%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET971+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 0.14s 0.44s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET971+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:16:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.44 Command-line arguments: --no-flatten-goal
% 0.14/0.44
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44
% 0.14/0.44 % SZS output start Proof
% 0.14/0.44 Axiom 1 (t124_zfmisc_1): subset(c, d) = true.
% 0.14/0.44 Axiom 2 (t124_zfmisc_1_1): subset(a, b) = true.
% 0.14/0.44 Axiom 3 (commutativity_k3_xboole_0): set_intersection2(X, Y) = set_intersection2(Y, X).
% 0.14/0.44 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.14/0.44 Axiom 5 (t123_zfmisc_1): cartesian_product2(set_intersection2(X, Y), set_intersection2(Z, W)) = set_intersection2(cartesian_product2(X, Z), cartesian_product2(Y, W)).
% 0.14/0.44 Axiom 6 (t28_xboole_1): ifeq(subset(X, Y), true, set_intersection2(X, Y), X) = X.
% 0.14/0.45
% 0.14/0.45 Goal 1 (t124_zfmisc_1_2): set_intersection2(cartesian_product2(a, d), cartesian_product2(b, c)) = cartesian_product2(a, c).
% 0.14/0.45 Proof:
% 0.14/0.45 set_intersection2(cartesian_product2(a, d), cartesian_product2(b, c))
% 0.14/0.45 = { by axiom 3 (commutativity_k3_xboole_0) }
% 0.14/0.45 set_intersection2(cartesian_product2(b, c), cartesian_product2(a, d))
% 0.14/0.45 = { by axiom 5 (t123_zfmisc_1) R->L }
% 0.14/0.45 cartesian_product2(set_intersection2(b, a), set_intersection2(c, d))
% 0.14/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.14/0.45 cartesian_product2(set_intersection2(b, a), ifeq(true, true, set_intersection2(c, d), c))
% 0.14/0.45 = { by axiom 1 (t124_zfmisc_1) R->L }
% 0.14/0.45 cartesian_product2(set_intersection2(b, a), ifeq(subset(c, d), true, set_intersection2(c, d), c))
% 0.14/0.45 = { by axiom 6 (t28_xboole_1) }
% 0.14/0.45 cartesian_product2(set_intersection2(b, a), c)
% 0.14/0.45 = { by axiom 3 (commutativity_k3_xboole_0) R->L }
% 0.14/0.45 cartesian_product2(set_intersection2(a, b), c)
% 0.14/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.14/0.45 cartesian_product2(ifeq(true, true, set_intersection2(a, b), a), c)
% 0.14/0.45 = { by axiom 2 (t124_zfmisc_1_1) R->L }
% 0.14/0.45 cartesian_product2(ifeq(subset(a, b), true, set_intersection2(a, b), a), c)
% 0.14/0.45 = { by axiom 6 (t28_xboole_1) }
% 0.14/0.45 cartesian_product2(a, c)
% 0.14/0.45 % SZS output end Proof
% 0.14/0.45
% 0.14/0.45 RESULT: Theorem (the conjecture is true).
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