%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:39:18 PM UTC 2026
% Result : Theorem 0.06s 0.34s
% Output : Proof 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 28 03:06:19 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.34 Command-line arguments: --no-flatten-goal
% 0.06/0.34
% 0.06/0.34 % SZS status Theorem
% 0.06/0.34
% 0.06/0.34 % SZS output start Proof
% 0.06/0.34 Axiom 1 (t69_enumset1): unordered_pair(X, X) = singleton(X).
% 0.06/0.34 Axiom 2 (commutativity_k2_tarski): unordered_pair(X, Y) = unordered_pair(Y, X).
% 0.06/0.34 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.06/0.35 Axiom 4 (t27_zfmisc_1): subset(unordered_pair(a, b), singleton(c)) = true.
% 0.06/0.35 Axiom 5 (t26_zfmisc_1): ifeq(subset(unordered_pair(X, Y), singleton(Z)), true, X, Z) = Z.
% 0.06/0.35
% 0.06/0.35 Lemma 6: c = a.
% 0.06/0.35 Proof:
% 0.06/0.35 c
% 0.06/0.35 = { by axiom 5 (t26_zfmisc_1) R->L }
% 0.06/0.35 ifeq(subset(unordered_pair(a, b), singleton(c)), true, a, c)
% 0.06/0.35 = { by axiom 4 (t27_zfmisc_1) }
% 0.06/0.35 ifeq(true, true, a, c)
% 0.06/0.35 = { by axiom 3 (ifeq_axiom) }
% 0.06/0.35 a
% 0.06/0.35
% 0.06/0.35 Goal 1 (t27_zfmisc_1_1): unordered_pair(a, b) = singleton(c).
% 0.06/0.35 Proof:
% 0.06/0.35 unordered_pair(a, b)
% 0.06/0.35 = { by axiom 3 (ifeq_axiom) R->L }
% 0.06/0.35 unordered_pair(a, ifeq(true, true, b, c))
% 0.06/0.35 = { by axiom 4 (t27_zfmisc_1) R->L }
% 0.06/0.35 unordered_pair(a, ifeq(subset(unordered_pair(a, b), singleton(c)), true, b, c))
% 0.06/0.35 = { by axiom 2 (commutativity_k2_tarski) R->L }
% 0.06/0.35 unordered_pair(a, ifeq(subset(unordered_pair(b, a), singleton(c)), true, b, c))
% 0.06/0.35 = { by axiom 5 (t26_zfmisc_1) }
% 0.06/0.35 unordered_pair(a, c)
% 0.06/0.35 = { by lemma 6 }
% 0.06/0.35 unordered_pair(a, a)
% 0.06/0.35 = { by axiom 1 (t69_enumset1) }
% 0.06/0.35 singleton(a)
% 0.06/0.35 = { by lemma 6 R->L }
% 0.06/0.35 singleton(c)
% 0.06/0.35 % SZS output end Proof
% 0.06/0.35
% 0.06/0.35 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------