TSTP Solution File: SEU146+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU146+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Tue Sep 20 07:27:45 EDT 2022
% Result : Theorem 0.64s 0.67s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU146+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 09:40:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.64/0.67 % SZS status Theorem
% 0.64/0.67 % SZS output start Proof
% 0.64/0.67 tff(subset_type, type, (
% 0.64/0.67 subset: ( $i * $i ) > $o)).
% 0.64/0.67 tff(set_difference_type, type, (
% 0.64/0.67 set_difference: ( $i * $i ) > $i)).
% 0.64/0.67 tff(singleton_type, type, (
% 0.64/0.67 singleton: $i > $i)).
% 0.64/0.67 tff(tptp_fun_B_0_type, type, (
% 0.64/0.67 tptp_fun_B_0: $i)).
% 0.64/0.67 tff(tptp_fun_A_1_type, type, (
% 0.64/0.67 tptp_fun_A_1: $i)).
% 0.64/0.67 tff(empty_set_type, type, (
% 0.64/0.67 empty_set: $i)).
% 0.64/0.67 tff(in_type, type, (
% 0.64/0.67 in: ( $i * $i ) > $o)).
% 0.64/0.67 tff(1,plain,
% 0.64/0.67 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 0.64/0.67 inference(bind,[status(th)],[])).
% 0.64/0.67 tff(2,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.64/0.67 inference(quant_intro,[status(thm)],[1])).
% 0.64/0.67 tff(3,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.64/0.67 inference(rewrite,[status(thm)],[])).
% 0.64/0.67 tff(4,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t37_xboole_1')).
% 0.64/0.67 tff(5,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.64/0.67 tff(6,plain,(
% 0.64/0.67 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.64/0.67 inference(skolemize,[status(sab)],[5])).
% 0.64/0.67 tff(7,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.64/0.67 tff(8,plain,
% 0.64/0.67 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(singleton(B!0), singleton(B!0)) = empty_set) <=> subset(singleton(B!0), singleton(B!0)))),
% 0.64/0.67 inference(quant_inst,[status(thm)],[])).
% 0.64/0.67 tff(9,plain,
% 0.64/0.67 ((set_difference(singleton(B!0), singleton(B!0)) = empty_set) <=> subset(singleton(B!0), singleton(B!0))),
% 0.64/0.67 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.64/0.67 tff(10,plain,
% 0.64/0.67 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.64/0.67 inference(bind,[status(th)],[])).
% 0.64/0.67 tff(11,plain,
% 0.64/0.67 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.64/0.67 inference(quant_intro,[status(thm)],[10])).
% 0.64/0.67 tff(12,plain,
% 0.64/0.67 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.64/0.67 inference(rewrite,[status(thm)],[])).
% 0.64/0.67 tff(13,plain,
% 0.64/0.67 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.64/0.67 inference(elim_unused_vars,[status(thm)],[])).
% 0.64/0.67 tff(14,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.64/0.67 tff(15,plain,
% 0.64/0.67 (![A: $i] : subset(A, A)),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.64/0.67 tff(16,plain,
% 0.64/0.67 (![A: $i] : subset(A, A)),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.64/0.67 tff(17,plain,(
% 0.64/0.67 ![A: $i] : subset(A, A)),
% 0.64/0.67 inference(skolemize,[status(sab)],[16])).
% 0.64/0.67 tff(18,plain,
% 0.64/0.67 (![A: $i] : subset(A, A)),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.64/0.67 tff(19,plain,
% 0.64/0.67 ((~![A: $i] : subset(A, A)) | subset(singleton(B!0), singleton(B!0))),
% 0.64/0.67 inference(quant_inst,[status(thm)],[])).
% 0.64/0.67 tff(20,plain,
% 0.64/0.67 (subset(singleton(B!0), singleton(B!0))),
% 0.64/0.67 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.64/0.67 tff(21,plain,
% 0.64/0.67 ((~((set_difference(singleton(B!0), singleton(B!0)) = empty_set) <=> subset(singleton(B!0), singleton(B!0)))) | (set_difference(singleton(B!0), singleton(B!0)) = empty_set) | (~subset(singleton(B!0), singleton(B!0)))),
% 0.64/0.67 inference(tautology,[status(thm)],[])).
