%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN940+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 0.06s 0.24s
% Output : Proof 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN940+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n015.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 17:17:46 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.24 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.06/0.24
% 0.06/0.24 % SZS status Theorem
% 0.06/0.24
% 0.06/0.25 % SZS output start Proof
% 0.06/0.25 Axiom 1 (prove_this): q(f(X)) = true.
% 0.06/0.25 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.06/0.25 Axiom 3 (prove_this_1): ifeq(q(X), true, p(f(Y)), true) = true.
% 0.06/0.25 Axiom 4 (prove_this_2): ifeq(p(X), true, ifeq(q(X), true, r(Y), true), true) = true.
% 0.06/0.25
% 0.06/0.25 Goal 1 (prove_this_3): tuple(q(X), p(X), r(b), r(c)) = tuple(true, true, true, true).
% 0.06/0.25 The goal is true when:
% 0.06/0.25 X = f(U)
% 0.06/0.25
% 0.06/0.25 Proof:
% 0.06/0.25 tuple(q(f(U)), p(f(U)), r(b), r(c))
% 0.06/0.25 = { by axiom 1 (prove_this) }
% 0.06/0.25 tuple(true, p(f(U)), r(b), r(c))
% 0.06/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.25 tuple(true, ifeq(true, true, p(f(U)), true), r(b), r(c))
% 0.06/0.25 = { by axiom 1 (prove_this) R->L }
% 0.06/0.25 tuple(true, ifeq(q(f(V)), true, p(f(U)), true), r(b), r(c))
% 0.06/0.25 = { by axiom 3 (prove_this_1) }
% 0.06/0.25 tuple(true, true, r(b), r(c))
% 0.06/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.25 tuple(true, true, ifeq(true, true, r(b), true), r(c))
% 0.06/0.25 = { by axiom 1 (prove_this) R->L }
% 0.06/0.25 tuple(true, true, ifeq(q(f(Z)), true, r(b), true), r(c))
% 0.06/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.25 tuple(true, true, ifeq(true, true, ifeq(q(f(Z)), true, r(b), true), true), r(c))
% 0.06/0.25 = { by axiom 3 (prove_this_1) R->L }
% 0.06/0.25 tuple(true, true, ifeq(ifeq(q(f(W)), true, p(f(Z)), true), true, ifeq(q(f(Z)), true, r(b), true), true), r(c))
% 0.06/0.25 = { by axiom 1 (prove_this) }
% 0.06/0.25 tuple(true, true, ifeq(ifeq(true, true, p(f(Z)), true), true, ifeq(q(f(Z)), true, r(b), true), true), r(c))
% 0.06/0.25 = { by axiom 2 (ifeq_axiom) }
% 0.06/0.25 tuple(true, true, ifeq(p(f(Z)), true, ifeq(q(f(Z)), true, r(b), true), true), r(c))
% 0.06/0.25 = { by axiom 4 (prove_this_2) }
% 0.06/0.25 tuple(true, true, true, r(c))
% 0.06/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.25 tuple(true, true, true, ifeq(true, true, r(c), true))
% 0.06/0.25 = { by axiom 1 (prove_this) R->L }
% 0.06/0.25 tuple(true, true, true, ifeq(q(f(X)), true, r(c), true))
% 0.06/0.25 = { by axiom 2 (ifeq_axiom) R->L }
% 0.06/0.25 tuple(true, true, true, ifeq(true, true, ifeq(q(f(X)), true, r(c), true), true))
% 0.06/0.25 = { by axiom 3 (prove_this_1) R->L }
% 0.06/0.25 tuple(true, true, true, ifeq(ifeq(q(f(Y)), true, p(f(X)), true), true, ifeq(q(f(X)), true, r(c), true), true))
% 0.06/0.25 = { by axiom 1 (prove_this) }
% 0.06/0.25 tuple(true, true, true, ifeq(ifeq(true, true, p(f(X)), true), true, ifeq(q(f(X)), true, r(c), true), true))
% 0.06/0.25 = { by axiom 2 (ifeq_axiom) }
% 0.06/0.25 tuple(true, true, true, ifeq(p(f(X)), true, ifeq(q(f(X)), true, r(c), true), true))
% 0.06/0.25 = { by axiom 4 (prove_this_2) }
% 0.06/0.25 tuple(true, true, true, true)
% 0.06/0.25 % SZS output end Proof
% 0.06/0.25
% 0.06/0.25 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------