%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN190-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:47:16 PM UTC 2026
% Result : Unsatisfiable 7.63s 1.27s
% Output : Proof 8.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN190-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n020.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 15:38:49 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.63/1.27 Command-line arguments: --flatten-regeneralise
% 7.63/1.27
% 7.63/1.27 % SZS status Unsatisfiable
% 7.63/1.27
% 8.41/1.30 % SZS output start Proof
% 8.41/1.30 Axiom 1 (axiom_20): l0(a) = true.
% 8.41/1.30 Axiom 2 (axiom_1): s0(d) = true.
% 8.41/1.30 Axiom 3 (axiom_15): n0(a, b) = true.
% 8.41/1.30 Axiom 4 (axiom_34): n0(c, d) = true.
% 8.41/1.30 Axiom 5 (axiom_37): n0(b, a) = true.
% 8.41/1.30 Axiom 6 (axiom_17): q0(X, d) = true.
% 8.41/1.30 Axiom 7 (axiom_14): p0(b, X) = true.
% 8.41/1.30 Axiom 8 (axiom_19): m0(X, d, Y) = true.
% 8.41/1.30 Axiom 9 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 8.41/1.30 Axiom 10 (rule_125): ifeq(p0(X, X), true, s1(X), true) = true.
% 8.41/1.30 Axiom 11 (rule_002): ifeq(n0(X, Y), true, l1(Y, Y), true) = true.
% 8.41/1.30 Axiom 12 (rule_085): ifeq(p0(X, Y), true, p1(Y, Y, Y), true) = true.
% 8.41/1.31 Axiom 13 (rule_141): ifeq(q1(X, a, X), true, p2(X, a, X), true) = true.
% 8.41/1.31 Axiom 14 (rule_005): ifeq(m0(X, X, Y), true, m1(Y, X, Y), true) = true.
% 8.41/1.31 Axiom 15 (rule_122): ifeq(m0(X, Y, X), true, q1(X, X, X), true) = true.
% 8.41/1.31 Axiom 16 (rule_176): ifeq(m1(X, Y, X), true, p2(Y, X, Y), true) = true.
% 8.41/1.31 Axiom 17 (rule_267): ifeq(p2(X, Y, Z), true, r3(X, Z, X), true) = true.
% 8.41/1.31 Axiom 18 (rule_188): ifeq(r1(X), true, ifeq(l0(X), true, r2(X), true), true) = true.
% 8.41/1.31 Axiom 19 (rule_126): ifeq(s1(X), true, ifeq(q0(Y, Z), true, s1(Y), true), true) = true.
% 8.41/1.31 Axiom 20 (rule_135): ifeq(l1(X, Y), true, ifeq(s0(Z), true, m2(Z), true), true) = true.
% 8.41/1.31 Axiom 21 (rule_092): ifeq(p0(X, Y), true, ifeq(n0(Z, W), true, q1(Y, W, Y), true), true) = true.
% 8.41/1.31 Axiom 22 (rule_235): ifeq(k3(X, Y, X), true, ifeq(r2(Y), true, m3(X, X, Y), true), true) = true.
% 8.41/1.31 Axiom 23 (rule_082): ifeq(p1(X, Y, Z), true, ifeq(m0(X, Y, Z), true, p1(Y, W, X), true), true) = true.
% 8.41/1.31 Axiom 24 (rule_124): ifeq(q1(d, X, d), true, ifeq(q0(Y, X), true, ifeq(s0(d), true, r1(Y), true), true), true) = true.
% 8.41/1.31 Axiom 25 (rule_192): ifeq(p2(X, Y, Z), true, ifeq(s1(Y), true, ifeq(n0(W, Z), true, k3(W, Y, W), true), true), true) = true.
% 8.41/1.31 Axiom 26 (rule_268): ifeq(r3(X, Y, Y), true, ifeq(m3(Z, b, W), true, ifeq(m2(X), true, r3(W, W, X), true), true), true) = true.
% 8.41/1.31 Axiom 27 (rule_146): ifeq(p2(X, Y, X), true, ifeq(p1(X, Z, W), true, ifeq(l1(Z, W), true, p2(X, Y, Y), true), true), true) = true.
% 8.41/1.31
% 8.41/1.31 Goal 1 (prove_this): r3(a, X, d) = true.