% 0.64/0.67 tff(22,plain,
% 0.64/0.67 ((~((set_difference(singleton(B!0), singleton(B!0)) = empty_set) <=> subset(singleton(B!0), singleton(B!0)))) | (set_difference(singleton(B!0), singleton(B!0)) = empty_set)),
% 0.64/0.67 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.64/0.67 tff(23,plain,
% 0.64/0.67 (set_difference(singleton(B!0), singleton(B!0)) = empty_set),
% 0.64/0.67 inference(unit_resolution,[status(thm)],[22, 9])).
% 0.64/0.67 tff(24,plain,
% 0.64/0.67 (subset(A!1, set_difference(singleton(B!0), singleton(B!0))) <=> subset(A!1, empty_set)),
% 0.64/0.67 inference(monotonicity,[status(thm)],[23])).
% 0.64/0.67 tff(25,plain,
% 0.64/0.67 (subset(A!1, empty_set) <=> subset(A!1, set_difference(singleton(B!0), singleton(B!0)))),
% 0.64/0.67 inference(symmetry,[status(thm)],[24])).
% 0.64/0.67 tff(26,plain,
% 0.64/0.67 ((~subset(A!1, empty_set)) <=> (~subset(A!1, set_difference(singleton(B!0), singleton(B!0))))),
% 0.64/0.67 inference(monotonicity,[status(thm)],[25])).
% 0.64/0.67 tff(27,plain,
% 0.64/0.67 (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.64/0.67 inference(bind,[status(th)],[])).
% 0.64/0.67 tff(28,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.64/0.67 inference(quant_intro,[status(thm)],[27])).
% 0.64/0.67 tff(29,plain,
% 0.64/0.67 (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.64/0.67 inference(bind,[status(th)],[])).
% 0.64/0.67 tff(30,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.64/0.67 inference(quant_intro,[status(thm)],[29])).
% 0.64/0.67 tff(31,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.64/0.67 inference(rewrite,[status(thm)],[])).
% 0.64/0.67 tff(32,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.64/0.67 tff(33,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.64/0.67 tff(34,plain,(
% 0.64/0.67 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.64/0.67 inference(skolemize,[status(sab)],[33])).
% 0.64/0.67 tff(35,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.64/0.67 tff(36,plain,
% 0.64/0.67 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.64/0.67 tff(37,plain,
% 0.64/0.67 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((A!1 = empty_set) <=> (~((~subset(A!1, empty_set)) | (~subset(empty_set, A!1)))))),
% 0.64/0.67 inference(quant_inst,[status(thm)],[])).
% 0.64/0.67 tff(38,plain,
% 0.64/0.67 ((A!1 = empty_set) <=> (~((~subset(A!1, empty_set)) | (~subset(empty_set, A!1))))),
% 0.64/0.67 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.64/0.67 tff(39,assumption,(~subset(A!1, singleton(B!0))), introduced(assumption)).
% 0.64/0.67 tff(40,plain,
% 0.64/0.67 ((~(subset(A!1, singleton(B!0)) <=> ((A!1 = empty_set) | (A!1 = singleton(B!0))))) <=> ((~subset(A!1, singleton(B!0))) <=> ((A!1 = empty_set) | (A!1 = singleton(B!0))))),
% 0.64/0.67 inference(rewrite,[status(thm)],[])).
% 0.64/0.67 tff(41,plain,
% 0.64/0.67 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) <=> (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))))),
% 0.64/0.67 inference(rewrite,[status(thm)],[])).
% 0.64/0.67 tff(42,axiom,(~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l4_zfmisc_1')).
