TSTP Solution File: SET079+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET079+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 05:05:26 EDT 2022
% Result : Theorem 3.47s 2.48s
% Output : Proof 3.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET079+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 02:04:13 EDT 2022
% 0.13/0.34 % 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.
% 3.47/2.48 % SZS status Theorem
% 3.47/2.48 % SZS output start Proof
% 3.47/2.48 tff(member_type, type, (
% 3.47/2.48 member: ( $i * $i ) > $o)).
% 3.47/2.48 tff(null_class_type, type, (
% 3.47/2.48 null_class: $i)).
% 3.47/2.48 tff(tptp_fun_X_7_type, type, (
% 3.47/2.48 tptp_fun_X_7: $i)).
% 3.47/2.48 tff(unordered_pair_type, type, (
% 3.47/2.48 unordered_pair: ( $i * $i ) > $i)).
% 3.47/2.48 tff(singleton_type, type, (
% 3.47/2.48 singleton: $i > $i)).
% 3.47/2.48 tff(universal_class_type, type, (
% 3.47/2.48 universal_class: $i)).
% 3.47/2.48 tff(1,plain,
% 3.47/2.48 ((~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))) <=> (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class))))),
% 3.47/2.48 inference(rewrite,[status(thm)],[])).
% 3.47/2.48 tff(2,plain,
% 3.47/2.48 ((~![X: $i] : (member(X, universal_class) => (~(singleton(X) = null_class)))) <=> (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class))))),
% 3.47/2.48 inference(rewrite,[status(thm)],[])).
% 3.47/2.48 tff(3,axiom,(~![X: $i] : (member(X, universal_class) => (~(singleton(X) = null_class)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary_to_set_in_its_singleton')).
% 3.47/2.48 tff(4,plain,
% 3.47/2.48 (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[3, 2])).
% 3.47/2.48 tff(5,plain,
% 3.47/2.48 (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[4, 1])).
% 3.47/2.48 tff(6,plain,
% 3.47/2.48 (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[5, 1])).
% 3.47/2.48 tff(7,plain,
% 3.47/2.48 (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[6, 1])).
% 3.47/2.48 tff(8,plain,
% 3.47/2.48 (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[7, 1])).
% 3.47/2.48 tff(9,plain,
% 3.47/2.48 (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[8, 1])).
% 3.47/2.48 tff(10,plain,
% 3.47/2.48 (~![X: $i] : ((~member(X, universal_class)) | (~(singleton(X) = null_class)))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[9, 1])).
% 3.47/2.48 tff(11,plain,(
% 3.47/2.48 ~((~member(X!7, universal_class)) | (~(singleton(X!7) = null_class)))),
% 3.47/2.48 inference(skolemize,[status(sab)],[10])).
% 3.47/2.48 tff(12,plain,
% 3.47/2.48 (singleton(X!7) = null_class),
% 3.47/2.48 inference(or_elim,[status(thm)],[11])).
% 3.47/2.48 tff(13,plain,
% 3.47/2.48 (^[X: $i] : refl((singleton(X) = unordered_pair(X, X)) <=> (singleton(X) = unordered_pair(X, X)))),
% 3.47/2.48 inference(bind,[status(th)],[])).
% 3.47/2.48 tff(14,plain,
% 3.47/2.48 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 3.47/2.48 inference(quant_intro,[status(thm)],[13])).
% 3.47/2.48 tff(15,plain,
% 3.47/2.48 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 3.47/2.48 inference(rewrite,[status(thm)],[])).
% 3.47/2.48 tff(16,axiom,(![X: $i] : (singleton(X) = unordered_pair(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','singleton_set_defn')).
% 3.47/2.48 tff(17,plain,
% 3.47/2.48 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.47/2.48 tff(18,plain,(
% 3.47/2.48 ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 3.47/2.48 inference(skolemize,[status(sab)],[17])).
% 3.47/2.48 tff(19,plain,
% 3.47/2.48 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.47/2.48 tff(20,plain,
% 3.47/2.48 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(X!7) = unordered_pair(X!7, X!7))),
% 3.47/2.48 inference(quant_inst,[status(thm)],[])).