% 8.41/1.31 The goal is true when:
% 8.41/1.31 X = a
% 8.41/1.31
% 8.41/1.31 Proof:
% 8.41/1.31 r3(a, a, d)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(true, true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 22 (rule_235) R->L }
% 8.41/1.31 ifeq(ifeq(k3(b, a, b), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(true, true, k3(b, a, b), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 5 (axiom_37) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(n0(b, a), true, k3(b, a, b), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(true, true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 19 (rule_126) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(s1(b), true, ifeq(q0(a, d), true, s1(a), true), true), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 6 (axiom_17) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(s1(b), true, ifeq(true, true, s1(a), true), true), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(s1(b), true, s1(a), true), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, s1(b), true), true, s1(a), true), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 7 (axiom_14) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(p0(b, b), true, s1(b), true), true, s1(a), true), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 10 (rule_125) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(true, true, s1(a), true), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(ifeq(ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(true, true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 13 (rule_141) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(q1(a, a, a), true, p2(a, a, a), true), true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, q1(a, a, a), true), true, p2(a, a, a), true), true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 5 (axiom_37) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(n0(b, a), true, q1(a, a, a), true), true, p2(a, a, a), true), true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(n0(b, a), true, q1(a, a, a), true), true), true, p2(a, a, a), true), true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 7 (axiom_14) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(p0(b, a), true, ifeq(n0(b, a), true, q1(a, a, a), true), true), true, p2(a, a, a), true), true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 21 (rule_092) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(true, true, p2(a, a, a), true), true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(ifeq(ifeq(p2(a, a, a), true, ifeq(s1(a), true, ifeq(n0(b, a), true, k3(b, a, b), true), true), true), true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 25 (rule_192) }
% 8.41/1.31 ifeq(ifeq(true, true, ifeq(r2(a), true, m3(b, b, a), true), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(ifeq(r2(a), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(true, true, r2(a), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(true, true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 24 (rule_124) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(a, d), true, ifeq(s0(d), true, r1(a), true), true), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 2 (axiom_1) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(a, d), true, ifeq(true, true, r1(a), true), true), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(q1(d, d, d), true, ifeq(q0(a, d), true, r1(a), true), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, q1(d, d, d), true), true, ifeq(q0(a, d), true, r1(a), true), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 8 (axiom_19) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(ifeq(m0(d, d, d), true, q1(d, d, d), true), true, ifeq(q0(a, d), true, r1(a), true), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 15 (rule_122) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(q0(a, d), true, r1(a), true), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(q0(a, d), true, r1(a), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 6 (axiom_17) }
% 8.41/1.31 ifeq(ifeq(ifeq(ifeq(true, true, r1(a), true), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(ifeq(ifeq(r1(a), true, ifeq(true, true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 1 (axiom_20) R->L }
% 8.41/1.31 ifeq(ifeq(ifeq(r1(a), true, ifeq(l0(a), true, r2(a), true), true), true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 18 (rule_188) }
% 8.41/1.31 ifeq(ifeq(true, true, m3(b, b, a), true), true, r3(a, a, d), true)
% 8.41/1.31 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.31 ifeq(m3(b, b, a), true, r3(a, a, d), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(true, true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 20 (rule_135) R->L }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(ifeq(l1(b, b), true, ifeq(s0(d), true, m2(d), true), true), true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(ifeq(ifeq(true, true, l1(b, b), true), true, ifeq(s0(d), true, m2(d), true), true), true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 3 (axiom_15) R->L }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(ifeq(ifeq(n0(a, b), true, l1(b, b), true), true, ifeq(s0(d), true, m2(d), true), true), true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 11 (rule_002) }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(ifeq(true, true, ifeq(s0(d), true, m2(d), true), true), true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(ifeq(s0(d), true, m2(d), true), true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 2 (axiom_1) }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(ifeq(true, true, m2(d), true), true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.32 ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(true, true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 17 (rule_267) R->L }
% 8.41/1.32 ifeq(ifeq(p2(d, d, d), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(true, true, p2(d, d, d), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 11 (rule_002) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(ifeq(n0(c, d), true, l1(d, d), true), true, p2(d, d, d), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 4 (axiom_34) }
% 8.41/1.32 ifeq(ifeq(ifeq(ifeq(true, true, l1(d, d), true), true, p2(d, d, d), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.32 ifeq(ifeq(ifeq(l1(d, d), true, p2(d, d, d), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(true, true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(true, true, ifeq(true, true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 16 (rule_176) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(ifeq(m1(d, d, d), true, p2(d, d, d), true), true, ifeq(true, true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, m1(d, d, d), true), true, p2(d, d, d), true), true, ifeq(true, true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 8 (axiom_19) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(ifeq(ifeq(m0(d, d, d), true, m1(d, d, d), true), true, p2(d, d, d), true), true, ifeq(true, true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 14 (rule_005) }
% 8.41/1.32 ifeq(ifeq(ifeq(ifeq(true, true, p2(d, d, d), true), true, ifeq(true, true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(true, true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 23 (rule_082) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(ifeq(p1(d, d, d), true, ifeq(m0(d, d, d), true, p1(d, d, d), true), true), true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 8 (axiom_19) }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(ifeq(p1(d, d, d), true, ifeq(true, true, p1(d, d, d), true), true), true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(ifeq(p1(d, d, d), true, p1(d, d, d), true), true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(ifeq(ifeq(true, true, p1(d, d, d), true), true, p1(d, d, d), true), true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 7 (axiom_14) R->L }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(ifeq(ifeq(p0(b, d), true, p1(d, d, d), true), true, p1(d, d, d), true), true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 12 (rule_085) }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(ifeq(true, true, p1(d, d, d), true), true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.32 ifeq(ifeq(ifeq(p2(d, d, d), true, ifeq(p1(d, d, d), true, ifeq(l1(d, d), true, p2(d, d, d), true), true), true), true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 27 (rule_146) }
% 8.41/1.32 ifeq(ifeq(true, true, r3(d, d, d), true), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 9 (ifeq_axiom) }
% 8.41/1.32 ifeq(r3(d, d, d), true, ifeq(m3(b, b, a), true, ifeq(m2(d), true, r3(a, a, d), true), true), true)
% 8.41/1.32 = { by axiom 26 (rule_268) }
% 8.41/1.32 true
% 8.41/1.32 % SZS output end Proof
% 8.41/1.32
% 8.41/1.32 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------