%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN941+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 01:48:39 PM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN941+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 17:17:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.26 Command-line arguments: --no-flatten-goal
% 0.20/0.26
% 0.20/0.26 % SZS status Theorem
% 0.20/0.26
% 0.20/0.27 % SZS output start Proof
% 0.20/0.27 Axiom 1 (prove_this): q(f(b)) = true.
% 0.20/0.27 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.27 Axiom 3 (prove_this_1): ifeq(q(X), true, p(f(Y)), true) = true.
% 0.20/0.27 Axiom 4 (prove_this_2): ifeq(p(X), true, ifeq(q(X), true, r(Y), true), true) = true.
% 0.20/0.27
% 0.20/0.27 Goal 1 (prove_this_3): tuple(q(X), p(X), r(b), r(c)) = tuple(true, true, true, true).
% 0.20/0.27 The goal is true when:
% 0.20/0.27 X = f(b)
% 0.20/0.27
% 0.20/0.27 Proof:
% 0.20/0.27 tuple(q(f(b)), p(f(b)), r(b), r(c))
% 0.20/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), ifeq(true, true, r(b), true), r(c))
% 0.20/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), ifeq(true, true, ifeq(true, true, r(b), true), true), r(c))
% 0.20/0.27 = { by axiom 3 (prove_this_1) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), ifeq(ifeq(q(f(b)), true, p(f(b)), true), true, ifeq(true, true, r(b), true), true), r(c))
% 0.20/0.27 = { by axiom 1 (prove_this) }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), ifeq(ifeq(true, true, p(f(b)), true), true, ifeq(true, true, r(b), true), true), r(c))
% 0.20/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), ifeq(p(f(b)), true, ifeq(true, true, r(b), true), true), r(c))
% 0.20/0.27 = { by axiom 1 (prove_this) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), ifeq(p(f(b)), true, ifeq(q(f(b)), true, r(b), true), true), r(c))
% 0.20/0.27 = { by axiom 4 (prove_this_2) }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), true, r(c))
% 0.20/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), true, ifeq(true, true, r(c), true))
% 0.20/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), true, ifeq(true, true, ifeq(true, true, r(c), true), true))
% 0.20/0.27 = { by axiom 3 (prove_this_1) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), true, ifeq(ifeq(q(f(b)), true, p(f(b)), true), true, ifeq(true, true, r(c), true), true))
% 0.20/0.27 = { by axiom 1 (prove_this) }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), true, ifeq(ifeq(true, true, p(f(b)), true), true, ifeq(true, true, r(c), true), true))
% 0.20/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), true, ifeq(p(f(b)), true, ifeq(true, true, r(c), true), true))
% 0.20/0.27 = { by axiom 1 (prove_this) R->L }
% 0.20/0.27 tuple(q(f(b)), p(f(b)), true, ifeq(p(f(b)), true, ifeq(q(f(b)), true, r(c), true), true))
% 0.20/0.28 = { by axiom 4 (prove_this_2) }
% 0.20/0.28 tuple(q(f(b)), p(f(b)), true, true)
% 0.20/0.28 = { by axiom 1 (prove_this) }
% 0.20/0.28 tuple(true, p(f(b)), true, true)
% 0.20/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.28 tuple(true, ifeq(true, true, p(f(b)), true), true, true)
% 0.20/0.28 = { by axiom 1 (prove_this) R->L }
% 0.20/0.28 tuple(true, ifeq(q(f(b)), true, p(f(b)), true), true, true)
% 0.20/0.28 = { by axiom 3 (prove_this_1) }
% 0.20/0.28 tuple(true, true, true, true)
% 0.20/0.28 % SZS output end Proof
% 0.20/0.28
% 0.20/0.28 RESULT: Theorem (the conjecture is true).
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