TSTP Solution File: SET054+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET054+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 05:05:10 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET054+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 01:59:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(subclass_type, type, (
% 0.20/0.41 subclass: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_X_7_type, type, (
% 0.20/0.41 tptp_fun_X_7: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 ((~![X: $i] : subclass(X, X)) <=> (~![X: $i] : subclass(X, X))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,axiom,(~![X: $i] : subclass(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_of_subclass')).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (~![X: $i] : subclass(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (~![X: $i] : subclass(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~![X: $i] : subclass(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (~![X: $i] : subclass(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (~![X: $i] : subclass(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (~![X: $i] : subclass(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (~![X: $i] : subclass(X, X)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.41 tff(10,plain,(
% 0.20/0.41 ~subclass(X!7, X!7)),
% 0.20/0.41 inference(skolemize,[status(sab)],[9])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl(((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X))))) <=> ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X))))) <=> ![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : rewrite(((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,axiom,(![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','extensionality')).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | subclass(X!7, X!7)) <=> ((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | subclass(X!7, X!7))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (($true <=> subclass(X!7, X!7)) <=> subclass(X!7, X!7)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~(~subclass(X!7, X!7))) <=> subclass(X!7, X!7)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (~subclass(X!7, X!7))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 ((~((~subclass(X!7, X!7)) | (~subclass(X!7, X!7)))) <=> (~(~subclass(X!7, X!7)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~((~subclass(X!7, X!7)) | (~subclass(X!7, X!7)))) <=> subclass(X!7, X!7)),
% 0.20/0.41 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((X!7 = X!7) <=> $true),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (((X!7 = X!7) <=> (~((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))))) <=> ($true <=> subclass(X!7, X!7))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (((X!7 = X!7) <=> (~((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))))) <=> subclass(X!7, X!7)),
% 0.20/0.41 inference(transitivity,[status(thm)],[28, 22])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | ((X!7 = X!7) <=> (~((~subclass(X!7, X!7)) | (~subclass(X!7, X!7)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | subclass(X!7, X!7))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | ((X!7 = X!7) <=> (~((~subclass(X!7, X!7)) | (~subclass(X!7, X!7)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | subclass(X!7, X!7))),
% 0.20/0.41 inference(transitivity,[status(thm)],[30, 21])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | ((X!7 = X!7) <=> (~((~subclass(X!7, X!7)) | (~subclass(X!7, X!7)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X)))))) | subclass(X!7, X!7)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 20, 10])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------