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
%------------------------------------------------------------------------------