%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:39:24 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 28 03:16:51 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 Command-line arguments: --no-flatten-goal
% 0.11/0.44
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44
% 0.11/0.44 % SZS output start Proof
% 0.11/0.44 Axiom 1 (commutativity_k2_xboole_0): set_union2(X, Y) = set_union2(Y, X).
% 0.11/0.44 Axiom 2 (t4_xboole_1): set_union2(set_union2(X, Y), Z) = set_union2(X, set_union2(Y, Z)).
% 0.11/0.44 Axiom 3 (t120_zfmisc_1_1): cartesian_product2(X, set_union2(Y, Z)) = set_union2(cartesian_product2(X, Y), cartesian_product2(X, Z)).
% 0.11/0.44 Axiom 4 (t120_zfmisc_1): cartesian_product2(set_union2(X, Y), Z) = set_union2(cartesian_product2(X, Z), cartesian_product2(Y, Z)).
% 0.11/0.44
% 0.11/0.44 Goal 1 (t121_zfmisc_1): cartesian_product2(set_union2(a, b), set_union2(c, d)) = set_union2(set_union2(set_union2(cartesian_product2(a, c), cartesian_product2(a, d)), cartesian_product2(b, c)), cartesian_product2(b, d)).
% 0.11/0.44 Proof:
% 0.11/0.44 cartesian_product2(set_union2(a, b), set_union2(c, d))
% 0.11/0.44 = { by axiom 4 (t120_zfmisc_1) }
% 0.11/0.44 set_union2(cartesian_product2(a, set_union2(c, d)), cartesian_product2(b, set_union2(c, d)))
% 0.11/0.44 = { by axiom 1 (commutativity_k2_xboole_0) R->L }
% 0.11/0.44 set_union2(cartesian_product2(a, set_union2(c, d)), cartesian_product2(b, set_union2(d, c)))
% 0.11/0.44 = { by axiom 1 (commutativity_k2_xboole_0) R->L }
% 0.11/0.44 set_union2(cartesian_product2(b, set_union2(d, c)), cartesian_product2(a, set_union2(c, d)))
% 0.11/0.44 = { by axiom 3 (t120_zfmisc_1_1) }
% 0.11/0.44 set_union2(set_union2(cartesian_product2(b, d), cartesian_product2(b, c)), cartesian_product2(a, set_union2(c, d)))
% 0.11/0.44 = { by axiom 2 (t4_xboole_1) }
% 0.11/0.44 set_union2(cartesian_product2(b, d), set_union2(cartesian_product2(b, c), cartesian_product2(a, set_union2(c, d))))
% 0.11/0.44 = { by axiom 3 (t120_zfmisc_1_1) }
% 0.11/0.44 set_union2(cartesian_product2(b, d), set_union2(cartesian_product2(b, c), set_union2(cartesian_product2(a, c), cartesian_product2(a, d))))
% 0.11/0.44 = { by axiom 1 (commutativity_k2_xboole_0) R->L }
% 0.11/0.44 set_union2(cartesian_product2(b, d), set_union2(set_union2(cartesian_product2(a, c), cartesian_product2(a, d)), cartesian_product2(b, c)))
% 0.11/0.44 = { by axiom 1 (commutativity_k2_xboole_0) R->L }
% 0.11/0.44 set_union2(set_union2(set_union2(cartesian_product2(a, c), cartesian_product2(a, d)), cartesian_product2(b, c)), cartesian_product2(b, d))
% 0.11/0.44 % SZS output end Proof
% 0.11/0.44
% 0.11/0.44 RESULT: Theorem (the conjecture is true).
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