%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:39:23 PM UTC 2026
% Result : Theorem 0.07s 0.35s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET954+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Mon Sep 28 03:15:49 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 Command-line arguments: --no-flatten-goal
% 0.07/0.35
% 0.07/0.35 % SZS status Theorem
% 0.07/0.35
% 0.07/0.35 % SZS output start Proof
% 0.07/0.35 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.35 Axiom 2 (t107_zfmisc_1): in(ordered_pair(a, b), cartesian_product2(c, d)) = true.
% 0.07/0.35 Axiom 3 (l55_zfmisc_1_1): ifeq(in(ordered_pair(X, Y), cartesian_product2(Z, W)), true, in(X, Z), true) = true.
% 0.07/0.35 Axiom 4 (l55_zfmisc_1_2): ifeq(in(ordered_pair(X, Y), cartesian_product2(Z, W)), true, in(Y, W), true) = true.
% 0.07/0.35 Axiom 5 (l55_zfmisc_1): ifeq(in(X, Y), true, ifeq(in(Z, W), true, in(ordered_pair(Z, X), cartesian_product2(W, Y)), true), true) = true.
% 0.07/0.35
% 0.07/0.35 Goal 1 (t107_zfmisc_1_1): in(ordered_pair(b, a), cartesian_product2(d, c)) = true.
% 0.07/0.35 Proof:
% 0.07/0.35 in(ordered_pair(b, a), cartesian_product2(d, c))
% 0.07/0.35 = { by axiom 1 (ifeq_axiom) R->L }
% 0.07/0.35 ifeq(true, true, in(ordered_pair(b, a), cartesian_product2(d, c)), true)
% 0.07/0.35 = { by axiom 4 (l55_zfmisc_1_2) R->L }
% 0.07/0.35 ifeq(ifeq(in(ordered_pair(a, b), cartesian_product2(c, d)), true, in(b, d), true), true, in(ordered_pair(b, a), cartesian_product2(d, c)), true)
% 0.07/0.35 = { by axiom 2 (t107_zfmisc_1) }
% 0.07/0.35 ifeq(ifeq(true, true, in(b, d), true), true, in(ordered_pair(b, a), cartesian_product2(d, c)), true)
% 0.07/0.35 = { by axiom 1 (ifeq_axiom) }
% 0.07/0.35 ifeq(in(b, d), true, in(ordered_pair(b, a), cartesian_product2(d, c)), true)
% 0.07/0.35 = { by axiom 1 (ifeq_axiom) R->L }
% 0.07/0.35 ifeq(true, true, ifeq(in(b, d), true, in(ordered_pair(b, a), cartesian_product2(d, c)), true), true)
% 0.07/0.35 = { by axiom 3 (l55_zfmisc_1_1) R->L }
% 0.07/0.35 ifeq(ifeq(in(ordered_pair(a, b), cartesian_product2(c, d)), true, in(a, c), true), true, ifeq(in(b, d), true, in(ordered_pair(b, a), cartesian_product2(d, c)), true), true)
% 0.07/0.35 = { by axiom 2 (t107_zfmisc_1) }
% 0.07/0.35 ifeq(ifeq(true, true, in(a, c), true), true, ifeq(in(b, d), true, in(ordered_pair(b, a), cartesian_product2(d, c)), true), true)
% 0.07/0.35 = { by axiom 1 (ifeq_axiom) }
% 0.07/0.35 ifeq(in(a, c), true, ifeq(in(b, d), true, in(ordered_pair(b, a), cartesian_product2(d, c)), true), true)
% 0.07/0.35 = { by axiom 5 (l55_zfmisc_1) }
% 0.07/0.35 true
% 0.07/0.35 % SZS output end Proof
% 0.07/0.35
% 0.07/0.35 RESULT: Theorem (the conjecture is true).
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