%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU153+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 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU153+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:08:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(empty_set_type, type, (
% 0.12/0.38 empty_set: $i)).
% 0.12/0.38 tff(singleton_type, type, (
% 0.12/0.38 singleton: $i > $i)).
% 0.12/0.38 tff(tptp_fun_A_9_type, type, (
% 0.12/0.38 tptp_fun_A_9: $i)).
% 0.12/0.38 tff(set_intersection2_type, type, (
% 0.12/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_8_type, type, (
% 0.12/0.38 tptp_fun_B_8: $i)).
% 0.12/0.38 tff(disjoint_type, type, (
% 0.12/0.38 disjoint: ( $i * $i ) > $o)).
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(singleton(A!9), B!8) <=> (set_intersection2(singleton(A!9), B!8) = empty_set))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (disjoint(singleton(A!9), B!8) <=> (set_intersection2(singleton(A!9), B!8) = empty_set)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))) <=> (~![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(11,axiom,(~![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l25_zfmisc_1')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.38 tff(16,plain,(
% 0.12/0.38 disjoint(singleton(A!9), B!8) & in(A!9, B!8)),
% 0.12/0.38 inference(skolemize,[status(sab)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (disjoint(singleton(A!9), B!8)),
% 0.12/0.38 inference(and_elim,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~(disjoint(singleton(A!9), B!8) <=> (set_intersection2(singleton(A!9), B!8) = empty_set))) | (~disjoint(singleton(A!9), B!8)) | (set_intersection2(singleton(A!9), B!8) = empty_set)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((~(disjoint(singleton(A!9), B!8) <=> (set_intersection2(singleton(A!9), B!8) = empty_set))) | (set_intersection2(singleton(A!9), B!8) = empty_set)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (set_intersection2(singleton(A!9), B!8) = empty_set),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 9])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(24,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.39 tff(26,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.12/0.39 inference(skolemize,[status(sab)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(A!9), B!8) <=> in(A!9, B!8))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (subset(singleton(A!9), B!8) <=> in(A!9, B!8)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (in(A!9, B!8)),
% 0.12/0.39 inference(and_elim,[status(thm)],[16])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~(subset(singleton(A!9), B!8) <=> in(A!9, B!8))) | subset(singleton(A!9), B!8) | (~in(A!9, B!8))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~(subset(singleton(A!9), B!8) <=> in(A!9, B!8))) | subset(singleton(A!9), B!8)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (subset(singleton(A!9), B!8)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 29])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_intersection2(A, B) = A)) <=> ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.39 tff(39,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.39 tff(42,plain,(
% 0.12/0.39 ![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(skolemize,[status(sab)],[41])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(singleton(A!9), B!8)) | (set_intersection2(singleton(A!9), B!8) = singleton(A!9)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(singleton(A!9), B!8)) | (set_intersection2(singleton(A!9), B!8) = singleton(A!9)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | ((~subset(singleton(A!9), B!8)) | (set_intersection2(singleton(A!9), B!8) = singleton(A!9)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) | (~subset(singleton(A!9), B!8)) | (set_intersection2(singleton(A!9), B!8) = singleton(A!9))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (set_intersection2(singleton(A!9), B!8) = singleton(A!9)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (singleton(A!9) = set_intersection2(singleton(A!9), B!8)),
% 0.12/0.39 inference(symmetry,[status(thm)],[47])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (singleton(A!9) = empty_set),
% 0.12/0.39 inference(transitivity,[status(thm)],[48, 20])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (^[A: $i] : refl((~(singleton(A) = empty_set)) <=> (~(singleton(A) = empty_set)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(53,axiom,(![A: $i] : (~(singleton(A) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1_zfmisc_1')).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.39 tff(55,plain,(
% 0.19/0.39 ![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.39 inference(skolemize,[status(sab)],[54])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![A: $i] : (~(singleton(A) = empty_set))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~![A: $i] : (~(singleton(A) = empty_set))) | (~(singleton(A!9) = empty_set))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (~(singleton(A!9) = empty_set)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 49])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------