TSTP Solution File: SET091+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 05:05:33 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 : Sat Sep 3 02:18:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(member_type, type, (
% 0.19/0.40 member: ( $i * $i ) > $o)).
% 0.19/0.40 tff(universal_class_type, type, (
% 0.19/0.40 universal_class: $i)).
% 0.19/0.40 tff(member_of_type, type, (
% 0.19/0.40 member_of: $i > $i)).
% 0.19/0.40 tff(tptp_fun_X_8_type, type, (
% 0.19/0.40 tptp_fun_X_8: $i)).
% 0.19/0.40 tff(tptp_fun_U_7_type, type, (
% 0.19/0.40 tptp_fun_U_7: $i)).
% 0.19/0.40 tff(singleton_type, type, (
% 0.19/0.40 singleton: $i > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (((![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7)) & (~(member_of(X!8) = U!7))) <=> (![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7) & (~(member_of(X!8) = U!7)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7)) <=> (![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (((![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7)) & (~(member_of(X!8) = U!7))) <=> ((![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7)) & (~(member_of(X!8) = U!7)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (((![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7)) & (~(member_of(X!8) = U!7))) <=> (![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7) & (~(member_of(X!8) = U!7)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[3, 1])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 ((~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))) <=> (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 ((~![X: $i, U: $i] : (((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U)) => (member_of(X) = U))) <=> (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(7,axiom,(~![X: $i, U: $i] : (((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U)) => (member_of(X) = U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','member_when_not_a_singleton')).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (~![X: $i, U: $i] : ((~((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U))) | (member_of(X) = U))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) & (X!8 = U!7) & (~(member_of(X!8) = U!7))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (X!8 = U!7),
% 0.19/0.40 inference(and_elim,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (U!7 = X!8),
% 0.19/0.40 inference(symmetry,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (member_of(U!7) = member_of(X!8)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (member_of(X!8) = member_of(U!7)),
% 0.19/0.41 inference(symmetry,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (member(member_of(X!8), universal_class) <=> member(member_of(U!7), universal_class)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (member(member_of(U!7), universal_class) <=> member(member_of(X!8), universal_class)),
% 0.19/0.41 inference(symmetry,[status(thm)],[20])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ((member_of(U!7) = U!7) <=> (member_of(X!8) = U!7)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((member_of(X!8) = U!7) <=> (member_of(U!7) = U!7)),
% 0.19/0.41 inference(symmetry,[status(thm)],[22])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~(member_of(X!8) = U!7)) <=> (~(member_of(U!7) = U!7))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (~(member_of(X!8) = U!7)),
% 0.19/0.41 inference(and_elim,[status(thm)],[15])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (~(member_of(U!7) = U!7)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (^[X: $i] : refl(((member_of(X) = X) | member(member_of(X), universal_class)) <=> ((member_of(X) = X) | member(member_of(X), universal_class)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class)) <=> ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class)) <=> ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (^[X: $i] : rewrite((member(member_of(X), universal_class) | (member_of(X) = X)) <=> ((member_of(X) = X) | member(member_of(X), universal_class)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X: $i] : (member(member_of(X), universal_class) | (member_of(X) = X)) <=> ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.41 tff(32,axiom,(![X: $i] : (member(member_of(X), universal_class) | (member_of(X) = X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','member_universal_self')).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.41 tff(35,plain,(
% 0.19/0.41 ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.19/0.41 inference(skolemize,[status(sab)],[34])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | ((member_of(U!7) = U!7) | member(member_of(U!7), universal_class))) <=> ((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | (member_of(U!7) = U!7) | member(member_of(U!7), universal_class))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | ((member_of(U!7) = U!7) | member(member_of(U!7), universal_class))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | (member_of(U!7) = U!7) | member(member_of(U!7), universal_class)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((member_of(U!7) = U!7) | member(member_of(U!7), universal_class)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (member(member_of(U!7), universal_class)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 26])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (member(member_of(X!8), universal_class)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 21])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (singleton(member_of(X!8)) = singleton(member_of(U!7))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (singleton(member_of(U!7)) = singleton(member_of(X!8))),
% 0.19/0.41 inference(symmetry,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (^[X: $i] : refl(((member_of(X) = X) | (singleton(member_of(X)) = X)) <=> ((member_of(X) = X) | (singleton(member_of(X)) = X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X)) <=> ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X)) <=> ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (^[X: $i] : rewrite(((singleton(member_of(X)) = X) | (member_of(X) = X)) <=> ((member_of(X) = X) | (singleton(member_of(X)) = X)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![X: $i] : ((singleton(member_of(X)) = X) | (member_of(X) = X)) <=> ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.41 tff(50,axiom,(![X: $i] : ((singleton(member_of(X)) = X) | (member_of(X) = X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','singleton_self')).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.41 tff(53,plain,(
% 0.19/0.41 ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.19/0.41 inference(skolemize,[status(sab)],[52])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | ((member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7))) <=> ((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | (member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | ((member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | (member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (singleton(member_of(U!7)) = U!7),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 26])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (U!7 = singleton(member_of(U!7))),
% 0.19/0.41 inference(symmetry,[status(thm)],[59])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (X!8 = singleton(member_of(X!8))),
% 0.19/0.41 inference(transitivity,[status(thm)],[16, 60, 44])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (^[Y: $i] : refl(((~member(Y, universal_class)) | (~(X!8 = singleton(Y)))) <=> ((~member(Y, universal_class)) | (~(X!8 = singleton(Y)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y)))) <=> ![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (^[Y: $i] : trans(monotonicity(rewrite((member(Y, universal_class) & (X!8 = singleton(Y))) <=> (~((~member(Y, universal_class)) | (~(X!8 = singleton(Y)))))), ((~(member(Y, universal_class) & (X!8 = singleton(Y)))) <=> (~(~((~member(Y, universal_class)) | (~(X!8 = singleton(Y)))))))), rewrite((~(~((~member(Y, universal_class)) | (~(X!8 = singleton(Y)))))) <=> ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))), ((~(member(Y, universal_class) & (X!8 = singleton(Y)))) <=> ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y)))) <=> ![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![Y: $i] : (~(member(Y, universal_class) & (X!8 = singleton(Y))))),
% 0.19/0.41 inference(and_elim,[status(thm)],[15])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))) | ((~member(member_of(X!8), universal_class)) | (~(X!8 = singleton(member_of(X!8)))))) <=> ((~![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))) | (~member(member_of(X!8), universal_class)) | (~(X!8 = singleton(member_of(X!8)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 ((~![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))) | ((~member(member_of(X!8), universal_class)) | (~(X!8 = singleton(member_of(X!8)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ((~![Y: $i] : ((~member(Y, universal_class)) | (~(X!8 = singleton(Y))))) | (~member(member_of(X!8), universal_class)) | (~(X!8 = singleton(member_of(X!8))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~member(member_of(X!8), universal_class)) | (~(X!8 = singleton(member_of(X!8))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 61, 42])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------