% 3.47/2.48 tff(21,plain,
% 3.47/2.48 (singleton(X!7) = unordered_pair(X!7, X!7)),
% 3.47/2.48 inference(unit_resolution,[status(thm)],[20, 19])).
% 3.47/2.48 tff(22,plain,
% 3.47/2.48 (unordered_pair(X!7, X!7) = singleton(X!7)),
% 3.47/2.48 inference(symmetry,[status(thm)],[21])).
% 3.47/2.48 tff(23,plain,
% 3.47/2.48 (unordered_pair(X!7, X!7) = null_class),
% 3.47/2.48 inference(transitivity,[status(thm)],[22, 12])).
% 3.47/2.48 tff(24,plain,
% 3.47/2.48 (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, null_class)),
% 3.47/2.48 inference(monotonicity,[status(thm)],[23])).
% 3.47/2.48 tff(25,plain,
% 3.47/2.48 (member(X!7, null_class) <=> member(X!7, unordered_pair(X!7, X!7))),
% 3.47/2.48 inference(symmetry,[status(thm)],[24])).
% 3.47/2.48 tff(26,plain,
% 3.47/2.48 ((~member(X!7, null_class)) <=> (~member(X!7, unordered_pair(X!7, X!7)))),
% 3.47/2.48 inference(monotonicity,[status(thm)],[25])).
% 3.47/2.48 tff(27,assumption,(~member(X!7, null_class)), introduced(assumption)).
% 3.47/2.48 tff(28,plain,
% 3.47/2.48 (~member(X!7, unordered_pair(X!7, X!7))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[27, 26])).
% 3.47/2.48 tff(29,plain,
% 3.47/2.48 (^[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)))))))),
% 3.47/2.48 inference(bind,[status(th)],[])).
% 3.47/2.48 tff(30,plain,
% 3.47/2.48 (![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))))))),
% 3.47/2.48 inference(quant_intro,[status(thm)],[29])).
% 3.47/2.48 tff(31,plain,
% 3.47/2.48 (^[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)))))))),
% 3.47/2.48 inference(bind,[status(th)],[])).
% 3.47/2.48 tff(32,plain,
% 3.47/2.48 (![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))))))),
% 3.47/2.48 inference(quant_intro,[status(thm)],[31])).
% 3.47/2.48 tff(33,plain,
% 3.47/2.48 (![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))))),
% 3.47/2.48 inference(rewrite,[status(thm)],[])).
% 3.47/2.48 tff(34,plain,
% 3.47/2.48 (^[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)))))),
% 3.47/2.48 inference(bind,[status(th)],[])).
% 3.47/2.48 tff(35,plain,
% 3.47/2.48 (![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))))),
% 3.47/2.48 inference(quant_intro,[status(thm)],[34])).
% 3.47/2.48 tff(36,axiom,(![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','unordered_pair_defn')).
% 3.47/2.48 tff(37,plain,
% 3.47/2.48 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[36, 35])).
% 3.47/2.48 tff(38,plain,
% 3.47/2.48 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[37, 33])).
% 3.47/2.48 tff(39,plain,(
% 3.47/2.48 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 3.47/2.48 inference(skolemize,[status(sab)],[38])).
% 3.47/2.48 tff(40,plain,
% 3.47/2.48 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[39, 32])).
% 3.47/2.48 tff(41,plain,
% 3.47/2.48 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[40, 30])).
% 3.47/2.48 tff(42,plain,
% 3.47/2.48 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class)))),
% 3.47/2.48 inference(rewrite,[status(thm)],[])).
% 3.47/2.48 tff(43,plain,
% 3.47/2.48 ((member(X!7, unordered_pair(X!7, X!7)) <=> (~((~member(X!7, universal_class)) | (~((X!7 = X!7) | (X!7 = X!7)))))) <=> (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class))),
% 3.47/2.48 inference(rewrite,[status(thm)],[])).
% 3.47/2.48 tff(44,plain,
% 3.47/2.48 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> (~((~member(X!7, universal_class)) | (~((X!7 = X!7) | (X!7 = X!7))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class)))),
% 3.47/2.48 inference(monotonicity,[status(thm)],[43])).
