TSTP Solution File: NUM490+3 by Z3---4.8.9.0

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%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM490+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n018.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 13:10:02 EDT 2022

% Result   : Theorem 0.20s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   26 (   8 unt;   7 typ;   0 def)
%            Number of atoms       :   30 (  23 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   23 (  12   ~;   1   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   0 usr;   2 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
    sdtasdt0: ( $i * $i ) > $i ).

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

tff(xn_type,type,
    xn: $i ).

tff(sdtpldt0_type,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(sdtmndt0_type,type,
    sdtmndt0: ( $i * $i ) > $i ).

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

tff(xr_type,type,
    xr: $i ).

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

tff(2,plain,
    ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,xm) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) )
  <=> ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) )
  <=> ( sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).

tff(6,plain,
    sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)),
    inference(modus_ponens,[status(thm)],[6,3]) ).

tff(8,plain,
    sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) = sdtasdt0(xn,xm),
    inference(symmetry,[status(thm)],[7]) ).

tff(9,plain,
    ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) = sdtasdt0(xn,xm) )
  <=> ( sdtasdt0(xn,xm) = sdtasdt0(xn,xm) ) ),
    inference(monotonicity,[status(thm)],[8]) ).

tff(10,plain,
    ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) = sdtasdt0(xn,xm) )
  <=> $true ),
    inference(transitivity,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[10]) ).

tff(12,plain,
    ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm) )
  <=> $false ),
    inference(transitivity,[status(thm)],[11,1]) ).

tff(13,plain,
    ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) )
  <=> ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) )
  <=> ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    ~ ( ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) )
      | ( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(16,plain,
    sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm),
    inference(or_elim,[status(thm)],[15]) ).

tff(17,plain,
    sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm),
    inference(modus_ponens,[status(thm)],[16,14]) ).

tff(18,plain,
    sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sdtmndt0(xn,xp),xm)) != sdtasdt0(xn,xm),
    inference(modus_ponens,[status(thm)],[17,13]) ).

tff(19,plain,
    $false,
    inference(modus_ponens,[status(thm)],[18,12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM490+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n018.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 : Fri Sep  2 11:07:43 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35  Usage: tptp [options] [-file:]file
% 0.20/0.35    -h, -?       prints this message.
% 0.20/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.20/0.35    -m, -model   generate model.
% 0.20/0.35    -p, -proof   generate proof.
% 0.20/0.35    -c, -core    generate unsat core of named formulas.
% 0.20/0.35    -st, -statistics display statistics.
% 0.20/0.35    -t:timeout   set timeout (in second).
% 0.20/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.20/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35    -<param>:<value> configuration parameter and value.
% 0.20/0.35    -o:<output-file> file to place output in.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------