%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:39:25 PM UTC 2026
% Result : Theorem 0.03s 0.45s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.03/0.37 % CPULimit : 300
% 0.03/0.37 % WCLimit : 300
% 0.03/0.37 % DateTime : Mon Sep 28 03:23:17 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.45 Command-line arguments: --no-flatten-goal
% 0.03/0.45
% 0.03/0.45 % SZS status Theorem
% 0.03/0.45
% 0.03/0.46 % SZS output start Proof
% 0.03/0.46 Axiom 1 (t41_enumset1): unordered_pair(X, Y) = set_union2(singleton(X), singleton(Y)).
% 0.17/0.46 Axiom 2 (t120_zfmisc_1_1): cartesian_product2(X, set_union2(Y, Z)) = set_union2(cartesian_product2(X, Y), cartesian_product2(X, Z)).
% 0.17/0.46 Axiom 3 (t120_zfmisc_1): cartesian_product2(set_union2(X, Y), Z) = set_union2(cartesian_product2(X, Z), cartesian_product2(Y, Z)).
% 0.17/0.46
% 0.17/0.46 Goal 1 (t132_zfmisc_1): tuple(cartesian_product2(unordered_pair(a2, b2), c2), cartesian_product2(c, unordered_pair(a, b))) = tuple(set_union2(cartesian_product2(singleton(a2), c2), cartesian_product2(singleton(b2), c2)), set_union2(cartesian_product2(c, singleton(a)), cartesian_product2(c, singleton(b)))).
% 0.17/0.46 Proof:
% 0.17/0.46 tuple(cartesian_product2(unordered_pair(a2, b2), c2), cartesian_product2(c, unordered_pair(a, b)))
% 0.17/0.46 = { by axiom 1 (t41_enumset1) }
% 0.17/0.46 tuple(cartesian_product2(set_union2(singleton(a2), singleton(b2)), c2), cartesian_product2(c, unordered_pair(a, b)))
% 0.17/0.46 = { by axiom 3 (t120_zfmisc_1) }
% 0.17/0.46 tuple(set_union2(cartesian_product2(singleton(a2), c2), cartesian_product2(singleton(b2), c2)), cartesian_product2(c, unordered_pair(a, b)))
% 0.17/0.46 = { by axiom 1 (t41_enumset1) }
% 0.17/0.46 tuple(set_union2(cartesian_product2(singleton(a2), c2), cartesian_product2(singleton(b2), c2)), cartesian_product2(c, set_union2(singleton(a), singleton(b))))
% 0.17/0.46 = { by axiom 2 (t120_zfmisc_1_1) }
% 0.17/0.46 tuple(set_union2(cartesian_product2(singleton(a2), c2), cartesian_product2(singleton(b2), c2)), set_union2(cartesian_product2(c, singleton(a)), cartesian_product2(c, singleton(b))))
% 0.17/0.46 % SZS output end Proof
% 0.17/0.46
% 0.17/0.46 RESULT: Theorem (the conjecture is true).
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