% 0.64/0.67 tff(43,plain,
% 0.64/0.67 (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.64/0.67 tff(44,plain,
% 0.64/0.67 (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.64/0.67 tff(45,plain,
% 0.64/0.67 (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.64/0.67 tff(46,plain,
% 0.64/0.67 (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.64/0.67 tff(47,plain,
% 0.64/0.67 (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.64/0.67 tff(48,plain,
% 0.64/0.67 (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.64/0.67 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.64/0.68 tff(49,plain,
% 0.64/0.68 (~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.64/0.68 tff(50,plain,(
% 0.64/0.68 ~(subset(A!1, singleton(B!0)) <=> ((A!1 = empty_set) | (A!1 = singleton(B!0))))),
% 0.64/0.68 inference(skolemize,[status(sab)],[49])).
% 0.64/0.68 tff(51,plain,
% 0.64/0.68 ((~subset(A!1, singleton(B!0))) <=> ((A!1 = empty_set) | (A!1 = singleton(B!0)))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.64/0.68 tff(52,plain,
% 0.64/0.68 (subset(A!1, singleton(B!0)) | ((A!1 = empty_set) | (A!1 = singleton(B!0))) | (~((~subset(A!1, singleton(B!0))) <=> ((A!1 = empty_set) | (A!1 = singleton(B!0)))))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(53,plain,
% 0.64/0.68 (subset(A!1, singleton(B!0)) | ((A!1 = empty_set) | (A!1 = singleton(B!0)))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.64/0.68 tff(54,plain,
% 0.64/0.68 ((A!1 = empty_set) | (A!1 = singleton(B!0))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.64/0.68 tff(55,plain,
% 0.64/0.68 (((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1))) | subset(A!1, singleton(B!0))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(56,plain,
% 0.64/0.68 ((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[55, 39])).
% 0.64/0.68 tff(57,plain,
% 0.64/0.68 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((A!1 = singleton(B!0)) <=> (~((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1)))))),
% 0.64/0.68 inference(quant_inst,[status(thm)],[])).
% 0.64/0.68 tff(58,plain,
% 0.64/0.68 ((A!1 = singleton(B!0)) <=> (~((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1))))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[57, 36])).
% 0.64/0.68 tff(59,plain,
% 0.64/0.68 ((~((A!1 = singleton(B!0)) <=> (~((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1)))))) | (~(A!1 = singleton(B!0))) | (~((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1))))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(60,plain,
% 0.64/0.68 ((~(A!1 = singleton(B!0))) | (~((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1))))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.64/0.68 tff(61,plain,
% 0.64/0.68 (~(A!1 = singleton(B!0))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.64/0.68 tff(62,plain,
% 0.64/0.68 ((~((A!1 = empty_set) | (A!1 = singleton(B!0)))) | (A!1 = empty_set) | (A!1 = singleton(B!0))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(63,plain,
% 0.64/0.68 (A!1 = empty_set),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[62, 61, 54])).
% 0.64/0.68 tff(64,plain,
% 0.64/0.68 (empty_set = A!1),
% 0.64/0.68 inference(symmetry,[status(thm)],[63])).
% 0.64/0.68 tff(65,plain,
% 0.64/0.68 (subset(empty_set, singleton(B!0)) <=> subset(A!1, singleton(B!0))),
% 0.64/0.68 inference(monotonicity,[status(thm)],[64])).
% 0.64/0.68 tff(66,plain,
% 0.64/0.68 (subset(A!1, singleton(B!0)) <=> subset(empty_set, singleton(B!0))),
% 0.64/0.68 inference(symmetry,[status(thm)],[65])).
% 0.64/0.68 tff(67,plain,
% 0.64/0.68 ((~subset(A!1, singleton(B!0))) <=> (~subset(empty_set, singleton(B!0)))),
% 0.64/0.68 inference(monotonicity,[status(thm)],[66])).
% 0.64/0.68 tff(68,plain,
% 0.64/0.68 (~subset(empty_set, singleton(B!0))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[39, 67])).
% 0.64/0.68 tff(69,plain,
% 0.64/0.68 (^[A: $i] : refl(subset(empty_set, A) <=> subset(empty_set, A))),
% 0.64/0.68 inference(bind,[status(th)],[])).
