%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:39:19 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET907+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 : n019.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:09:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 Command-line arguments: --no-flatten-goal
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem
% 0.18/0.47
% 0.18/0.47 % SZS output start Proof
% 0.18/0.47 Axiom 1 (commutativity_k2_tarski): unordered_pair(X, Y) = unordered_pair(Y, X).
% 0.18/0.47 Axiom 2 (t48_zfmisc_1): in(c, b) = true.
% 0.18/0.47 Axiom 3 (t48_zfmisc_1_1): in(a, b) = true.
% 0.18/0.47 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.18/0.47 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.18/0.47 Axiom 6 (t12_xboole_1): ifeq2(subset(X, Y), true, set_union2(X, Y), Y) = Y.
% 0.18/0.47 Axiom 7 (t38_zfmisc_1): ifeq(in(X, Y), true, ifeq(in(Z, Y), true, subset(unordered_pair(Z, X), Y), true), true) = true.
% 0.18/0.47
% 0.18/0.47 Goal 1 (t48_zfmisc_1_2): set_union2(unordered_pair(a, c), b) = b.
% 0.18/0.47 Proof:
% 0.18/0.47 set_union2(unordered_pair(a, c), b)
% 0.18/0.47 = { by axiom 1 (commutativity_k2_tarski) }
% 0.18/0.47 set_union2(unordered_pair(c, a), b)
% 0.18/0.47 = { by axiom 4 (ifeq_axiom) R->L }
% 0.18/0.47 ifeq2(true, true, set_union2(unordered_pair(c, a), b), b)
% 0.18/0.47 = { by axiom 7 (t38_zfmisc_1) R->L }
% 0.18/0.47 ifeq2(ifeq(in(c, b), true, ifeq(in(a, b), true, subset(unordered_pair(a, c), b), true), true), true, set_union2(unordered_pair(c, a), b), b)
% 0.18/0.47 = { by axiom 2 (t48_zfmisc_1) }
% 0.18/0.47 ifeq2(ifeq(true, true, ifeq(in(a, b), true, subset(unordered_pair(a, c), b), true), true), true, set_union2(unordered_pair(c, a), b), b)
% 0.18/0.47 = { by axiom 5 (ifeq_axiom) }
% 0.18/0.47 ifeq2(ifeq(in(a, b), true, subset(unordered_pair(a, c), b), true), true, set_union2(unordered_pair(c, a), b), b)
% 0.18/0.47 = { by axiom 3 (t48_zfmisc_1_1) }
% 0.18/0.47 ifeq2(ifeq(true, true, subset(unordered_pair(a, c), b), true), true, set_union2(unordered_pair(c, a), b), b)
% 0.18/0.47 = { by axiom 5 (ifeq_axiom) }
% 0.18/0.47 ifeq2(subset(unordered_pair(a, c), b), true, set_union2(unordered_pair(c, a), b), b)
% 0.18/0.47 = { by axiom 1 (commutativity_k2_tarski) }
% 0.18/0.47 ifeq2(subset(unordered_pair(c, a), b), true, set_union2(unordered_pair(c, a), b), b)
% 0.18/0.47 = { by axiom 6 (t12_xboole_1) }
% 0.18/0.47 b
% 0.18/0.47 % SZS output end Proof
% 0.18/0.47
% 0.18/0.47 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------