TSTP Solution File: SYN053+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN053+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n014.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 23:53:23 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
% 0.06/0.12  % Problem  : SYN053+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Sep  5 01:36:14 EDT 2022
% 0.12/0.33  % 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(big_f_type, type, (
% 0.19/0.39     big_f: $i > $o)).
% 0.19/0.39  tff(tptp_fun_X_0_type, type, (
% 0.19/0.39     tptp_fun_X_0: $i)).
% 0.19/0.39  tff(p_type, type, (
% 0.19/0.39     p: $o)).
% 0.19/0.39  tff(tptp_fun_X1_1_type, type, (
% 0.19/0.39     tptp_fun_X1_1: $i)).
% 0.19/0.39  tff(1,assumption,(~(p | big_f(X1!1))), introduced(assumption)).
% 0.19/0.39  tff(2,plain,
% 0.19/0.39      ((p | big_f(X1!1)) | (~big_f(X1!1))),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(3,plain,
% 0.19/0.39      (~big_f(X1!1)),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.39  tff(4,plain,
% 0.19/0.39      ((p | big_f(X1!1)) | (~p)),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(5,plain,
% 0.19/0.39      (~p),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.39  tff(6,assumption,(~big_f(X1!1)), introduced(assumption)).
% 0.19/0.39  tff(7,assumption,(![X1: $i] : big_f(X1)), introduced(assumption)).
% 0.19/0.39  tff(8,plain,
% 0.19/0.39      ((~![X1: $i] : big_f(X1)) | big_f(X1!1)),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(9,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[8, 7, 6])).
% 0.19/0.39  tff(10,plain,((~![X1: $i] : big_f(X1)) | big_f(X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39  tff(11,plain,
% 0.19/0.39      (~![X1: $i] : big_f(X1)),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[10, 3])).
% 0.19/0.39  tff(12,plain,
% 0.19/0.39      ((p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(13,plain,
% 0.19/0.39      (((![X: $i] : (p | big_f(X)) | (p | ![X1: $i] : big_f(X1))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1))))) <=> ((p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1)))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(14,plain,
% 0.19/0.39      ((p | ![X1: $i] : big_f(X1)) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(15,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (~![X: $i] : (p | big_f(X)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(16,plain,
% 0.19/0.39      (((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39      inference(monotonicity,[status(thm)],[15, 14])).
% 0.19/0.39  tff(17,plain,
% 0.19/0.39      (((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(18,plain,
% 0.19/0.39      ((~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(19,plain,
% 0.19/0.39      ((![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1))) <=> (![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(20,plain,
% 0.19/0.39      ((~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))) <=> (~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1))))),
% 0.19/0.39      inference(monotonicity,[status(thm)],[19])).
% 0.19/0.39  tff(21,plain,
% 0.19/0.39      ((~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))) <=> ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1)))),
% 0.19/0.39      inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.39  tff(22,axiom,(~(![X: $i] : (p | big_f(X)) <=> (p | ![X1: $i] : big_f(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel23')).
% 0.19/0.39  tff(23,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.39  tff(24,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.39  tff(25,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.39  tff(26,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[25, 16])).
% 0.19/0.39  tff(27,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.39  tff(28,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[27, 16])).
% 0.19/0.39  tff(29,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) <=> (p | ![X1: $i] : big_f(X1))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[28, 16])).
% 0.19/0.39  tff(30,plain,(
% 0.19/0.39      (![X: $i] : (p | big_f(X)) | (p | ![X1: $i] : big_f(X1))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1))))),
% 0.19/0.39      inference(skolemize,[status(sab)],[29])).
% 0.19/0.39  tff(31,plain,
% 0.19/0.39      ((p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))) & ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1))))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[30, 13])).
% 0.19/0.39  tff(32,plain,
% 0.19/0.39      (p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))),
% 0.19/0.39      inference(and_elim,[status(thm)],[31])).
% 0.19/0.39  tff(33,plain,
% 0.19/0.39      (p | ![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[32, 12])).
% 0.19/0.39  tff(34,plain,
% 0.19/0.39      (![X: $i] : (p | big_f(X))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[33, 11, 5])).
% 0.19/0.39  tff(35,plain,
% 0.19/0.39      (((~![X: $i] : (p | big_f(X))) | (p | big_f(X1!1))) <=> ((~![X: $i] : (p | big_f(X))) | p | big_f(X1!1))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(36,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) | (p | big_f(X1!1))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(37,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) | p | big_f(X1!1)),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.39  tff(38,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[37, 5, 34, 3])).
% 0.19/0.39  tff(39,plain,(p | big_f(X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39  tff(40,plain,
% 0.19/0.39      (((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1)))) <=> ((~(p | big_f(X!0))) | (~(p | big_f(X1!1))))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(41,plain,
% 0.19/0.39      ((~(p | big_f(X!0))) | ((~p) & (~big_f(X1!1)))),
% 0.19/0.39      inference(and_elim,[status(thm)],[31])).
% 0.19/0.39  tff(42,plain,
% 0.19/0.39      ((~(p | big_f(X!0))) | (~(p | big_f(X1!1)))),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.39  tff(43,plain,
% 0.19/0.39      (~(p | big_f(X!0))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[42, 39])).
% 0.19/0.39  tff(44,plain,
% 0.19/0.39      ((p | big_f(X!0)) | (~big_f(X!0))),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(45,plain,
% 0.19/0.39      (~big_f(X!0)),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.39  tff(46,assumption,(![X: $i] : (p | big_f(X))), introduced(assumption)).
% 0.19/0.39  tff(47,plain,
% 0.19/0.39      ((p | big_f(X!0)) | (~p)),
% 0.19/0.39      inference(tautology,[status(thm)],[])).
% 0.19/0.39  tff(48,plain,
% 0.19/0.39      (~p),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[47, 43])).
% 0.19/0.39  tff(49,plain,
% 0.19/0.39      (((~![X: $i] : (p | big_f(X))) | (p | big_f(X!0))) <=> ((~![X: $i] : (p | big_f(X))) | p | big_f(X!0))),
% 0.19/0.39      inference(rewrite,[status(thm)],[])).
% 0.19/0.39  tff(50,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) | (p | big_f(X!0))),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(51,plain,
% 0.19/0.39      ((~![X: $i] : (p | big_f(X))) | p | big_f(X!0)),
% 0.19/0.39      inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.39  tff(52,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[51, 48, 46, 45])).
% 0.19/0.39  tff(53,plain,(~![X: $i] : (p | big_f(X))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39  tff(54,plain,
% 0.19/0.39      (![X1: $i] : big_f(X1) | ![X: $i] : (p | big_f(X))),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[33, 48])).
% 0.19/0.39  tff(55,plain,
% 0.19/0.39      (![X1: $i] : big_f(X1)),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.39  tff(56,plain,
% 0.19/0.39      ((~![X1: $i] : big_f(X1)) | big_f(X!0)),
% 0.19/0.39      inference(quant_inst,[status(thm)],[])).
% 0.19/0.39  tff(57,plain,
% 0.19/0.39      ($false),
% 0.19/0.39      inference(unit_resolution,[status(thm)],[56, 55, 45])).
% 0.19/0.39  % SZS output end Proof
%------------------------------------------------------------------------------