% 0.64/0.68 tff(70,plain,
% 0.64/0.68 (![A: $i] : subset(empty_set, A) <=> ![A: $i] : subset(empty_set, A)),
% 0.64/0.68 inference(quant_intro,[status(thm)],[69])).
% 0.64/0.68 tff(71,plain,
% 0.64/0.68 (![A: $i] : subset(empty_set, A) <=> ![A: $i] : subset(empty_set, A)),
% 0.64/0.68 inference(rewrite,[status(thm)],[])).
% 0.64/0.68 tff(72,axiom,(![A: $i] : subset(empty_set, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_xboole_1')).
% 0.64/0.68 tff(73,plain,
% 0.64/0.68 (![A: $i] : subset(empty_set, A)),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.64/0.68 tff(74,plain,(
% 0.64/0.68 ![A: $i] : subset(empty_set, A)),
% 0.64/0.68 inference(skolemize,[status(sab)],[73])).
% 0.64/0.68 tff(75,plain,
% 0.64/0.68 (![A: $i] : subset(empty_set, A)),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.64/0.68 tff(76,plain,
% 0.64/0.68 ((~![A: $i] : subset(empty_set, A)) | subset(empty_set, singleton(B!0))),
% 0.64/0.68 inference(quant_inst,[status(thm)],[])).
% 0.64/0.68 tff(77,plain,
% 0.64/0.68 (subset(empty_set, singleton(B!0))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.64/0.68 tff(78,plain,
% 0.64/0.68 ($false),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[77, 68])).
% 0.64/0.68 tff(79,plain,(subset(A!1, singleton(B!0))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.68 tff(80,plain,
% 0.64/0.68 ((~subset(A!1, singleton(B!0))) | (~((A!1 = empty_set) | (A!1 = singleton(B!0)))) | (~((~subset(A!1, singleton(B!0))) <=> ((A!1 = empty_set) | (A!1 = singleton(B!0)))))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(81,plain,
% 0.64/0.68 ((~subset(A!1, singleton(B!0))) | (~((A!1 = empty_set) | (A!1 = singleton(B!0))))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[80, 51])).
% 0.64/0.68 tff(82,plain,
% 0.64/0.68 (~((A!1 = empty_set) | (A!1 = singleton(B!0)))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[81, 79])).
% 0.64/0.68 tff(83,plain,
% 0.64/0.68 (((A!1 = empty_set) | (A!1 = singleton(B!0))) | (~(A!1 = empty_set))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(84,plain,
% 0.64/0.68 (~(A!1 = empty_set)),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.64/0.68 tff(85,plain,
% 0.64/0.68 ((~((A!1 = empty_set) <=> (~((~subset(A!1, empty_set)) | (~subset(empty_set, A!1)))))) | (A!1 = empty_set) | ((~subset(A!1, empty_set)) | (~subset(empty_set, A!1)))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(86,plain,
% 0.64/0.68 ((~((A!1 = empty_set) <=> (~((~subset(A!1, empty_set)) | (~subset(empty_set, A!1)))))) | ((~subset(A!1, empty_set)) | (~subset(empty_set, A!1)))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.64/0.68 tff(87,plain,
% 0.64/0.68 ((~subset(A!1, empty_set)) | (~subset(empty_set, A!1))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[86, 38])).
% 0.64/0.68 tff(88,plain,
% 0.64/0.68 ((~![A: $i] : subset(empty_set, A)) | subset(empty_set, A!1)),
% 0.64/0.68 inference(quant_inst,[status(thm)],[])).
% 0.64/0.68 tff(89,plain,
% 0.64/0.68 (subset(empty_set, A!1)),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[88, 75])).
