TSTP Solution File: LCL684+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL684+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Sun Sep 18 04:57:53 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL684+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n022.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 : Fri Sep 2 00:17:55 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.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(p101_type, type, (
% 0.19/0.41 p101: $i > $o)).
% 0.19/0.41 tff(p201_type, type, (
% 0.19/0.41 p201: $i > $o)).
% 0.19/0.41 tff(r1_type, type, (
% 0.19/0.41 r1: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_X_0_type, type, (
% 0.19/0.41 tptp_fun_X_0: $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X: $i] : r1(X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![X: $i] : r1(X, X)),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![X: $i] : r1(X, X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (r1(X!0, X!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[13, 11])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (((p201(X!0) & p101(X!0)) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) <=> (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~(~(p201(X!0) & p101(X!0)))) <=> (p201(X!0) & p101(X!0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (((~(~(p201(X!0) & p101(X!0)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) <=> ((p201(X!0) & p101(X!0)) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (((~(~(p201(X!0) & p101(X!0)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) <=> (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[19, 17])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ((~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X)))))) <=> (~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X))))))) <=> (~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[24, 22])).
% 0.19/0.41 tff(26,axiom,(~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))) | (~(p201(X) & p101(X))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p201(X) & p101(X)))))),
% 0.19/0.41 inference(and_elim,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 16])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 14])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | ((~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | (~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | ((~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p201(X)) | (~p101(X))))) | (~r1(X!0, X!0)) | ![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[35, 32, 9])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (p101(X!0)),
% 0.19/0.41 inference(and_elim,[status(thm)],[29])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (p201(X!0)),
% 0.19/0.41 inference(and_elim,[status(thm)],[29])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))) <=> ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | (~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![X: $i] : ((~r1(X!0, X)) | (~p201(X)) | (~p101(X)))) | (~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 38, 37, 9, 36])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------