%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET891+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:37 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET891+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:50:05 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(unordered_pair_type, type, (
% 0.13/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.13/0.38 tff(tptp_fun_B_2_type, type, (
% 0.13/0.38 tptp_fun_B_2: $i)).
% 0.13/0.38 tff(tptp_fun_A_3_type, type, (
% 0.13/0.38 tptp_fun_A_3: $i)).
% 0.13/0.38 tff(union_type, type, (
% 0.13/0.38 union: $i > $i)).
% 0.13/0.38 tff(singleton_type, type, (
% 0.13/0.38 singleton: $i > $i)).
% 0.13/0.38 tff(set_union2_type, type, (
% 0.13/0.38 set_union2: ( $i * $i ) > $i)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 ((set_union2(singleton(A!3), singleton(B!2)) = unordered_pair(A!3, B!2)) <=> (unordered_pair(A!3, B!2) = set_union2(singleton(A!3), singleton(B!2)))),
% 0.13/0.38 inference(commutativity,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((union(unordered_pair(A, B)) = set_union2(A, B)) <=> (union(unordered_pair(A, B)) = set_union2(A, B)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(5,axiom,(![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l52_zfmisc_1')).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.38 tff(7,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B))),
% 0.13/0.38 inference(skolemize,[status(sab)],[6])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 ((~![A: $i, B: $i] : (union(unordered_pair(A, B)) = set_union2(A, B))) | (union(unordered_pair(singleton(A!3), singleton(B!2))) = set_union2(singleton(A!3), singleton(B!2)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (union(unordered_pair(singleton(A!3), singleton(B!2))) = set_union2(singleton(A!3), singleton(B!2))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 ((union(unordered_pair(singleton(A!3), singleton(B!2))) = unordered_pair(A!3, B!2)) <=> (set_union2(singleton(A!3), singleton(B!2)) = unordered_pair(A!3, B!2))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 ((union(unordered_pair(singleton(A!3), singleton(B!2))) = unordered_pair(A!3, B!2)) <=> (unordered_pair(A!3, B!2) = set_union2(singleton(A!3), singleton(B!2)))),
% 0.13/0.38 inference(transitivity,[status(thm)],[11, 1])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 ((unordered_pair(A!3, B!2) = set_union2(singleton(A!3), singleton(B!2))) <=> (union(unordered_pair(singleton(A!3), singleton(B!2))) = unordered_pair(A!3, B!2))),
% 0.13/0.38 inference(symmetry,[status(thm)],[12])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = set_union2(singleton(A), singleton(B))) <=> (unordered_pair(A, B) = set_union2(singleton(A), singleton(B))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(17,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t41_enumset1')).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.38 tff(19,plain,(
% 0.13/0.38 ![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[18])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))) | (unordered_pair(A!3, B!2) = set_union2(singleton(A!3), singleton(B!2)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (unordered_pair(A!3, B!2) = set_union2(singleton(A!3), singleton(B!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (union(unordered_pair(singleton(A!3), singleton(B!2))) = unordered_pair(A!3, B!2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (union(unordered_pair(singleton(A), singleton(B))) = unordered_pair(A, B))) <=> (~![A: $i, B: $i] : (union(unordered_pair(singleton(A), singleton(B))) = unordered_pair(A, B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,axiom,(~![A: $i, B: $i] : (union(unordered_pair(singleton(A), singleton(B))) = unordered_pair(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_zfmisc_1')).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (union(unordered_pair(singleton(A), singleton(B))) = unordered_pair(A, B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (union(unordered_pair(singleton(A), singleton(B))) = unordered_pair(A, B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (union(unordered_pair(singleton(A), singleton(B))) = unordered_pair(A, B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (union(unordered_pair(singleton(A), singleton(B))) = unordered_pair(A, B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.39 tff(30,plain,(
% 0.13/0.39 ~(union(unordered_pair(singleton(A!3), singleton(B!2))) = unordered_pair(A!3, B!2))),
% 0.13/0.39 inference(skolemize,[status(sab)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[30, 23])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------