% 0.64/0.68 tff(90,plain,
% 0.64/0.68 ((~((~subset(A!1, empty_set)) | (~subset(empty_set, A!1)))) | (~subset(A!1, empty_set)) | (~subset(empty_set, A!1))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(91,plain,
% 0.64/0.68 ((~((~subset(A!1, empty_set)) | (~subset(empty_set, A!1)))) | (~subset(A!1, empty_set))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.64/0.68 tff(92,plain,
% 0.64/0.68 (~subset(A!1, empty_set)),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[91, 87])).
% 0.64/0.68 tff(93,plain,
% 0.64/0.68 (~subset(A!1, set_difference(singleton(B!0), singleton(B!0)))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[92, 26])).
% 0.64/0.68 tff(94,plain,
% 0.64/0.68 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 0.64/0.68 inference(bind,[status(th)],[])).
% 0.64/0.68 tff(95,plain,
% 0.64/0.68 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.64/0.68 inference(quant_intro,[status(thm)],[94])).
% 0.64/0.68 tff(96,plain,
% 0.64/0.68 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.64/0.68 inference(rewrite,[status(thm)],[])).
% 0.64/0.68 tff(97,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.64/0.68 tff(98,plain,
% 0.64/0.68 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.64/0.68 tff(99,plain,(
% 0.64/0.68 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.64/0.68 inference(skolemize,[status(sab)],[98])).
% 0.64/0.68 tff(100,plain,
% 0.64/0.68 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.64/0.68 tff(101,plain,
% 0.64/0.68 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(B!0), A!1) <=> in(B!0, A!1))),
% 0.64/0.68 inference(quant_inst,[status(thm)],[])).
% 0.64/0.68 tff(102,plain,
% 0.64/0.68 (subset(singleton(B!0), A!1) <=> in(B!0, A!1)),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.64/0.68 tff(103,plain,
% 0.64/0.68 (((A!1 = empty_set) | (A!1 = singleton(B!0))) | (~(A!1 = singleton(B!0)))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(104,plain,
% 0.64/0.68 (~(A!1 = singleton(B!0))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[103, 82])).
% 0.64/0.68 tff(105,plain,
% 0.64/0.68 ((~((A!1 = singleton(B!0)) <=> (~((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1)))))) | (A!1 = singleton(B!0)) | ((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1)))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(106,plain,
% 0.64/0.68 ((A!1 = singleton(B!0)) | ((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1)))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[105, 58])).
% 0.64/0.68 tff(107,plain,
% 0.64/0.68 ((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[106, 104])).
% 0.64/0.68 tff(108,plain,
% 0.64/0.68 ((~((~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1)))) | (~subset(A!1, singleton(B!0))) | (~subset(singleton(B!0), A!1))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(109,plain,
% 0.64/0.68 (~subset(singleton(B!0), A!1)),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[108, 107, 79])).
% 0.64/0.68 tff(110,plain,
% 0.64/0.68 ((~(subset(singleton(B!0), A!1) <=> in(B!0, A!1))) | subset(singleton(B!0), A!1) | (~in(B!0, A!1))),
% 0.64/0.68 inference(tautology,[status(thm)],[])).
% 0.64/0.68 tff(111,plain,
% 0.64/0.68 ((~(subset(singleton(B!0), A!1) <=> in(B!0, A!1))) | (~in(B!0, A!1))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.64/0.68 tff(112,plain,
% 0.64/0.68 (~in(B!0, A!1)),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[111, 102])).
% 0.64/0.68 tff(113,plain,
% 0.64/0.68 (^[A: $i, B: $i, C: $i] : refl((subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B))) <=> (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B))))),
% 0.64/0.68 inference(bind,[status(th)],[])).
% 0.64/0.68 tff(114,plain,
% 0.64/0.68 (![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))),
% 0.64/0.68 inference(quant_intro,[status(thm)],[113])).
% 0.64/0.68 tff(115,plain,
% 0.64/0.68 (![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))),
% 0.64/0.68 inference(rewrite,[status(thm)],[])).
% 0.64/0.68 tff(116,plain,
% 0.64/0.68 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, B) => (in(C, A) | subset(A, set_difference(B, singleton(C))))) <=> (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B))))),
% 0.64/0.68 inference(bind,[status(th)],[])).
