%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN003-1.006 : TPTP v9.3.1. Released v1.0.0.
% 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 01:46:52 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.24s
% Output : Proof 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN003-1.006 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.16 % Computer : n005.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Mon Sep 28 15:19:50 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24 Command-line arguments: --no-flatten-goal
% 0.07/0.24
% 0.07/0.24 % SZS status Unsatisfiable
% 0.07/0.24
% 0.07/0.28 % SZS output start Proof
% 0.07/0.28 Axiom 1 (base_1): p_1 = true.
% 0.07/0.28 Axiom 2 (base_3): q = true.
% 0.07/0.28 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.28 Axiom 4 (qq_1): ifeq(q, true, q_1, true) = true.
% 0.07/0.28 Axiom 5 (qq_2): ifeq(q, true, q_2, true) = true.
% 0.07/0.28 Axiom 6 (qq_3): ifeq(q, true, q_3, true) = true.
% 0.07/0.28 Axiom 7 (qq_4): ifeq(q, true, q_4, true) = true.
% 0.07/0.28 Axiom 8 (qq_5): ifeq(q, true, q_5, true) = true.
% 0.07/0.28 Axiom 9 (pqp_1): ifeq(q_1, true, ifeq(p_1, true, p_2, true), true) = true.
% 0.07/0.28 Axiom 10 (pqp_2): ifeq(q_2, true, ifeq(p_2, true, p_3, true), true) = true.
% 0.07/0.28 Axiom 11 (pqp_3): ifeq(q_3, true, ifeq(p_3, true, p_4, true), true) = true.
% 0.07/0.28 Axiom 12 (pqp_4): ifeq(q_4, true, ifeq(p_4, true, p_5, true), true) = true.
% 0.07/0.28 Axiom 13 (pqp_5): ifeq(q_5, true, ifeq(p_5, true, p_6, true), true) = true.
% 0.07/0.28
% 0.07/0.28 Lemma 14: q = p_1.
% 0.07/0.28 Proof:
% 0.07/0.28 q
% 0.07/0.28 = { by axiom 2 (base_3) }
% 0.07/0.28 true
% 0.07/0.28 = { by axiom 1 (base_1) R->L }
% 0.07/0.28 p_1
% 0.07/0.28
% 0.07/0.28 Lemma 15: p_1 = q_1.
% 0.07/0.28 Proof:
% 0.07/0.28 p_1
% 0.07/0.28 = { by axiom 1 (base_1) }
% 0.07/0.28 true
% 0.07/0.28 = { by axiom 4 (qq_1) R->L }
% 0.07/0.28 ifeq(q, true, q_1, true)
% 0.07/0.28 = { by lemma 14 }
% 0.07/0.28 ifeq(p_1, true, q_1, true)
% 0.07/0.28 = { by axiom 1 (base_1) R->L }
% 0.07/0.28 ifeq(p_1, p_1, q_1, true)
% 0.07/0.28 = { by axiom 1 (base_1) R->L }
% 0.07/0.28 ifeq(p_1, p_1, q_1, p_1)
% 0.07/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.35/0.28 q_1
% 0.35/0.28
% 0.35/0.28 Goal 1 (base_2): p_6 = true.
