TSTP Solution File: SET093+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET093+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 05:05:34 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
% 0.07/0.12 % Problem : SET093+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 02:19:59 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.
% 0.19/0.40 % 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(unordered_pair_type, type, (
% 0.19/0.40 unordered_pair: ( $i * $i ) > $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_7_type, type, (
% 0.19/0.40 tptp_fun_X_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 ((~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))) <=> (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![X: $i] : ((singleton(member_of(X)) = X) => member(X, universal_class))) <=> (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,axiom,(~![X: $i] : ((singleton(member_of(X)) = X) => member(X, universal_class))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary_2_to_singletons_are_sets')).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ~((~(singleton(member_of(X!7)) = X!7)) | member(X!7, universal_class))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (singleton(member_of(X!7)) = X!7),
% 0.19/0.40 inference(or_elim,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (^[X: $i] : refl((singleton(X) = unordered_pair(X, X)) <=> (singleton(X) = unordered_pair(X, X)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,axiom,(![X: $i] : (singleton(X) = unordered_pair(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','singleton_set_defn')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,(
% 0.19/0.40 ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.19/0.40 inference(skolemize,[status(sab)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(member_of(X!7)) = unordered_pair(member_of(X!7), member_of(X!7)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (singleton(member_of(X!7)) = unordered_pair(member_of(X!7), member_of(X!7))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (unordered_pair(member_of(X!7), member_of(X!7)) = singleton(member_of(X!7))),
% 0.19/0.40 inference(symmetry,[status(thm)],[21])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (unordered_pair(member_of(X!7), member_of(X!7)) = X!7),
% 0.19/0.40 inference(transitivity,[status(thm)],[22, 12])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class) <=> member(X!7, universal_class)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.41 (member(X!7, universal_class) <=> member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.19/0.41 inference(symmetry,[status(thm)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~member(X!7, universal_class)) <=> (~member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (~member(X!7, universal_class)),
% 0.19/0.41 inference(or_elim,[status(thm)],[11])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (~member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,axiom,(![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','unordered_pair')).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X: $i, Y: $i] : member(unordered_pair(X, Y), 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, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.19/0.41 inference(skolemize,[status(sab)],[33])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[37, 28])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------