TSTP Solution File: ARI688_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI688_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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 : Tue Sep  6 17:02:36 EDT 2022

% Result   : Theorem 0.19s 0.37s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   37 (  20 unt;   3 typ;   0 def)
%            Number of atoms       :   48 (  41 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   28 (  14   ~;   0   |;   0   &)
%                                         (  14 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number arithmetic     :  246 (   0 atm; 132 fun; 114 num;   0 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   0 usr;   2 prp; 0-2 aty)
%            Number of functors    :   16 (   3 usr;  13 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(a_type,type,
    a: $int ).

tff(b_type,type,
    b: $int ).

tff(x_type,type,
    x: $int ).

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

tff(2,plain,
    ( ( 0 = 0 )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    $sum($product(8,x),$sum($product(-28173120816,x),$product(28173120808,x))) = 0,
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    $product(287,$product(98164184,x)) = $product(28173120808,x),
    inference(rewrite,[status(thm)],]) ).

tff(5,plain,
    ( ( $product(98164184,x) = a )
  <=> ( a = $product(98164184,x) ) ),
    inference(commutativity,[status(thm)],]) ).

tff(6,plain,
    ( ( $product(98164184,x) = a )
  <=> ( $product(98164184,x) = a ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    $product(98164184,x) = a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq1) ).

tff(8,plain,
    $product(98164184,x) = a,
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    a = $product(98164184,x),
    inference(modus_ponens,[status(thm)],[8,5]) ).

tff(10,plain,
    $product(287,a) = $product(287,$product(98164184,x)),
    inference(monotonicity,[status(thm)],[9]) ).

tff(11,plain,
    $product(287,a) = $product(28173120808,x),
    inference(transitivity,[status(thm)],[10,4]) ).

tff(12,plain,
    $product(-4353078,$product(6472,x)) = $product(-28173120816,x),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ( ( $product(6472,x) = b )
  <=> ( b = $product(6472,x) ) ),
    inference(commutativity,[status(thm)],]) ).

tff(14,plain,
    ( ( $product(6472,x) = b )
  <=> ( $product(6472,x) = b ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    $product(6472,x) = b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq2) ).

tff(16,plain,
    $product(6472,x) = b,
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    b = $product(6472,x),
    inference(modus_ponens,[status(thm)],[16,13]) ).

tff(18,plain,
    $product(-4353078,b) = $product(-4353078,$product(6472,x)),
    inference(monotonicity,[status(thm)],[17]) ).

tff(19,plain,
    $product(-4353078,b) = $product(-28173120816,x),
    inference(transitivity,[status(thm)],[18,12]) ).

tff(20,plain,
    $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = $sum($product(8,x),$sum($product(-28173120816,x),$product(28173120808,x))),
    inference(monotonicity,[status(thm)],[19,11]) ).

tff(21,plain,
    $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0,
    inference(transitivity,[status(thm)],[20,3]) ).

tff(22,plain,
    ( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 )
  <=> ( 0 = 0 ) ),
    inference(monotonicity,[status(thm)],[21]) ).

tff(23,plain,
    ( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 )
  <=> $true ),
    inference(transitivity,[status(thm)],[22,2]) ).

tff(24,plain,
    ( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[23]) ).

tff(25,plain,
    ( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
  <=> $false ),
    inference(transitivity,[status(thm)],[24,1]) ).

tff(26,plain,
    ( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 )
  <=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) = 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
  <=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 ) ),
    inference(monotonicity,[status(thm)],[26]) ).

tff(28,plain,
    ( ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 )
  <=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,plain,
    ( ( $sum($product(8,x),$product(-1,$difference($product(4353078,b),$product(287,a)))) != 0 )
  <=> ( $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0 ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,axiom,
    $sum($product(8,x),$product(-1,$difference($product(4353078,b),$product(287,a)))) != 0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

tff(31,plain,
    $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0,
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0,
    inference(modus_ponens,[status(thm)],[31,28]) ).

tff(33,plain,
    $sum($product(8,x),$sum($product(-4353078,b),$product(287,a))) != 0,
    inference(modus_ponens,[status(thm)],[32,27]) ).

tff(34,plain,
    $false,
    inference(modus_ponens,[status(thm)],[33,25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ARI688_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n006.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue Aug 30 01:38:40 EDT 2022
% 0.13/0.33  % 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.
% 0.19/0.37  % SZS status Theorem
% 0.19/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------