% 0.64/0.68 tff(117,plain,
% 0.64/0.68 (![A: $i, B: $i, C: $i] : (subset(A, B) => (in(C, A) | subset(A, set_difference(B, singleton(C))))) <=> ![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))),
% 0.64/0.68 inference(quant_intro,[status(thm)],[116])).
% 0.64/0.68 tff(118,axiom,(![A: $i, B: $i, C: $i] : (subset(A, B) => (in(C, A) | subset(A, set_difference(B, singleton(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l3_zfmisc_1')).
% 0.64/0.68 tff(119,plain,
% 0.64/0.68 (![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.64/0.68 tff(120,plain,
% 0.64/0.68 (![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.64/0.68 tff(121,plain,(
% 0.64/0.68 ![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))),
% 0.64/0.68 inference(skolemize,[status(sab)],[120])).
% 0.64/0.68 tff(122,plain,
% 0.64/0.68 (![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.64/0.68 tff(123,plain,
% 0.64/0.68 (((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | ((~subset(A!1, singleton(B!0))) | in(B!0, A!1) | subset(A!1, set_difference(singleton(B!0), singleton(B!0))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | (~subset(A!1, singleton(B!0))) | in(B!0, A!1) | subset(A!1, set_difference(singleton(B!0), singleton(B!0))))),
% 0.64/0.68 inference(rewrite,[status(thm)],[])).
% 0.64/0.68 tff(124,plain,
% 0.64/0.68 ((subset(A!1, set_difference(singleton(B!0), singleton(B!0))) | in(B!0, A!1) | (~subset(A!1, singleton(B!0)))) <=> ((~subset(A!1, singleton(B!0))) | in(B!0, A!1) | subset(A!1, set_difference(singleton(B!0), singleton(B!0))))),
% 0.64/0.68 inference(rewrite,[status(thm)],[])).
% 0.64/0.68 tff(125,plain,
% 0.64/0.68 (((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | (subset(A!1, set_difference(singleton(B!0), singleton(B!0))) | in(B!0, A!1) | (~subset(A!1, singleton(B!0))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | ((~subset(A!1, singleton(B!0))) | in(B!0, A!1) | subset(A!1, set_difference(singleton(B!0), singleton(B!0)))))),
% 0.64/0.68 inference(monotonicity,[status(thm)],[124])).
% 0.64/0.68 tff(126,plain,
% 0.64/0.68 (((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | (subset(A!1, set_difference(singleton(B!0), singleton(B!0))) | in(B!0, A!1) | (~subset(A!1, singleton(B!0))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | (~subset(A!1, singleton(B!0))) | in(B!0, A!1) | subset(A!1, set_difference(singleton(B!0), singleton(B!0))))),
% 0.64/0.68 inference(transitivity,[status(thm)],[125, 123])).
% 0.64/0.68 tff(127,plain,
% 0.64/0.68 ((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | (subset(A!1, set_difference(singleton(B!0), singleton(B!0))) | in(B!0, A!1) | (~subset(A!1, singleton(B!0))))),
% 0.64/0.68 inference(quant_inst,[status(thm)],[])).
% 0.64/0.68 tff(128,plain,
% 0.64/0.68 ((~![A: $i, B: $i, C: $i] : (subset(A, set_difference(B, singleton(C))) | in(C, A) | (~subset(A, B)))) | (~subset(A!1, singleton(B!0))) | in(B!0, A!1) | subset(A!1, set_difference(singleton(B!0), singleton(B!0)))),
% 0.64/0.68 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.64/0.68 tff(129,plain,
% 0.64/0.68 (subset(A!1, set_difference(singleton(B!0), singleton(B!0)))),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[128, 122, 79, 112])).
% 0.64/0.68 tff(130,plain,
% 0.64/0.68 ($false),
% 0.64/0.68 inference(unit_resolution,[status(thm)],[129, 93])).
% 0.64/0.68 % SZS output end Proof
%------------------------------------------------------------------------------