TSTP Solution File: NUN088+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN088+3 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 13:27:59 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUN088+3 : TPTP v8.1.0. Released v7.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.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 : Fri Sep 2 16:18:03 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(tptp_fun_Y1_21_type, type, (
% 0.19/0.39 tptp_fun_Y1_21: $i)).
% 0.19/0.39 tff(r1_type, type, (
% 0.19/0.39 r1: $i > $o)).
% 0.19/0.39 tff(r2_type, type, (
% 0.19/0.39 r2: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y0_20_type, type, (
% 0.19/0.39 tptp_fun_Y0_20: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (((~(~r1(Y0!20))) & (~((~(Y0!20 = Y1!21)) | (~r2(Y0!20, Y1!21))))) <=> (r1(Y0!20) & (~((~(Y0!20 = Y1!21)) | (~r2(Y0!20, Y1!21)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))) <=> (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~![Y0: $i] : (![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))) | (~r1(Y0)))) <=> (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(~![Y0: $i] : (![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))) | (~r1(Y0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zerouneqone2')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![Y0: $i] : ((~r1(Y0)) | ![Y1: $i] : ((~(Y0 = Y1)) | (~r2(Y0, Y1))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (r1(Y0!20) & (~((~(Y0!20 = Y1!21)) | (~r2(Y0!20, Y1!21))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~((~(Y0!20 = Y1!21)) | (~r2(Y0!20, Y1!21)))),
% 0.19/0.39 inference(and_elim,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (Y0!20 = Y1!21),
% 0.19/0.39 inference(or_elim,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (Y1!21 = Y0!20),
% 0.19/0.39 inference(symmetry,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (r2(Y1!21, Y1!21) <=> r2(Y0!20, Y1!21)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (r2(Y0!20, Y1!21) <=> r2(Y1!21, Y1!21)),
% 0.19/0.39 inference(symmetry,[status(thm)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (r2(Y0!20, Y1!21)),
% 0.19/0.39 inference(or_elim,[status(thm)],[13])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (r2(Y1!21, Y1!21)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.39 tff(31,plain,(
% 0.19/0.39 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y1!21, Y1!21)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y1!21, Y1!21)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y1!21, Y1!21)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y1!21, Y1!21)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~r2(Y1!21, Y1!21)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 19])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (r1(Y1!21) <=> r1(Y0!20)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (r1(Y0!20) <=> r1(Y1!21)),
% 0.19/0.39 inference(symmetry,[status(thm)],[38])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (r1(Y0!20)),
% 0.19/0.39 inference(and_elim,[status(thm)],[12])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (r1(Y1!21)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | (~r1(Y1!21))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | (~r1(Y1!21)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (((~r1(Y1!21)) | $false) <=> (~r1(Y1!21))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~$true) <=> $false),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ((Y1!21 = Y1!21) <=> $true),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~(Y1!21 = Y1!21)) <=> (~$true)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~(Y1!21 = Y1!21)) <=> $false),
% 0.19/0.39 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (((~r1(Y1!21)) | (~(Y1!21 = Y1!21))) <=> ((~r1(Y1!21)) | $false)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((~r1(Y1!21)) | (~(Y1!21 = Y1!21))) <=> (~r1(Y1!21))),
% 0.19/0.39 inference(transitivity,[status(thm)],[48, 43])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | ((~r1(Y1!21)) | (~(Y1!21 = Y1!21)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | (~r1(Y1!21)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | ((~r1(Y1!21)) | (~(Y1!21 = Y1!21)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | (~r1(Y1!21)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[50, 42])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | ((~r1(Y1!21)) | (~(Y1!21 = Y1!21)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!21)))) | (~r1(Y1!21))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 41, 37])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------