%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN204-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 01:47:18 PM UTC 2026
% Result : Unsatisfiable 12.18s 1.84s
% Output : Proof 12.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN204-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n016.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 15:43:18 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.18/1.84 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 12.18/1.84
% 12.18/1.84 % SZS status Unsatisfiable
% 12.18/1.84
% 12.18/1.88 % SZS output start Proof
% 12.18/1.88 Axiom 1 (axiom_9): r0(b) = true.
% 12.18/1.88 Axiom 2 (axiom_5): s0(b) = true.
% 12.18/1.88 Axiom 3 (axiom_20): l0(a) = true.
% 12.18/1.88 Axiom 4 (axiom_32): k0(b) = true.
% 12.18/1.88 Axiom 5 (axiom_14): p0(b, X) = true.
% 12.18/1.88 Axiom 6 (axiom_37): n0(b, a) = true.
% 12.18/1.88 Axiom 7 (axiom_19): m0(X, d, Y) = true.
% 12.18/1.88 Axiom 8 (axiom_35): m0(d, e, c) = true.
% 12.18/1.88 Axiom 9 (axiom_12): m0(a, X, a) = true.
% 12.18/1.88 Axiom 10 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 12.18/1.88 Axiom 11 (rule_125): ifeq(p0(X, X), true, s1(X), true) = true.
% 12.18/1.88 Axiom 12 (rule_088): ifeq(l0(a), true, p1(a, a, a), true) = true.
% 12.18/1.88 Axiom 13 (rule_002): ifeq(n0(X, Y), true, l1(Y, Y), true) = true.
% 12.18/1.88 Axiom 14 (rule_085): ifeq(p0(X, Y), true, p1(Y, Y, Y), true) = true.
% 12.18/1.88 Axiom 15 (rule_186): ifeq(l1(X, Y), true, q2(Y, Y, X), true) = true.
% 12.18/1.88 Axiom 16 (rule_189): ifeq(q2(b, X, b), true, ifeq(s1(b), true, s2(X), true), true) = true.
% 12.18/1.88 Axiom 17 (rule_177): ifeq(p1(X, X, X), true, ifeq(k0(Y), true, q2(X, Y, Y), true), true) = true.
% 12.18/1.88 Axiom 18 (rule_082): ifeq(p1(X, Y, Z), true, ifeq(m0(X, Y, Z), true, p1(Y, W, X), true), true) = true.
% 12.18/1.88 Axiom 19 (rule_050): ifeq(l0(X), true, ifeq(p0(b, Y), true, ifeq(s0(b), true, n1(X, Y, X), true), true), true) = true.
% 12.18/1.88 Axiom 20 (rule_003): ifeq(p0(X, Y), true, ifeq(r0(Z), true, ifeq(m0(W, Y, X), true, l1(Y, W), true), true), true) = true.
% 12.18/1.88 Axiom 21 (rule_273): ifeq(s2(X), true, ifeq(q2(Y, X, Y), true, ifeq(m0(Y, Z, W), true, s3(X, W), true), true), true) = true.
% 12.18/1.88 Axiom 22 (rule_054): ifeq(n1(X, Y, X), true, ifeq(l1(Z, X), true, ifeq(l0(Z), true, n1(X, Y, Y), true), true), true) = true.
% 12.18/1.88 Axiom 23 (rule_182): ifeq(q2(X, Y, Z), true, ifeq(p1(Z, Z, Y), true, ifeq(n1(X, Z, Y), true, q2(Z, X, Z), true), true), true) = true.
% 12.18/1.88
% 12.18/1.88 Goal 1 (prove_this): s3(a, c) = true.