% 0.35/0.28 Proof:
% 0.35/0.28 p_6
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(q_1, q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(p_1, q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(true, q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 12 (pqp_4) R->L }
% 0.35/0.28 ifeq(ifeq(q_4, true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, q_1, q_4, q_1), true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, p_1, q_4, q_1), true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, p_1, q_4, p_1), true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, true, q_4, p_1), true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, true, q_4, true), true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(p_1, true, q_4, true), true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 14 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q, true, q_4, true), true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 7 (qq_4) }
% 0.35/0.28 ifeq(ifeq(true, true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(p_1, true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, true, ifeq(p_4, true, p_5, true), true), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(q_1, true, ifeq(p_4, true, p_5, true), p_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(q_1, true, ifeq(p_4, true, p_5, p_1), p_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(q_1, true, ifeq(p_4, p_1, p_5, p_1), p_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(q_1, p_1, ifeq(p_4, p_1, p_5, p_1), p_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, p_1, ifeq(p_4, p_1, p_5, p_1), q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, p_1, ifeq(p_4, p_1, p_5, q_1), q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, p_1, ifeq(p_4, q_1, p_5, q_1), q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, q_1, ifeq(p_4, q_1, p_5, q_1), q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.35/0.28 ifeq(ifeq(p_4, q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(p_1, q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(true, q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 10 (pqp_2) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_2, true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, q_1, q_2, q_1), true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, p_1, q_2, q_1), true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, p_1, q_2, p_1), true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, true, q_2, p_1), true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, true, q_2, true), true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(p_1, true, q_2, true), true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 14 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q, true, q_2, true), true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 5 (qq_2) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(p_1, true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_2, true, p_3, true), true), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_2, true, p_3, true), p_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_2, true, p_3, p_1), p_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_2, p_1, p_3, p_1), p_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_2, p_1, p_3, p_1), p_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_2, p_1, p_3, p_1), q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_2, p_1, p_3, q_1), q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_2, q_1, p_3, q_1), q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, q_1, ifeq(p_2, q_1, p_3, q_1), q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(p_2, q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, q_1, p_2, q_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, q_1, ifeq(q_1, q_1, p_2, q_1), q_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(q_1, q_1, p_2, q_1), q_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_1, q_1, p_2, q_1), q_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_1, p_1, p_2, q_1), q_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_1, p_1, p_2, p_1), q_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_1, p_1, p_2, p_1), p_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_1, p_1, p_2, p_1), p_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_1, true, p_2, p_1), p_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_1, true, p_2, true), p_1), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(ifeq(q_1, true, ifeq(p_1, true, p_2, true), true), q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 9 (pqp_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(true, q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(p_1, q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, q_1, p_3, q_1), q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.35/0.28 ifeq(ifeq(ifeq(p_3, q_1, p_4, q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, q_1, ifeq(p_3, q_1, p_4, q_1), q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_3, q_1, p_4, q_1), q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_3, p_1, p_4, q_1), q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_3, p_1, p_4, p_1), q_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, p_1, ifeq(p_3, p_1, p_4, p_1), p_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, true, ifeq(p_3, p_1, p_4, p_1), p_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, true, ifeq(p_3, true, p_4, p_1), p_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, true, ifeq(p_3, true, p_4, true), p_1), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(q_1, true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(p_1, true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(ifeq(ifeq(true, true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 6 (qq_3) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q, true, q_3, true), true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 14 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(p_1, true, q_3, true), true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, true, q_3, true), true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, true, q_3, p_1), true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, p_1, q_3, p_1), true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, p_1, q_3, q_1), true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(ifeq(ifeq(q_1, q_1, q_3, q_1), true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.35/0.28 ifeq(ifeq(ifeq(q_3, true, ifeq(p_3, true, p_4, true), true), q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 11 (pqp_3) }
% 0.35/0.28 ifeq(ifeq(true, q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(p_1, q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, q_1, p_5, q_1), q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.35/0.28 ifeq(p_5, q_1, p_6, q_1)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.35/0.28 ifeq(q_1, q_1, ifeq(p_5, q_1, p_6, q_1), q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(q_1, p_1, ifeq(p_5, q_1, p_6, q_1), q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(q_1, p_1, ifeq(p_5, p_1, p_6, q_1), q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(q_1, p_1, ifeq(p_5, p_1, p_6, p_1), q_1)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(q_1, p_1, ifeq(p_5, p_1, p_6, p_1), p_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(q_1, true, ifeq(p_5, p_1, p_6, p_1), p_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(q_1, true, ifeq(p_5, true, p_6, p_1), p_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(q_1, true, ifeq(p_5, true, p_6, true), p_1)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(q_1, true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by lemma 15 R->L }
% 0.35/0.28 ifeq(p_1, true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by axiom 1 (base_1) }
% 0.35/0.28 ifeq(true, true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by axiom 8 (qq_5) R->L }
% 0.35/0.28 ifeq(ifeq(q, true, q_5, true), true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by lemma 14 }
% 0.35/0.28 ifeq(ifeq(p_1, true, q_5, true), true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, true, q_5, true), true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(q_1, true, q_5, p_1), true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by axiom 1 (base_1) R->L }
% 0.35/0.28 ifeq(ifeq(q_1, p_1, q_5, p_1), true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, p_1, q_5, q_1), true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by lemma 15 }
% 0.35/0.28 ifeq(ifeq(q_1, q_1, q_5, q_1), true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by axiom 3 (ifeq_axiom) }
% 0.35/0.28 ifeq(q_5, true, ifeq(p_5, true, p_6, true), true)
% 0.35/0.28 = { by axiom 13 (pqp_5) }
% 0.35/0.28 true
% 0.35/0.28 % SZS output end Proof
% 0.35/0.28
% 0.35/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------