%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET574+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:38:48 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET574+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.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 02:12:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 Command-line arguments: --flatten --complete-subsets
% 0.10/0.44
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44
% 0.10/0.44 % SZS output start Proof
% 0.10/0.44 Axiom 1 (prove_th13): member(b, c) = true.
% 0.10/0.44 Axiom 2 (prove_th13_1): member(b, d) = true.
% 0.10/0.44 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.44 Axiom 4 (symmetry_of_intersect): ifeq(intersect(X, Y), true, intersect(Y, X), true) = true.
% 0.10/0.44 Axiom 5 (intersect_defn_2): ifeq(member(X, Y), true, ifeq(member(X, Z), true, intersect(Z, Y), true), true) = true.
% 0.10/0.44
% 0.10/0.44 Goal 1 (prove_th13_2): intersect(c, d) = true.
% 0.10/0.44 Proof:
% 0.10/0.44 intersect(c, d)
% 0.10/0.44 = { by axiom 3 (ifeq_axiom) R->L }
% 0.10/0.44 ifeq(member(b, c), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) }
% 0.10/0.44 ifeq(true, member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 5 (intersect_defn_2) R->L }
% 0.10/0.44 ifeq(ifeq(member(b, c), true, ifeq(member(b, d), true, intersect(d, c), true), true), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) R->L }
% 0.10/0.44 ifeq(ifeq(member(b, c), true, ifeq(member(b, d), true, intersect(d, c), true), member(b, c)), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) R->L }
% 0.10/0.44 ifeq(ifeq(member(b, c), true, ifeq(member(b, d), true, intersect(d, c), member(b, c)), member(b, c)), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) R->L }
% 0.10/0.44 ifeq(ifeq(member(b, c), true, ifeq(member(b, d), member(b, c), intersect(d, c), member(b, c)), member(b, c)), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) R->L }
% 0.10/0.44 ifeq(ifeq(member(b, c), member(b, c), ifeq(member(b, d), member(b, c), intersect(d, c), member(b, c)), member(b, c)), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 3 (ifeq_axiom) }
% 0.10/0.44 ifeq(ifeq(member(b, d), member(b, c), intersect(d, c), member(b, c)), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 2 (prove_th13_1) }
% 0.10/0.44 ifeq(ifeq(true, member(b, c), intersect(d, c), member(b, c)), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) R->L }
% 0.10/0.44 ifeq(ifeq(member(b, c), member(b, c), intersect(d, c), member(b, c)), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 3 (ifeq_axiom) }
% 0.10/0.44 ifeq(intersect(d, c), member(b, c), intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) }
% 0.10/0.44 ifeq(intersect(d, c), true, intersect(c, d), member(b, c))
% 0.10/0.44 = { by axiom 1 (prove_th13) }
% 0.10/0.44 ifeq(intersect(d, c), true, intersect(c, d), true)
% 0.10/0.44 = { by axiom 4 (symmetry_of_intersect) }
% 0.10/0.44 true
% 0.10/0.44 % SZS output end Proof
% 0.10/0.44
% 0.10/0.44 RESULT: Theorem (the conjecture is true).
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