TSTP Solution File: SYN143-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN143-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:33:20 EDT 2023
% Result : Unsatisfiable 7.11s 1.25s
% Output : Proof 7.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN143-10 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.32 % Computer : n009.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sat Aug 26 20:16:20 EDT 2023
% 0.13/0.32 % CPUTime :
% 7.11/1.25 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 7.11/1.25
% 7.11/1.25 % SZS status Unsatisfiable
% 7.11/1.25
% 7.11/1.29 % SZS output start Proof
% 7.11/1.29 Axiom 1 (axiom_5): s0(b) = true.
% 7.11/1.29 Axiom 2 (axiom_20): l0(a) = true.
% 7.11/1.29 Axiom 3 (axiom_32): k0(b) = true.
% 7.11/1.29 Axiom 4 (axiom_28): k0(e) = true.
% 7.11/1.29 Axiom 5 (axiom_14): p0(b, X) = true.
% 7.11/1.29 Axiom 6 (axiom_17): q0(X, d) = true.
% 7.11/1.29 Axiom 7 (axiom_37): n0(b, a) = true.
% 7.11/1.29 Axiom 8 (axiom_7): n0(d, b) = true.
% 7.11/1.29 Axiom 9 (axiom_34): n0(c, d) = true.
% 7.11/1.29 Axiom 10 (axiom_19): m0(X, d, Y) = true.
% 7.11/1.29 Axiom 11 (axiom_31): m0(b, b, e) = true.
% 7.11/1.29 Axiom 12 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 7.11/1.30 Axiom 13 (rule_125): ifeq(p0(X, X), true, s1(X), true) = true.
% 7.11/1.30 Axiom 14 (rule_001): ifeq(n0(X, Y), true, k1(Y), true) = true.
% 7.11/1.30 Axiom 15 (rule_002): ifeq(n0(X, Y), true, l1(Y, Y), true) = true.
% 7.11/1.30 Axiom 16 (rule_085): ifeq(p0(X, Y), true, p1(Y, Y, Y), true) = true.
% 7.11/1.30 Axiom 17 (rule_045): ifeq(q0(d, d), true, n1(d, d, d), true) = true.
% 7.11/1.30 Axiom 18 (rule_181): ifeq(p1(X, X, X), true, q2(X, X, X), true) = true.
% 7.11/1.30 Axiom 19 (rule_126): ifeq(s1(X), true, ifeq(q0(Y, Z), true, s1(Y), true), true) = true.
% 7.11/1.30 Axiom 20 (rule_305): ifeq(s4(X), true, ifeq(m4(e, e), true, m5(X, X), true), true) = true.
% 7.11/1.30 Axiom 21 (rule_189): ifeq(q2(b, X, b), true, ifeq(s1(b), true, s2(X), true), true) = true.
% 7.11/1.30 Axiom 22 (rule_063): ifeq(k0(X), true, ifeq(n0(d, Y), true, p1(Y, Y, X), true), true) = true.
% 7.11/1.30 Axiom 23 (rule_279): ifeq(s3(a, X), true, ifeq(l2(Y, Z), true, m4(X, Z), true), true) = true.
% 7.11/1.30 Axiom 24 (rule_299): ifeq(p3(X, Y, Z), true, ifeq(l1(W, Y), true, s4(W), true), true) = true.
% 7.11/1.30 Axiom 25 (rule_177): ifeq(p1(X, X, X), true, ifeq(k0(Y), true, q2(X, Y, Y), true), true) = true.
% 7.11/1.30 Axiom 26 (rule_250): ifeq(q2(X, Y, Z), true, ifeq(k1(Z), true, p3(Z, Z, Z), true), true) = true.
% 7.11/1.30 Axiom 27 (rule_178): ifeq(n1(X, Y, Z), true, ifeq(q0(X, Y), true, q2(Y, Y, Y), true), true) = true.
% 7.11/1.30 Axiom 28 (rule_082): ifeq(p1(X, Y, Z), true, ifeq(m0(X, Y, Z), true, p1(Y, W, X), true), true) = true.
% 7.11/1.30 Axiom 29 (rule_050): ifeq(l0(X), true, ifeq(p0(b, Y), true, ifeq(s0(b), true, n1(X, Y, X), true), true), true) = true.
% 7.11/1.30 Axiom 30 (rule_133): ifeq(s1(X), true, ifeq(p0(Y, Y), true, ifeq(m0(Z, X, W), true, l2(W, W), true), true), true) = true.
% 7.11/1.30 Axiom 31 (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.
