TSTP Solution File: SYN052+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n005.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 23:53:22 EDT 2022

% Result   : Theorem 0.20s 0.38s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Sep  5 01:23:03 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34  Usage: tptp [options] [-file:]file
% 0.14/0.34    -h, -?       prints this message.
% 0.14/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.34    -m, -model   generate model.
% 0.14/0.34    -p, -proof   generate proof.
% 0.14/0.34    -c, -core    generate unsat core of named formulas.
% 0.14/0.34    -st, -statistics display statistics.
% 0.14/0.34    -t:timeout   set timeout (in second).
% 0.14/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34    -<param>:<value> configuration parameter and value.
% 0.14/0.34    -o:<output-file> file to place output in.
% 0.20/0.38  % SZS status Theorem
% 0.20/0.38  % SZS output start Proof
% 0.20/0.38  tff(big_f_type, type, (
% 0.20/0.38     big_f: $i > $o)).
% 0.20/0.38  tff(tptp_fun_X1_0_type, type, (
% 0.20/0.38     tptp_fun_X1_0: $i)).
% 0.20/0.38  tff(p_type, type, (
% 0.20/0.38     p: $o)).
% 0.20/0.38  tff(1,assumption,(~big_f(X1!0)), introduced(assumption)).
% 0.20/0.38  tff(2,plain,
% 0.20/0.38      (^[X: $i] : refl((p <=> big_f(X)) <=> (p <=> big_f(X)))),
% 0.20/0.38      inference(bind,[status(th)],[])).
% 0.20/0.38  tff(3,plain,
% 0.20/0.38      (![X: $i] : (p <=> big_f(X)) <=> ![X: $i] : (p <=> big_f(X))),
% 0.20/0.38      inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38  tff(4,plain,
% 0.20/0.38      (![X: $i] : (p <=> big_f(X)) <=> ![X: $i] : (p <=> big_f(X))),
% 0.20/0.38      inference(rewrite,[status(thm)],[])).
% 0.20/0.38  tff(5,plain,
% 0.20/0.38      ((~(![X: $i] : (p <=> big_f(X)) => (p <=> ![X1: $i] : big_f(X1)))) <=> (~((~![X: $i] : (p <=> big_f(X))) | (p <=> ![X1: $i] : big_f(X1))))),
% 0.20/0.38      inference(rewrite,[status(thm)],[])).
% 0.20/0.38  tff(6,axiom,(~(![X: $i] : (p <=> big_f(X)) => (p <=> ![X1: $i] : big_f(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel22')).
% 0.20/0.38  tff(7,plain,
% 0.20/0.38      (~((~![X: $i] : (p <=> big_f(X))) | (p <=> ![X1: $i] : big_f(X1)))),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38  tff(8,plain,
% 0.20/0.38      (![X: $i] : (p <=> big_f(X))),
% 0.20/0.38      inference(or_elim,[status(thm)],[7])).
% 0.20/0.38  tff(9,plain,
% 0.20/0.38      (![X: $i] : (p <=> big_f(X))),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.38  tff(10,plain,(
% 0.20/0.38      ![X: $i] : (p <=> big_f(X))),
% 0.20/0.38      inference(skolemize,[status(sab)],[9])).
% 0.20/0.38  tff(11,plain,
% 0.20/0.38      (![X: $i] : (p <=> big_f(X))),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.38  tff(12,plain,
% 0.20/0.38      ((~![X: $i] : (p <=> big_f(X))) | (p <=> big_f(X1!0))),
% 0.20/0.38      inference(quant_inst,[status(thm)],[])).
% 0.20/0.38  tff(13,plain,
% 0.20/0.38      (p <=> big_f(X1!0)),
% 0.20/0.38      inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.38  tff(14,plain,
% 0.20/0.38      ((~(p <=> big_f(X1!0))) | (~p) | big_f(X1!0)),
% 0.20/0.38      inference(tautology,[status(thm)],[])).
% 0.20/0.38  tff(15,plain,
% 0.20/0.38      ((~(p <=> big_f(X1!0))) | (~p)),
% 0.20/0.38      inference(unit_resolution,[status(thm)],[14, 1])).
