TSTP Solution File: SYN398+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN398+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Thu Sep 29 23:55:09 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN398+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 : Mon Sep 5 03:20:18 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(f_type, type, (
% 0.21/0.39 f: $i > $o)).
% 0.21/0.39 tff(tptp_fun_X_0_type, type, (
% 0.21/0.39 tptp_fun_X_0: $i)).
% 0.21/0.39 tff(p_type, type, (
% 0.21/0.39 p: $o)).
% 0.21/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.39 tptp_fun_Y_1: $i)).
% 0.21/0.39 tff(1,assumption,(![X: $i] : (~((~p) | (~f(X))))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![X: $i] : (~((~p) | (~f(X))))) | (~((~p) | (~f(Y!1))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (~((~p) | (~f(Y!1)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (((~p) | (~f(Y!1))) | p),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (p),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.21/0.39 tff(6,assumption,(~f(Y!1)), introduced(assumption)).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (((~p) | (~f(Y!1))) | f(Y!1)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~p) | (~f(Y!1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.21/0.39 tff(9,assumption,(![Y: $i] : f(Y)), introduced(assumption)).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 ((~![Y: $i] : f(Y)) | f(Y!1)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[10, 9, 6])).
% 0.21/0.39 tff(12,plain,((~![Y: $i] : f(Y)) | f(Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~![Y: $i] : f(Y)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[12, 6])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (((~p) | (~![Y: $i] : f(Y))) | ![Y: $i] : f(Y)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 ((~p) | (~![Y: $i] : f(Y))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (((~((~p) | (~![Y: $i] : f(Y)))) | ![X: $i] : (~((~p) | (~f(X))))) <=> ((~((~p) | (~![Y: $i] : f(Y)))) | ![X: $i] : (~((~p) | (~f(X)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (((p & ![Y: $i] : f(Y)) | ![X: $i] : (p & f(X))) <=> ((~((~p) | (~![Y: $i] : f(Y)))) | ![X: $i] : (~((~p) | (~f(X)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (((![X: $i] : (p & f(X)) | (p & ![Y: $i] : f(Y))) & ((~(p & f(X!0))) | ((~p) | (~f(Y!1))))) <=> (((p & ![Y: $i] : f(Y)) | ![X: $i] : (p & f(X))) & ((~(p & f(X!0))) | (~p) | (~f(Y!1))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 ((p & ![Y: $i] : f(Y)) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (~![X: $i] : (p & f(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))) <=> ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[20, 19])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))) <=> ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 ((~(![X: $i] : (p & f(X)) <=> (p & ![Y: $i] : f(Y)))) <=> ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 ((![X: $i] : (p & f(X)) <=> (p & ![Y: $i] : f(Y))) <=> (![X: $i] : (p & f(X)) <=> (p & ![Y: $i] : f(Y)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~(![X: $i] : (p & f(X)) <=> (p & ![Y: $i] : f(Y)))) <=> (~(![X: $i] : (p & f(X)) <=> (p & ![Y: $i] : f(Y))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 ((~(![X: $i] : (p & f(X)) <=> (p & ![Y: $i] : f(Y)))) <=> ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.21/0.39 tff(27,axiom,(~(![X: $i] : (p & f(X)) <=> (p & ![Y: $i] : f(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish215')).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[32, 21])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 ((~![X: $i] : (p & f(X))) <=> (p & ![Y: $i] : f(Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[33, 21])).
% 0.21/0.39 tff(35,plain,(
% 0.21/0.39 (![X: $i] : (p & f(X)) | (p & ![Y: $i] : f(Y))) & ((~(p & f(X!0))) | ((~p) | (~f(Y!1))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[34])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (((p & ![Y: $i] : f(Y)) | ![X: $i] : (p & f(X))) & ((~(p & f(X!0))) | (~p) | (~f(Y!1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[35, 18])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 ((p & ![Y: $i] : f(Y)) | ![X: $i] : (p & f(X))),
% 0.21/0.39 inference(and_elim,[status(thm)],[36])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 ((~((~p) | (~![Y: $i] : f(Y)))) | ![X: $i] : (~((~p) | (~f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[37, 17])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 ((~((~p) | (~![Y: $i] : f(Y)))) | ![X: $i] : (~((~p) | (~f(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 16])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![X: $i] : (~((~p) | (~f(X))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 15])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[2, 40, 8])).
% 0.21/0.39 tff(42,plain,(f(Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 ((((~p) | (~f(X!0))) | (~p) | (~f(Y!1))) <=> ((~p) | (~f(Y!1)) | (~f(X!0)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~(~((~p) | (~f(X!0))))) <=> ((~p) | (~f(X!0)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 ((p & f(X!0)) <=> (~((~p) | (~f(X!0))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 ((~(p & f(X!0))) <=> (~(~((~p) | (~f(X!0)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 ((~(p & f(X!0))) <=> ((~p) | (~f(X!0)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[46, 44])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (((~(p & f(X!0))) | (~p) | (~f(Y!1))) <=> (((~p) | (~f(X!0))) | (~p) | (~f(Y!1)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (((~(p & f(X!0))) | (~p) | (~f(Y!1))) <=> ((~p) | (~f(Y!1)) | (~f(X!0)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[48, 43])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 ((~(p & f(X!0))) | (~p) | (~f(Y!1))),
% 0.21/0.39 inference(and_elim,[status(thm)],[36])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 ((~p) | (~f(Y!1)) | (~f(X!0))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 ((~p) | (~f(X!0))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[51, 42])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (~f(X!0)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[52, 5])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 (((~p) | (~f(X!0))) | f(X!0)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 ((~p) | (~f(X!0))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 ((~![X: $i] : (~((~p) | (~f(X))))) | (~((~p) | (~f(X!0))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[56, 1, 55])).
% 0.21/0.39 tff(58,plain,(~![X: $i] : (~((~p) | (~f(X))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 (~((~p) | (~![Y: $i] : f(Y)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 58])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (((~p) | (~![Y: $i] : f(Y))) | p),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (p),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (~f(X!0)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[52, 61])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (![Y: $i] : f(Y)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[14, 59])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 ((~![Y: $i] : f(Y)) | f(X!0)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[64, 63, 62])).
% 0.21/0.39 % SZS output end Proof
%------------------------------------------------------------------------------