TSTP Solution File: LCL666+1.001 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 04:57:38 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL666+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 : Thu Sep 1 23:38:09 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(r1_type, type, (
% 0.13/0.39 r1: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: $i)).
% 0.13/0.39 tff(p101_type, type, (
% 0.13/0.39 p101: $i > $o)).
% 0.13/0.39 tff(p201_type, type, (
% 0.13/0.39 p201: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[Y: $i] : refl(((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y))) <=> ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((p201(Y) & p101(Y)) <=> (~((~p201(Y)) | (~p101(Y))))), ((~(p201(Y) & p101(Y))) <=> (~(~((~p201(Y)) | (~p101(Y))))))), rewrite((~(~((~p201(Y)) | (~p101(Y))))) <=> ((~p201(Y)) | (~p101(Y)))), ((~(p201(Y) & p101(Y))) <=> ((~p201(Y)) | (~p101(Y))))), (((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))) <=> ((~r1(X!0, Y)) | ((~p201(Y)) | (~p101(Y)))))), rewrite(((~r1(X!0, Y)) | ((~p201(Y)) | (~p101(Y)))) <=> ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))), (((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))) <=> ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (((p201(X!0) & p101(X!0)) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))) <=> (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 ((~(~(p201(X!0) & p101(X!0)))) <=> (p201(X!0) & p101(X!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (((~(~(p201(X!0) & p101(X!0)))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))) <=> ((p201(X!0) & p101(X!0)) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (((~(~(p201(X!0) & p101(X!0)))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))) <=> (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y)))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[7, 5])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ((~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X)))))) <=> (~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X))))))) <=> (~(~?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X))))))) <=> ?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[12, 10])).
% 0.13/0.39 tff(14,axiom,(~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y))))) | (~(p201(X) & p101(X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (?[X: $i] : (~((~(p201(X) & p101(X))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p201(Y) & p101(Y)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (p201(X!0) & p101(X!0) & ![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 8])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![Y: $i] : ((~r1(X!0, Y)) | (~(p201(Y) & p101(Y))))),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 4])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 2])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (p101(X!0)),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (p201(X!0)),
% 0.13/0.39 inference(and_elim,[status(thm)],[17])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | (~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | ((~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~![Y: $i] : ((~r1(X!0, Y)) | (~p201(Y)) | (~p101(Y)))) | (~r1(X!0, X!0)) | (~p201(X!0)) | (~p101(X!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~r1(X!0, X!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[25, 22, 21, 20])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(30,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity')).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![X: $i] : r1(X, X)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.39 tff(32,plain,(
% 0.13/0.39 ![X: $i] : r1(X, X)),
% 0.13/0.39 inference(skolemize,[status(sab)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![X: $i] : r1(X, X)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((~![X: $i] : r1(X, X)) | r1(X!0, X!0)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[34, 33, 26])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------