%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU152+2 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:03 AM UTC 2025
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU152+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.32 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Fri Jun 20 06:07:50 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(in_type, type, (
% 0.18/0.38 in: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_B_8_type, type, (
% 0.18/0.38 tptp_fun_B_8: $i)).
% 0.18/0.38 tff(tptp_fun_A_9_type, type, (
% 0.18/0.38 tptp_fun_A_9: $i)).
% 0.18/0.38 tff(subset_type, type, (
% 0.18/0.38 subset: ( $i * $i ) > $o)).
% 0.18/0.38 tff(singleton_type, type, (
% 0.18/0.38 singleton: $i > $i)).
% 0.18/0.38 tff(set_union2_type, type, (
% 0.18/0.38 set_union2: ( $i * $i ) > $i)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(4,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.38 tff(6,plain,(
% 0.18/0.38 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.18/0.38 inference(skolemize,[status(sab)],[5])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(A!9), B!8) <=> in(A!9, B!8))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (subset(singleton(A!9), B!8) <=> in(A!9, B!8)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.38 tff(15,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.38 tff(18,plain,(
% 0.18/0.38 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.38 inference(skolemize,[status(sab)],[17])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : (in(A, B) => (set_union2(singleton(A), B) = B))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(22,axiom,(~![A: $i, B: $i] : (in(A, B) => (set_union2(singleton(A), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l23_zfmisc_1')).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.18/0.38 tff(27,plain,(
% 0.18/0.38 ~((~in(A!9, B!8)) | (set_union2(singleton(A!9), B!8) = B!8))),
% 0.18/0.38 inference(skolemize,[status(sab)],[26])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (~(set_union2(singleton(A!9), B!8) = B!8)),
% 0.18/0.38 inference(or_elim,[status(thm)],[27])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(singleton(A!9), B!8)) | (set_union2(singleton(A!9), B!8) = B!8))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(singleton(A!9), B!8)) | (set_union2(singleton(A!9), B!8) = B!8))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(singleton(A!9), B!8)) | (set_union2(singleton(A!9), B!8) = B!8))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(singleton(A!9), B!8)) | (set_union2(singleton(A!9), B!8) = B!8)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (~subset(singleton(A!9), B!8)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[31, 28, 19])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (in(A!9, B!8)),
% 0.18/0.38 inference(or_elim,[status(thm)],[27])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 ((~(subset(singleton(A!9), B!8) <=> in(A!9, B!8))) | subset(singleton(A!9), B!8) | (~in(A!9, B!8))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 ((~(subset(singleton(A!9), B!8) <=> in(A!9, B!8))) | subset(singleton(A!9), B!8)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[35, 32, 9])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------