% 12.18/1.88 Proof:
% 12.18/1.88 s3(a, c)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(true, true, s3(a, c), true)
% 12.18/1.88 = { by axiom 8 (axiom_35) R->L }
% 12.18/1.88 ifeq(m0(d, e, c), true, s3(a, c), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(true, true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 16 (rule_189) R->L }
% 12.18/1.88 ifeq(ifeq(q2(b, a, b), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(true, true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 17 (rule_177) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(ifeq(p1(a, a, a), true, ifeq(k0(b), true, q2(a, b, b), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(a, a, a), true), true, ifeq(k0(b), true, q2(a, b, b), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 3 (axiom_20) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, p1(a, a, a), true), true, ifeq(k0(b), true, q2(a, b, b), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 12 (rule_088) }
% 12.18/1.88 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(k0(b), true, q2(a, b, b), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.88 ifeq(ifeq(ifeq(ifeq(k0(b), true, q2(a, b, b), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 4 (axiom_32) }
% 12.18/1.88 ifeq(ifeq(ifeq(ifeq(true, true, q2(a, b, b), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(true, true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(true, true, ifeq(true, true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 14 (rule_085) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(ifeq(p0(b, b), true, p1(b, b, b), true), true, ifeq(true, true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 5 (axiom_14) }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(ifeq(true, true, p1(b, b, b), true), true, ifeq(true, true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(true, true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 22 (rule_054) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(n1(a, b, a), true, ifeq(l1(a, a), true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(n1(a, b, a), true, ifeq(ifeq(true, true, l1(a, a), true), true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 6 (axiom_37) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(n1(a, b, a), true, ifeq(ifeq(n0(b, a), true, l1(a, a), true), true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 13 (rule_002) }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(n1(a, b, a), true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(ifeq(true, true, n1(a, b, a), true), true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 3 (axiom_20) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(ifeq(l0(a), true, n1(a, b, a), true), true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, n1(a, b, a), true), true), true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 2 (axiom_5) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(s0(b), true, n1(a, b, a), true), true), true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, ifeq(s0(b), true, n1(a, b, a), true), true), true), true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 5 (axiom_14) R->L }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(p0(b, b), true, ifeq(s0(b), true, n1(a, b, a), true), true), true), true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 19 (rule_050) }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(true, true, ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.88 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(true, true, ifeq(l0(a), true, n1(a, b, b), true), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.88 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.90 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(l0(a), true, n1(a, b, b), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 3 (axiom_20) }
% 12.18/1.90 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(ifeq(true, true, n1(a, b, b), true), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.90 ifeq(ifeq(ifeq(q2(a, b, b), true, ifeq(p1(b, b, b), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 23 (rule_182) }
% 12.18/1.90 ifeq(ifeq(true, true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.90 ifeq(ifeq(s1(b), true, s2(a), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.90 ifeq(ifeq(ifeq(true, true, s1(b), true), true, s2(a), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 5 (axiom_14) R->L }
% 12.18/1.90 ifeq(ifeq(ifeq(p0(b, b), true, s1(b), true), true, s2(a), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 11 (rule_125) }
% 12.18/1.90 ifeq(ifeq(true, true, s2(a), true), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.90 ifeq(s2(a), true, ifeq(true, true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 23 (rule_182) R->L }
% 12.18/1.90 ifeq(s2(a), true, ifeq(ifeq(q2(a, a, d), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.18/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(true, true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 20 (rule_003) R->L }
% 12.18/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(p0(b, d), true, ifeq(r0(b), true, ifeq(m0(a, d, b), true, l1(d, a), true), true), true), true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 7 (axiom_19) }
% 12.18/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(p0(b, d), true, ifeq(r0(b), true, ifeq(true, true, l1(d, a), true), true), true), true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.18/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(p0(b, d), true, ifeq(r0(b), true, l1(d, a), true), true), true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.18/1.90 = { by axiom 5 (axiom_14) }
% 12.18/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(r0(b), true, l1(d, a), true), true), true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(r0(b), true, l1(d, a), true), true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 1 (axiom_9) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(true, true, l1(d, a), true), true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(l1(d, a), true, q2(a, a, d), true), true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 15 (rule_186) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(true, true, ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(p1(d, d, a), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(true, true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 18 (rule_082) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(p1(a, a, a), true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(a, a, a), true), true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 9 (axiom_12) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(ifeq(m0(a, a, a), true, p1(a, a, a), true), true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(m0(a, a, a), true, p1(a, a, a), true), true), true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 12 (rule_088) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, p1(a, a, a), true), true, ifeq(m0(a, a, a), true, p1(a, a, a), true), true), true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 3 (axiom_20) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(a, a, a), true), true, ifeq(m0(a, a, a), true, p1(a, a, a), true), true), true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(ifeq(p1(a, a, a), true, ifeq(m0(a, a, a), true, p1(a, a, a), true), true), true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 18 (rule_082) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(m0(a, a, a), true, p1(a, d, a), true), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(m0(a, a, a), true, p1(a, d, a), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 9 (axiom_12) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(ifeq(true, true, p1(a, d, a), true), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(p1(a, d, a), true, p1(d, d, a), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(p1(a, d, a), true, ifeq(true, true, p1(d, d, a), true), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 7 (axiom_19) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(p1(a, d, a), true, ifeq(m0(a, d, a), true, p1(d, d, a), true), true), true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 18 (rule_082) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(true, true, ifeq(n1(a, d, a), true, q2(d, a, d), true), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(n1(a, d, a), true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(true, true, n1(a, d, a), true), true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 3 (axiom_20) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(l0(a), true, n1(a, d, a), true), true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, n1(a, d, a), true), true), true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 2 (axiom_5) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(s0(b), true, n1(a, d, a), true), true), true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, ifeq(s0(b), true, n1(a, d, a), true), true), true), true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 5 (axiom_14) R->L }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(ifeq(l0(a), true, ifeq(p0(b, d), true, ifeq(s0(b), true, n1(a, d, a), true), true), true), true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 19 (rule_050) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(ifeq(true, true, q2(d, a, d), true), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 10 (ifeq_axiom) }
% 12.87/1.90 ifeq(s2(a), true, ifeq(q2(d, a, d), true, ifeq(m0(d, e, c), true, s3(a, c), true), true), true)
% 12.87/1.90 = { by axiom 21 (rule_273) }
% 12.87/1.90 true
% 12.87/1.90 % SZS output end Proof
% 12.87/1.90
% 12.87/1.90 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------