X, Y, X), true) = true.
% 18.34/2.75 Axiom 13 (rule_021): ifeq(k0(X), true, ifeq(l0(Y), true, m1(Y, X, Y), true), true) = true.
% 18.34/2.75 Axiom 14 (rule_029): ifeq(p0(X, Y), true, ifeq(s0(X), true, m1(X, Y, X), true), true) = true.
% 18.34/2.75 Axiom 15 (rule_107): ifeq(m0(e, d, X), true, ifeq(m0(X, d, X), true, q1(e, X, X), true), true) = true.
% 18.34/2.75 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.
% 18.34/2.75
% 18.34/2.75 Goal 1 (prove_this): p4(e, c, e) = true.
% 18.34/2.75 Proof:
% 18.34/2.75 p4(e, c, e)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.75 ifeq(true, true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 10 (rule_194) R->L }
% 18.34/2.75 ifeq(ifeq(k2(c, e), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(true, true, k2(c, e), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 13 (rule_021) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k0(e), true, ifeq(l0(c), true, m1(c, e, c), true), true), true, k2(c, e), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 1 (axiom_28) }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(l0(c), true, m1(c, e, c), true), true), true, k2(c, e), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(l0(c), true, m1(c, e, c), true), true, k2(c, e), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 2 (axiom_24) }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(true, true, m1(c, e, c), true), true, k2(c, e), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.75 ifeq(ifeq(ifeq(m1(c, e, c), true, k2(c, e), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(m1(c, e, c), true, ifeq(true, true, k2(c, e), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 9 (rule_001) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(m1(c, e, c), true, ifeq(ifeq(n0(a, b), true, k1(b), true), true, k2(c, e), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 4 (axiom_15) }
% 18.34/2.75 ifeq(ifeq(ifeq(m1(c, e, c), true, ifeq(ifeq(true, true, k1(b), true), true, k2(c, e), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.75 ifeq(ifeq(ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(true, true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 16 (rule_127) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k2(e, e), true, ifeq(m1(b, e, b), true, ifeq(k1(e), true, k2(b, e), true), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k2(e, e), true, ifeq(ifeq(true, true, m1(b, e, b), true), true, ifeq(k1(e), true, k2(b, e), true), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k2(e, e), true, ifeq(ifeq(true, true, ifeq(true, true, m1(b, e, b), true), true), true, ifeq(k1(e), true, k2(b, e), true), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 6 (axiom_14) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k2(e, e), true, ifeq(ifeq(p0(b, e), true, ifeq(true, true, m1(b, e, b), true), true), true, ifeq(k1(e), true, k2(b, e), true), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 3 (axiom_5) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k2(e, e), true, ifeq(ifeq(p0(b, e), true, ifeq(s0(b), true, m1(b, e, b), true), true), true, ifeq(k1(e), true, k2(b, e), true), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 14 (rule_029) }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k2(e, e), true, ifeq(true, true, ifeq(k1(e), true, k2(b, e), true), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(k2(e, e), true, ifeq(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.75 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, k2(e, e), true), true, ifeq(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.75 = { by axiom 15 (rule_107) R->L }
% 18.34/2.75 ifeq(ifeq(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(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 7 (axiom_19) }
% 18.34/2.76 ifeq(ifeq(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(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(m0(e, d, e), true, q1(e, e, e), true), true, k2(e, e), true), true, ifeq(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 7 (axiom_19) }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, q1(e, e, e), true), true, k2(e, e), true), true, ifeq(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(ifeq(q1(e, e, e), true, k2(e, e), true), true, ifeq(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 11 (rule_129) }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(k1(e), true, k2(b, e), true), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(k1(e), true, k2(b, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 8 (ifeq_axiom) R->L }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, k1(e), true), true, k2(b, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 5 (axiom_3) R->L }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(ifeq(n0(d, e), true, k1(e), true), true, k2(b, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 9 (rule_001) }
% 18.34/2.76 ifeq(ifeq(ifeq(ifeq(true, true, k2(b, e), true), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.76 ifeq(ifeq(ifeq(k2(b, e), true, ifeq(m1(c, e, c), true, ifeq(k1(b), true, k2(c, e), true), true), true), true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 16 (rule_127) }
% 18.34/2.76 ifeq(ifeq(true, true, k3(e, e, c), true), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 8 (ifeq_axiom) }
% 18.34/2.76 ifeq(k3(e, e, c), true, p4(e, c, e), true)
% 18.34/2.76 = { by axiom 12 (rule_287) }
% 18.34/2.76 true
% 18.34/2.76 % SZS output end Proof
% 18.34/2.76
% 18.34/2.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------