% 7.11/1.30 Axiom 32 (rule_054): ifeq(n1(X, Y, X), true, ifeq(l0(Z), true, ifeq(l1(Z, X), true, n1(X, Y, Y), true), true), true) = true.
% 7.11/1.30 Axiom 33 (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.
% 7.11/1.30
% 7.11/1.30 Lemma 34: s1(b) = true.
% 7.11/1.30 Proof:
% 7.11/1.30 s1(b)
% 7.11/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.11/1.30 ifeq(true, true, s1(b), true)
% 7.11/1.30 = { by axiom 5 (axiom_14) R->L }
% 7.11/1.30 ifeq(p0(b, b), true, s1(b), true)
% 7.11/1.30 = { by axiom 13 (rule_125) }
% 7.11/1.30 true
% 7.11/1.30
% 7.11/1.30 Lemma 35: p1(X, X, X) = true.
% 7.11/1.30 Proof:
% 7.11/1.30 p1(X, X, X)
% 7.11/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.11/1.30 ifeq(true, true, p1(X, X, X), true)
% 7.11/1.30 = { by axiom 5 (axiom_14) R->L }
% 7.11/1.30 ifeq(p0(b, X), true, p1(X, X, X), true)
% 7.11/1.30 = { by axiom 16 (rule_085) }
% 7.11/1.30 true
% 7.11/1.30
% 7.11/1.30 Goal 1 (prove_this): m5(d, d) = true.
% 7.11/1.30 Proof:
% 7.11/1.30 m5(d, d)
% 7.11/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.11/1.30 ifeq(true, true, m5(d, d), true)
% 7.11/1.30 = { by axiom 23 (rule_279) R->L }
% 7.11/1.30 ifeq(ifeq(s3(a, e), true, ifeq(l2(e, e), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.11/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.11/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(true, true, l2(e, e), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.11/1.30 = { by axiom 5 (axiom_14) R->L }
% 7.11/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(p0(b, b), true, l2(e, e), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.11/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(p0(b, b), true, ifeq(true, true, l2(e, e), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(true, true, ifeq(p0(b, b), true, ifeq(true, true, l2(e, e), true), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 19 (rule_126) R->L }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(ifeq(s1(b), true, ifeq(q0(d, d), true, s1(d), true), true), true, ifeq(p0(b, b), true, ifeq(true, true, l2(e, e), true), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 6 (axiom_17) }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(ifeq(s1(b), true, ifeq(true, true, s1(d), true), true), true, ifeq(p0(b, b), true, ifeq(true, true, l2(e, e), true), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(ifeq(s1(b), true, s1(d), true), true, ifeq(p0(b, b), true, ifeq(true, true, l2(e, e), true), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by lemma 34 }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(ifeq(true, true, s1(d), true), true, ifeq(p0(b, b), true, ifeq(true, true, l2(e, e), true), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(s1(d), true, ifeq(p0(b, b), true, ifeq(true, true, l2(e, e), true), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 10 (axiom_19) R->L }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(ifeq(s1(d), true, ifeq(p0(b, b), true, ifeq(m0(X, d, e), true, l2(e, e), true), true), true), true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 30 (rule_133) }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, ifeq(true, true, m4(e, e), true), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.30 ifeq(ifeq(s3(a, e), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(true, true, s3(a, e), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(true, true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 21 (rule_189) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(q2(b, a, b), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 32 (rule_054) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(n1(a, b, a), true, ifeq(l0(a), true, ifeq(l1(a, a), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(n1(a, b, a), true, ifeq(l0(a), true, ifeq(ifeq(true, true, l1(a, a), true), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 7 (axiom_37) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(n1(a, b, a), true, ifeq(l0(a), true, ifeq(ifeq(n0(b, a), true, l1(a, a), true), true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 15 (rule_002) }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(n1(a, b, a), true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, n1(a, b, a), true), true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 2 (axiom_20) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, n1(a, b, a), true), true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, n1(a, b, a), true), true), true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 1 (axiom_5) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, ifeq(s0(b), true, n1(a, b, a), true), true), true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.30 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, ifeq(s0(b), true, n1(a, b, a), true), true), true), true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 5 (axiom_14) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, ifeq(p0(b, b), true, ifeq(s0(b), true, n1(a, b, a), true), true), true), true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 29 (rule_050) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(l0(a), true, ifeq(true, true, n1(a, b, b), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 2 (axiom_20) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, n1(a, b, b), true), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, n1(a, b, b), true), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(n1(a, b, b), true, q2(b, a, b), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 28 (rule_082) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p1(b, b, e), true, ifeq(m0(b, b, e), true, p1(b, b, b), true), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(b, b, e), true), true, ifeq(m0(b, b, e), true, p1(b, b, b), true), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 4 (axiom_28) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(k0(e), true, p1(b, b, e), true), true, ifeq(m0(b, b, e), true, p1(b, b, b), true), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(k0(e), true, ifeq(true, true, p1(b, b, e), true), true), true, ifeq(m0(b, b, e), true, p1(b, b, b), true), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 