%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:45:23 PM UTC 2026
% Result : Theorem 0.08s 0.46s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n001.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 28 03:57:47 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.46 Command-line arguments: --no-flatten-goal
% 0.08/0.46
% 0.08/0.46 % SZS status Theorem
% 0.08/0.46
% 0.08/0.46 % SZS output start Proof
% 0.08/0.46 Axiom 1 (t119_zfmisc_1): subset(c, d) = true.
% 0.08/0.46 Axiom 2 (t119_zfmisc_1_1): subset(a, b) = true.
% 0.08/0.46 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.46 Axiom 4 (t118_zfmisc_1): ifeq(subset(X, Y), true, subset(cartesian_product2(X, Z), cartesian_product2(Y, Z)), true) = true.
% 0.08/0.46 Axiom 5 (t118_zfmisc_1_1): ifeq(subset(X, Y), true, subset(cartesian_product2(Z, X), cartesian_product2(Z, Y)), true) = true.
% 0.08/0.46 Axiom 6 (t1_xboole_1): ifeq(subset(X, Y), true, ifeq(subset(Z, X), true, subset(Z, Y), true), true) = true.
% 0.08/0.46
% 0.08/0.46 Goal 1 (t119_zfmisc_1_2): subset(cartesian_product2(a, c), cartesian_product2(b, d)) = true.
% 0.08/0.46 Proof:
% 0.08/0.46 subset(cartesian_product2(a, c), cartesian_product2(b, d))
% 0.08/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.08/0.46 ifeq(true, true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true)
% 0.08/0.46 = { by axiom 5 (t118_zfmisc_1_1) R->L }
% 0.08/0.46 ifeq(ifeq(subset(c, d), true, subset(cartesian_product2(a, c), cartesian_product2(a, d)), true), true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true)
% 0.08/0.46 = { by axiom 1 (t119_zfmisc_1) }
% 0.08/0.46 ifeq(ifeq(true, true, subset(cartesian_product2(a, c), cartesian_product2(a, d)), true), true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true)
% 0.08/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.08/0.46 ifeq(subset(cartesian_product2(a, c), cartesian_product2(a, d)), true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true)
% 0.08/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.08/0.46 ifeq(true, true, ifeq(subset(cartesian_product2(a, c), cartesian_product2(a, d)), true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true), true)
% 0.08/0.46 = { by axiom 4 (t118_zfmisc_1) R->L }
% 0.08/0.46 ifeq(ifeq(subset(a, b), true, subset(cartesian_product2(a, d), cartesian_product2(b, d)), true), true, ifeq(subset(cartesian_product2(a, c), cartesian_product2(a, d)), true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true), true)
% 0.08/0.46 = { by axiom 2 (t119_zfmisc_1_1) }
% 0.08/0.46 ifeq(ifeq(true, true, subset(cartesian_product2(a, d), cartesian_product2(b, d)), true), true, ifeq(subset(cartesian_product2(a, c), cartesian_product2(a, d)), true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true), true)
% 0.08/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.08/0.46 ifeq(subset(cartesian_product2(a, d), cartesian_product2(b, d)), true, ifeq(subset(cartesian_product2(a, c), cartesian_product2(a, d)), true, subset(cartesian_product2(a, c), cartesian_product2(b, d)), true), true)
% 0.08/0.46 = { by axiom 6 (t1_xboole_1) }
% 0.08/0.46 true
% 0.08/0.46 % SZS output end Proof
% 0.08/0.46
% 0.08/0.46 RESULT: Theorem (the conjecture is true).
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