% 3.47/2.48 tff(45,plain,
% 3.47/2.48 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> (~((~member(X!7, universal_class)) | (~((X!7 = X!7) | (X!7 = X!7))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class)))),
% 3.47/2.48 inference(transitivity,[status(thm)],[44, 42])).
% 3.47/2.48 tff(46,plain,
% 3.47/2.48 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> (~((~member(X!7, universal_class)) | (~((X!7 = X!7) | (X!7 = X!7))))))),
% 3.47/2.48 inference(quant_inst,[status(thm)],[])).
% 3.47/2.48 tff(47,plain,
% 3.47/2.48 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.47/2.48 tff(48,plain,
% 3.47/2.48 (member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class)),
% 3.47/2.48 inference(unit_resolution,[status(thm)],[47, 41])).
% 3.47/2.48 tff(49,plain,
% 3.47/2.48 (member(X!7, universal_class)),
% 3.47/2.48 inference(or_elim,[status(thm)],[11])).
% 3.47/2.48 tff(50,plain,
% 3.47/2.48 ((~(member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class))) | member(X!7, unordered_pair(X!7, X!7)) | (~member(X!7, universal_class))),
% 3.47/2.48 inference(tautology,[status(thm)],[])).
% 3.47/2.48 tff(51,plain,
% 3.47/2.48 ((~(member(X!7, unordered_pair(X!7, X!7)) <=> member(X!7, universal_class))) | member(X!7, unordered_pair(X!7, X!7))),
% 3.47/2.48 inference(unit_resolution,[status(thm)],[50, 49])).
% 3.47/2.48 tff(52,plain,
% 3.47/2.48 (member(X!7, unordered_pair(X!7, X!7))),
% 3.47/2.48 inference(unit_resolution,[status(thm)],[51, 48])).
% 3.47/2.48 tff(53,plain,
% 3.47/2.48 ($false),
% 3.47/2.48 inference(unit_resolution,[status(thm)],[52, 28])).
% 3.47/2.48 tff(54,plain,(member(X!7, null_class)), inference(lemma,lemma(discharge,[]))).
% 3.47/2.48 tff(55,plain,
% 3.47/2.48 (^[X: $i] : refl((~member(X, null_class)) <=> (~member(X, null_class)))),
% 3.47/2.48 inference(bind,[status(th)],[])).
% 3.47/2.48 tff(56,plain,
% 3.47/2.48 (![X: $i] : (~member(X, null_class)) <=> ![X: $i] : (~member(X, null_class))),
% 3.47/2.48 inference(quant_intro,[status(thm)],[55])).
% 3.47/2.48 tff(57,plain,
% 3.47/2.48 (![X: $i] : (~member(X, null_class)) <=> ![X: $i] : (~member(X, null_class))),
% 3.47/2.48 inference(rewrite,[status(thm)],[])).
% 3.47/2.48 tff(58,axiom,(![X: $i] : (~member(X, null_class))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','null_class_defn')).
% 3.47/2.48 tff(59,plain,
% 3.47/2.48 (![X: $i] : (~member(X, null_class))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[58, 57])).
% 3.47/2.48 tff(60,plain,(
% 3.47/2.48 ![X: $i] : (~member(X, null_class))),
% 3.47/2.48 inference(skolemize,[status(sab)],[59])).
% 3.47/2.48 tff(61,plain,
% 3.47/2.48 (![X: $i] : (~member(X, null_class))),
% 3.47/2.48 inference(modus_ponens,[status(thm)],[60, 56])).
% 3.47/2.48 tff(62,plain,
% 3.47/2.48 ((~![X: $i] : (~member(X, null_class))) | (~member(X!7, null_class))),
% 3.47/2.48 inference(quant_inst,[status(thm)],[])).
% 3.47/2.48 tff(63,plain,
% 3.47/2.48 ($false),
% 3.47/2.48 inference(unit_resolution,[status(thm)],[62, 61, 54])).
% 3.47/2.48 % SZS output end Proof
%------------------------------------------------------------------------------