% 0.20/0.38  tff(16,plain,
% 0.20/0.38      (~p),
% 0.20/0.38      inference(unit_resolution,[status(thm)],[15, 13])).
% 0.20/0.38  tff(17,plain,
% 0.20/0.38      ((p | ![X1: $i] : big_f(X1)) <=> (p | ![X1: $i] : big_f(X1))),
% 0.20/0.38      inference(rewrite,[status(thm)],[])).
% 0.20/0.38  tff(18,plain,
% 0.20/0.38      ((((~(~p)) | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0)))) <=> ((p | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0))))),
% 0.20/0.38      inference(rewrite,[status(thm)],[])).
% 0.20/0.38  tff(19,plain,
% 0.20/0.38      (((~p) <=> ![X1: $i] : big_f(X1)) <=> ((~p) <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38      inference(rewrite,[status(thm)],[])).
% 0.20/0.38  tff(20,plain,
% 0.20/0.38      ((~(p <=> ![X1: $i] : big_f(X1))) <=> ((~p) <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38      inference(rewrite,[status(thm)],[])).
% 0.20/0.38  tff(21,plain,
% 0.20/0.38      ((p <=> ![X1: $i] : big_f(X1)) <=> (p <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38      inference(rewrite,[status(thm)],[])).
% 0.20/0.38  tff(22,plain,
% 0.20/0.38      ((~(p <=> ![X1: $i] : big_f(X1))) <=> (~(p <=> ![X1: $i] : big_f(X1)))),
% 0.20/0.38      inference(monotonicity,[status(thm)],[21])).
% 0.20/0.38  tff(23,plain,
% 0.20/0.38      ((~(p <=> ![X1: $i] : big_f(X1))) <=> ((~p) <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38      inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.38  tff(24,plain,
% 0.20/0.38      (~(p <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38      inference(or_elim,[status(thm)],[7])).
% 0.20/0.38  tff(25,plain,
% 0.20/0.38      ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38  tff(26,plain,
% 0.20/0.38      ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[25, 19])).
% 0.20/0.38  tff(27,plain,
% 0.20/0.38      ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.38  tff(28,plain,
% 0.20/0.38      ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[27, 19])).
% 0.20/0.38  tff(29,plain,
% 0.20/0.38      ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[28, 19])).
% 0.20/0.38  tff(30,plain,
% 0.20/0.38      ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[29, 19])).
% 0.20/0.38  tff(31,plain,(
% 0.20/0.38      ((~(~p)) | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0)))),
% 0.20/0.38      inference(skolemize,[status(sab)],[30])).
% 0.20/0.38  tff(32,plain,
% 0.20/0.38      ((p | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0)))),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[31, 18])).
% 0.20/0.38  tff(33,plain,
% 0.20/0.38      (p | ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(and_elim,[status(thm)],[32])).
% 0.20/0.38  tff(34,plain,
% 0.20/0.38      (p | ![X1: $i] : big_f(X1)),
% 0.20/0.38      inference(modus_ponens,[status(thm)],[33, 17])).
% 0.20/0.39  tff(35,plain,
% 0.20/0.39      (![X1: $i] : big_f(X1)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[34, 16])).
% 0.20/0.39  tff(36,plain,
% 0.20/0.39      ((~![X1: $i] : big_f(X1)) | big_f(X1!0)),
% 0.20/0.39      inference(quant_inst,[status(thm)],[])).
% 0.20/0.39  tff(37,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[36, 35, 1])).
% 0.20/0.39  tff(38,plain,(big_f(X1!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39  tff(39,plain,
% 0.20/0.39      ((~p) | (~big_f(X1!0))),
% 0.20/0.39      inference(and_elim,[status(thm)],[32])).
% 0.20/0.39  tff(40,plain,
% 0.20/0.39      (~p),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.39  tff(41,plain,
% 0.20/0.39      ((~(p <=> big_f(X1!0))) | p | (~big_f(X1!0))),
% 0.20/0.39      inference(tautology,[status(thm)],[])).
% 0.20/0.39  tff(42,plain,
% 0.20/0.39      (~(p <=> big_f(X1!0))),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[41, 40, 38])).
% 0.20/0.39  tff(43,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[12, 11, 42])).
% 0.20/0.39  % SZS output end Proof
%------------------------------------------------------------------------------