TSTP Solution File: SET094+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET094+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 05:05:35 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET094+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 02:16:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(member_of_type, type, (
% 0.13/0.40 member_of: $i > $i)).
% 0.13/0.40 tff(tptp_fun_X_8_type, type, (
% 0.13/0.40 tptp_fun_X_8: $i)).
% 0.13/0.40 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.40 tptp_fun_Y_7: $i)).
% 0.13/0.40 tff(member_type, type, (
% 0.13/0.40 member: ( $i * $i ) > $o)).
% 0.13/0.40 tff(singleton_type, type, (
% 0.13/0.40 singleton: $i > $i)).
% 0.13/0.40 tff(universal_class_type, type, (
% 0.13/0.40 universal_class: $i)).
% 0.13/0.40 tff(unordered_pair_type, type, (
% 0.13/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 ((Y!7 = member_of(X!8)) <=> (member_of(X!8) = Y!7)),
% 0.13/0.40 inference(commutativity,[status(thm)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((member_of(X!8) = Y!7) <=> (Y!7 = member_of(X!8))),
% 0.13/0.40 inference(symmetry,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 ((~(member_of(X!8) = Y!7)) <=> (~(Y!7 = member_of(X!8)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))) <=> (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : (((singleton(member_of(X)) = X) & member(Y, X)) => (member_of(X) = Y))) <=> (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,axiom,(~![X: $i, Y: $i] : (((singleton(member_of(X)) = X) & member(Y, X)) => (member_of(X) = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','property_of_singletons1_1')).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : ((~((singleton(member_of(X)) = X) & member(Y, X))) | (member_of(X) = Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.13/0.40 tff(14,plain,(
% 0.13/0.40 ~((~((singleton(member_of(X!8)) = X!8) & member(Y!7, X!8))) | (member_of(X!8) = Y!7))),
% 0.13/0.40 inference(skolemize,[status(sab)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (~(member_of(X!8) = Y!7)),
% 0.13/0.40 inference(or_elim,[status(thm)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (~(Y!7 = member_of(X!8))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 3])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (^[U: $i, X: $i, Y: $i] : refl((member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.40 tff(24,axiom,(![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','unordered_pair_defn')).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.13/0.40 tff(27,plain,(
% 0.13/0.40 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[26])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8)))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~((Y!7 = member_of(X!8)) | (Y!7 = member_of(X!8))))))) <=> (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~((Y!7 = member_of(X!8)) | (Y!7 = member_of(X!8)))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8)))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~((Y!7 = member_of(X!8)) | (Y!7 = member_of(X!8)))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[32, 30])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~((Y!7 = member_of(X!8)) | (Y!7 = member_of(X!8)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8)))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[35, 29])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ((singleton(member_of(X!8)) = X!8) & member(Y!7, X!8)),
% 0.13/0.41 inference(or_elim,[status(thm)],[14])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (singleton(member_of(X!8)) = X!8),
% 0.13/0.41 inference(and_elim,[status(thm)],[37])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (^[X: $i] : refl((singleton(X) = unordered_pair(X, X)) <=> (singleton(X) = unordered_pair(X, X)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(42,axiom,(![X: $i] : (singleton(X) = unordered_pair(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','singleton_set_defn')).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.41 tff(44,plain,(
% 0.13/0.41 ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.41 inference(skolemize,[status(sab)],[43])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(member_of(X!8)) = unordered_pair(member_of(X!8), member_of(X!8)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (singleton(member_of(X!8)) = unordered_pair(member_of(X!8), member_of(X!8))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (unordered_pair(member_of(X!8), member_of(X!8)) = singleton(member_of(X!8))),
% 0.13/0.41 inference(symmetry,[status(thm)],[47])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (unordered_pair(member_of(X!8), member_of(X!8)) = X!8),
% 0.13/0.41 inference(transitivity,[status(thm)],[48, 38])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> member(Y!7, X!8)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (member(Y!7, X!8) <=> member(Y!7, unordered_pair(member_of(X!8), member_of(X!8)))),
% 0.13/0.41 inference(symmetry,[status(thm)],[50])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (member(Y!7, X!8)),
% 0.13/0.41 inference(and_elim,[status(thm)],[37])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (member(Y!7, unordered_pair(member_of(X!8), member_of(X!8)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((~(member(Y!7, unordered_pair(member_of(X!8), member_of(X!8))) <=> (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8))))))) | (~member(Y!7, unordered_pair(member_of(X!8), member_of(X!8)))) | (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8)))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (~((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[54, 53, 36])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (((~member(Y!7, universal_class)) | (~(Y!7 = member_of(X!8)))) | (Y!7 = member_of(X!8))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 55, 16])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------