%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN221-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 01:47:20 PM UTC 2026
% Result : Unsatisfiable 5.17s 0.93s
% Output : Proof 5.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN221-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n005.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 15:38:31 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.17/0.93 Command-line arguments: --flatten --complete-subsets
% 5.17/0.93
% 5.17/0.93 % SZS status Unsatisfiable
% 5.17/0.93
% 5.17/0.93 % SZS output start Proof
% 5.17/0.93 Axiom 1 (axiom_13): r0(e) = true.
% 5.17/0.93 Axiom 2 (axiom_1): s0(d) = true.
% 5.17/0.93 Axiom 3 (axiom_15): n0(a, b) = true.
% 5.17/0.93 Axiom 4 (axiom_14): p0(b, X) = true.
% 5.17/0.93 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 5.17/0.94 Axiom 6 (rule_136): ifeq(k1(b), true, m2(b), true) = true.
% 5.17/0.94 Axiom 7 (rule_001): ifeq(n0(X, Y), true, k1(Y), true) = true.
% 5.17/0.94 Axiom 8 (rule_137): ifeq(p1(X, Y, Z), true, n2(Z), true) = true.
% 5.17/0.94 Axiom 9 (rule_085): ifeq(p0(X, Y), true, p1(Y, Y, Y), true) = true.
% 5.17/0.94 Axiom 10 (rule_217): ifeq(n2(X), true, ifeq(m2(b), true, l3(X, X), true), true) = true.
% 5.17/0.94
% 5.17/0.94 Lemma 11: s0(d) = r0(e).
% 5.17/0.94 Proof:
% 5.17/0.94 s0(d)
% 5.17/0.94 = { by axiom 2 (axiom_1) }
% 5.17/0.94 true
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 r0(e)
% 5.17/0.94
% 5.17/0.94 Goal 1 (prove_this): l3(X, c) = true.
% 5.17/0.94 The goal is true when:
% 5.17/0.94 X = c
% 5.17/0.94
% 5.17/0.94 Proof:
% 5.17/0.94 l3(c, c)
% 5.17/0.94 = { by axiom 5 (ifeq_axiom) R->L }
% 5.17/0.94 ifeq(s0(d), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(r0(e), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(true, s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 6 (rule_136) R->L }
% 5.17/0.94 ifeq(ifeq(k1(b), true, m2(b), true), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 ifeq(ifeq(k1(b), true, m2(b), r0(e)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 ifeq(ifeq(k1(b), r0(e), m2(b), r0(e)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by lemma 11 R->L }
% 5.17/0.94 ifeq(ifeq(k1(b), r0(e), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by lemma 11 R->L }
% 5.17/0.94 ifeq(ifeq(k1(b), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 5 (ifeq_axiom) R->L }
% 5.17/0.94 ifeq(ifeq(ifeq(s0(d), s0(d), k1(b), s0(d)), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(ifeq(ifeq(r0(e), s0(d), k1(b), s0(d)), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(ifeq(ifeq(true, s0(d), k1(b), s0(d)), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 3 (axiom_15) R->L }
% 5.17/0.94 ifeq(ifeq(ifeq(n0(a, b), s0(d), k1(b), s0(d)), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(ifeq(ifeq(n0(a, b), r0(e), k1(b), s0(d)), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(ifeq(ifeq(n0(a, b), r0(e), k1(b), r0(e)), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(ifeq(ifeq(n0(a, b), true, k1(b), r0(e)), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(ifeq(ifeq(n0(a, b), true, k1(b), true), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 7 (rule_001) }
% 5.17/0.94 ifeq(ifeq(true, s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 ifeq(ifeq(r0(e), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by lemma 11 R->L }
% 5.17/0.94 ifeq(ifeq(s0(d), s0(d), m2(b), s0(d)), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 5 (ifeq_axiom) }
% 5.17/0.94 ifeq(m2(b), s0(d), l3(c, c), s0(d))
% 5.17/0.94 = { by axiom 5 (ifeq_axiom) R->L }
% 5.17/0.94 ifeq(s0(d), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(r0(e), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(true, s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 8 (rule_137) R->L }
% 5.17/0.94 ifeq(ifeq(p1(c, c, c), true, n2(c), true), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 ifeq(ifeq(p1(c, c, c), true, n2(c), r0(e)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 ifeq(ifeq(p1(c, c, c), r0(e), n2(c), r0(e)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 R->L }
% 5.17/0.94 ifeq(ifeq(p1(c, c, c), r0(e), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 R->L }
% 5.17/0.94 ifeq(ifeq(p1(c, c, c), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 5 (ifeq_axiom) R->L }
% 5.17/0.94 ifeq(ifeq(ifeq(s0(d), s0(d), p1(c, c, c), s0(d)), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(ifeq(ifeq(r0(e), s0(d), p1(c, c, c), s0(d)), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(ifeq(ifeq(true, s0(d), p1(c, c, c), s0(d)), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 4 (axiom_14) R->L }
% 5.17/0.94 ifeq(ifeq(ifeq(p0(b, c), s0(d), p1(c, c, c), s0(d)), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(ifeq(ifeq(p0(b, c), r0(e), p1(c, c, c), s0(d)), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(ifeq(ifeq(p0(b, c), r0(e), p1(c, c, c), r0(e)), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(ifeq(ifeq(p0(b, c), true, p1(c, c, c), r0(e)), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(ifeq(ifeq(p0(b, c), true, p1(c, c, c), true), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 9 (rule_085) }
% 5.17/0.94 ifeq(ifeq(true, s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 ifeq(ifeq(r0(e), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 R->L }
% 5.17/0.94 ifeq(ifeq(s0(d), s0(d), n2(c), s0(d)), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by axiom 5 (ifeq_axiom) }
% 5.17/0.94 ifeq(n2(c), s0(d), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(n2(c), r0(e), ifeq(m2(b), s0(d), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(n2(c), r0(e), ifeq(m2(b), r0(e), l3(c, c), s0(d)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(n2(c), r0(e), ifeq(m2(b), r0(e), l3(c, c), r0(e)), s0(d))
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 ifeq(n2(c), r0(e), ifeq(m2(b), r0(e), l3(c, c), r0(e)), r0(e))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(n2(c), true, ifeq(m2(b), r0(e), l3(c, c), r0(e)), r0(e))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(n2(c), true, ifeq(m2(b), true, l3(c, c), r0(e)), r0(e))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(n2(c), true, ifeq(m2(b), true, l3(c, c), true), r0(e))
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 ifeq(n2(c), true, ifeq(m2(b), true, l3(c, c), true), true)
% 5.17/0.94 = { by axiom 10 (rule_217) }
% 5.17/0.94 true
% 5.17/0.94 = { by axiom 1 (axiom_13) R->L }
% 5.17/0.94 r0(e)
% 5.17/0.94 = { by lemma 11 R->L }
% 5.17/0.94 s0(d)
% 5.17/0.94 = { by lemma 11 }
% 5.17/0.94 r0(e)
% 5.17/0.94 = { by axiom 1 (axiom_13) }
% 5.17/0.94 true
% 5.17/0.94 % SZS output end Proof
% 5.17/0.94
% 5.17/0.94 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------