8 (axiom_7) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(k0(e), true, ifeq(n0(d, b), true, p1(b, b, e), true), true), true, ifeq(m0(b, b, e), true, p1(b, b, b), true), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 22 (rule_063) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(m0(b, b, e), true, p1(b, b, b), true), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(m0(b, b, e), true, p1(b, b, b), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 11 (axiom_31) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p1(b, b, b), true), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(p1(b, b, b), true, ifeq(n1(a, b, b), true, q2(b, a, b), true), true), true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, 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, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 25 (rule_177) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p1(a, a, a), true, ifeq(k0(b), true, q2(a, b, b), true), true), 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, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 3 (axiom_32) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p1(a, a, a), true, ifeq(true, true, q2(a, b, b), true), true), 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, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by lemma 35 }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(true, true, q2(a, b, b), true), true), 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, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, q2(a, b, b), true), 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, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(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, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 33 (rule_182) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(s1(b), true, s2(a), true), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(s1(b), true, s2(a), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by lemma 34 }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(true, true, s2(a), true), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(s2(a), true, ifeq(true, true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 18 (rule_181) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(s2(a), true, ifeq(ifeq(p1(a, a, a), true, q2(a, a, a), true), true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by lemma 35 }
% 7.70/1.31 ifeq(ifeq(ifeq(s2(a), true, ifeq(ifeq(true, true, q2(a, a, a), true), true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(s2(a), true, ifeq(q2(a, a, a), true, s3(a, e), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(s2(a), true, ifeq(q2(a, a, a), true, ifeq(true, true, s3(a, e), true), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 10 (axiom_19) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(s2(a), true, ifeq(q2(a, a, a), true, ifeq(m0(a, d, e), true, s3(a, e), true), true), true), true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 31 (rule_273) }
% 7.70/1.31 ifeq(ifeq(true, true, m4(e, e), true), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(m4(e, e), true, m5(d, d), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(true, true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 24 (rule_299) R->L }
% 7.70/1.31 ifeq(ifeq(p3(d, d, d), true, ifeq(l1(d, d), true, s4(d), true), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(p3(d, d, d), true, ifeq(ifeq(true, true, l1(d, d), true), true, s4(d), true), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 9 (axiom_34) R->L }
% 7.70/1.31 ifeq(ifeq(p3(d, d, d), true, ifeq(ifeq(n0(c, d), true, l1(d, d), true), true, s4(d), true), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 15 (rule_002) }
% 7.70/1.31 ifeq(ifeq(p3(d, d, d), true, ifeq(true, true, s4(d), true), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(p3(d, d, d), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(true, true, p3(d, d, d), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 14 (rule_001) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(n0(c, d), true, k1(d), true), true, p3(d, d, d), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 9 (axiom_34) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(true, true, k1(d), true), true, p3(d, d, d), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(k1(d), true, p3(d, d, d), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(true, true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 27 (rule_178) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(n1(d, d, d), true, ifeq(q0(d, d), true, q2(d, d, d), true), true), true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, n1(d, d, d), true), true, ifeq(q0(d, d), true, q2(d, d, d), true), true), true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 6 (axiom_17) R->L }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(q0(d, d), true, n1(d, d, d), true), true, ifeq(q0(d, d), true, q2(d, d, d), true), true), true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 17 (rule_045) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(q0(d, d), true, q2(d, d, d), true), true), true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(q0(d, d), true, q2(d, d, d), true), true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 6 (axiom_17) }
% 7.70/1.31 ifeq(ifeq(ifeq(ifeq(true, true, q2(d, d, d), true), true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(ifeq(ifeq(q2(d, d, d), true, ifeq(k1(d), true, p3(d, d, d), true), true), true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 26 (rule_250) }
% 7.70/1.31 ifeq(ifeq(true, true, s4(d), true), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 12 (ifeq_axiom) }
% 7.70/1.31 ifeq(s4(d), true, ifeq(m4(e, e), true, m5(d, d), true), true)
% 7.70/1.31 = { by axiom 20 (rule_305) }
% 7.70/1.31 true
% 7.70/1.31 % SZS output end Proof
% 7.70/1.31
% 7.70/1.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------