TSTP Solution File: NUN088+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN088+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN088+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 : Fri Sep 2 16:35:50 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.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(tptp_fun_Y1_20_type, type, (
% 0.20/0.39 tptp_fun_Y1_20: $i)).
% 0.20/0.39 tff(r1_type, type, (
% 0.20/0.39 r1: $i > $o)).
% 0.20/0.39 tff(r2_type, type, (
% 0.20/0.39 r2: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Y3_22_type, type, (
% 0.20/0.39 tptp_fun_Y3_22: $i)).
% 0.20/0.39 tff(tptp_fun_Y2_21_type, type, (
% 0.20/0.39 tptp_fun_Y2_21: $i)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 ((~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,axiom,(~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','zerouneqone')).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~![Y1: $i] : (![Y2: $i] : ((~r1(Y2)) | (~(Y2 = Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~((~r1(Y3!22)) | (~r2(Y3!22, Y1!20)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[9])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (r2(Y3!22, Y1!20)),
% 0.20/0.39 inference(or_elim,[status(thm)],[10])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.39 tff(20,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.40 tff(23,plain,(
% 0.20/0.40 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y3!22, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y3!22, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y3!22, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y3!22, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~((~r1(Y2!21)) | (~(Y2!21 = Y1!20)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[9])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (Y2!21 = Y1!20),
% 0.20/0.40 inference(or_elim,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (Y1!20 = Y2!21),
% 0.20/0.40 inference(symmetry,[status(thm)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (r1(Y1!20) <=> r1(Y2!21)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (r1(Y2!21) <=> r1(Y1!20)),
% 0.20/0.40 inference(symmetry,[status(thm)],[32])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (r1(Y2!21)),
% 0.20/0.40 inference(or_elim,[status(thm)],[29])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (r1(Y1!20)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | (~r1(Y1!20))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | (~r1(Y1!20)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (((~r1(Y1!20)) | $false) <=> (~r1(Y1!20))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~$true) <=> $false),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((Y1!20 = Y1!20) <=> $true),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~(Y1!20 = Y1!20)) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~(Y1!20 = Y1!20)) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (((~r1(Y1!20)) | (~(Y1!20 = Y1!20))) <=> ((~r1(Y1!20)) | $false)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (((~r1(Y1!20)) | (~(Y1!20 = Y1!20))) <=> (~r1(Y1!20))),
% 0.20/0.40 inference(transitivity,[status(thm)],[42, 37])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | ((~r1(Y1!20)) | (~(Y1!20 = Y1!20)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | (~r1(Y1!20)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | ((~r1(Y1!20)) | (~(Y1!20 = Y1!20)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | (~r1(Y1!20)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[44, 36])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | ((~r1(Y1!20)) | (~(Y1!20 = Y1!20)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | (~r1(Y1!20))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 35, 28])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------