TSTP Solution File: NUM625+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM625+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n001.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 13:10:59 EDT 2022

% Result   : Theorem 0.17s 0.42s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   30 (   8 unt;  10 typ;   0 def)
%            Number of atoms       :   35 (  23 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   28 (  13   ~;   0   |;   5   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(szmzizndt0_type,type,
    szmzizndt0: $i > $i ).

tff(xQ_type,type,
    xQ: $i ).

tff(sdtlpdtrp0_type,type,
    sdtlpdtrp0: ( $i * $i ) > $i ).

tff(xm_type,type,
    xm: $i ).

tff(xe_type,type,
    xe: $i ).

tff(xx_type,type,
    xx: $i ).

tff(xp_type,type,
    xp: $i ).

tff(aElementOf0_type,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(aElement0_type,type,
    aElement0: $i > $o ).

tff(xP_type,type,
    xP: $i ).

tff(1,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ( szmzizndt0(xQ) = szmzizndt0(xQ) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( xp = xx )
  <=> ( szmzizndt0(xQ) = sdtlpdtrp0(xe,xm) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ( xp = xx )
  <=> ( xp = xx ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    xp = xx,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5496) ).

tff(6,plain,
    xp = xx,
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    szmzizndt0(xQ) = sdtlpdtrp0(xe,xm),
    inference(modus_ponens,[status(thm)],[6,3]) ).

tff(8,plain,
    sdtlpdtrp0(xe,xm) = szmzizndt0(xQ),
    inference(symmetry,[status(thm)],[7]) ).

tff(9,plain,
    ( ( sdtlpdtrp0(xe,xm) = szmzizndt0(xQ) )
  <=> ( szmzizndt0(xQ) = szmzizndt0(xQ) ) ),
    inference(monotonicity,[status(thm)],[8]) ).

tff(10,plain,
    ( ( sdtlpdtrp0(xe,xm) = szmzizndt0(xQ) )
  <=> $true ),
    inference(transitivity,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ( sdtlpdtrp0(xe,xm) != szmzizndt0(xQ) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[10]) ).

tff(12,plain,
    ( ( sdtlpdtrp0(xe,xm) != szmzizndt0(xQ) )
  <=> $false ),
    inference(transitivity,[status(thm)],[11,1]) ).

tff(13,plain,
    ( ( xx != szmzizndt0(xQ) )
  <=> ( sdtlpdtrp0(xe,xm) != szmzizndt0(xQ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( ( xx != szmzizndt0(xQ) )
  <=> ( xx != szmzizndt0(xQ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    ( aElement0(xx)
    & aElementOf0(xx,xQ)
    & ( xx != szmzizndt0(xQ) )
    & aElementOf0(xx,xP) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).

tff(16,plain,
    ( aElement0(xx)
    & aElementOf0(xx,xQ)
    & ( xx != szmzizndt0(xQ) ) ),
    inference(and_elim,[status(thm)],[15]) ).

tff(17,plain,
    xx != szmzizndt0(xQ),
    inference(and_elim,[status(thm)],[16]) ).

tff(18,plain,
    xx != szmzizndt0(xQ),
    inference(modus_ponens,[status(thm)],[17,14]) ).

tff(19,plain,
    sdtlpdtrp0(xe,xm) != szmzizndt0(xQ),
    inference(modus_ponens,[status(thm)],[18,13]) ).

tff(20,plain,
    $false,
    inference(modus_ponens,[status(thm)],[19,12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : NUM625+3 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.11  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31  % Computer : n001.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Fri Sep  2 12:49:53 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.11/0.32  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32  Usage: tptp [options] [-file:]file
% 0.11/0.32    -h, -?       prints this message.
% 0.11/0.32    -smt2        print SMT-LIB2 benchmark.
% 0.11/0.32    -m, -model   generate model.
% 0.11/0.32    -p, -proof   generate proof.
% 0.11/0.32    -c, -core    generate unsat core of named formulas.
% 0.11/0.32    -st, -statistics display statistics.
% 0.11/0.32    -t:timeout   set timeout (in second).
% 0.11/0.32    -smt2status  display status in smt2 format instead of SZS.
% 0.11/0.32    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32    -<param>:<value> configuration parameter and value.
% 0.11/0.32    -o:<output-file> file to place output in.
% 0.17/0.42  % SZS status Theorem
% 0.17/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------