TSTP Solution File: SWW600_2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Mon Jun 24 18:17:46 EDT 2024

% Result   : Theorem 3.66s 1.05s
% Output   : CNFRefutation 3.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   14 (   5 unt;   0 typ;   0 def)
%            Number of atoms       :  190 (  48 equ)
%            Maximal formula atoms :   18 (  13 avg)
%            Number of connectives :  141 (  55   ~;   0   |;  72   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (  11 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   90 (  90 fml;   0 var)
%            Number arithmetic     :  299 (  51 atm; 105 fun;  51 num;  92 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   13 (   9 usr;   9 prp; 0-2 aty)
%            Number of functors    :    5 (   0 usr;   1 con; 0-2 aty)
%            Number of variables   :   94 (   2 sgn  48   !;  44   ?;  92   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f83,conjecture,
    ! [X1: $int,X7: $int] :
      ( ( $lesseq(0,X7)
        & $lesseq(0,X1) )
     => ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
          ( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
            & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
            & ( gcd(X1,X7) = gcd(X2,X14) )
            & $lesseq(0,X14)
            & $lesseq(0,X2) )
         => ( ~ $less(0,X14)
           => ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_gcd) ).

tff(f84,negated_conjecture,
    ~ ! [X1: $int,X7: $int] :
        ( ( $lesseq(0,X7)
          & $lesseq(0,X1) )
       => ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
            ( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
              & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
              & ( gcd(X1,X7) = gcd(X2,X14) )
              & $lesseq(0,X14)
              & $lesseq(0,X2) )
           => ( ~ $less(0,X14)
             => ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    inference(negated_conjecture,[],[f83]) ).

tff(f106,plain,
    ~ ! [X1: $int,X7: $int] :
        ( ( ~ $less(X7,0)
          & ~ $less(X1,0) )
       => ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
            ( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
              & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
              & ( gcd(X1,X7) = gcd(X2,X14) )
              & ~ $less(X14,0)
              & ~ $less(X2,0) )
           => ( ~ $less(0,X14)
             => ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    inference(theory_normalization,[],[f84]) ).

tff(f203,plain,
    ~ ! [X0: $int,X1: $int] :
        ( ( ~ $less(X1,0)
          & ~ $less(X0,0) )
       => ! [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
            ( ( ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
              & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
              & ( gcd(X0,X1) = gcd(X7,X6) )
              & ~ $less(X6,0)
              & ~ $less(X7,0) )
           => ( ~ $less(0,X6)
             => ? [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) = X7 ) ) ) ),
    inference(rectify,[],[f106]) ).

tff(f277,plain,
    ? [X0: $int,X1: $int] :
      ( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
          ( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
          & ~ $less(0,X6)
          & ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
          & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
          & ( gcd(X0,X1) = gcd(X7,X6) )
          & ~ $less(X6,0)
          & ~ $less(X7,0) )
      & ~ $less(X1,0)
      & ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f203]) ).

tff(f278,plain,
    ? [X0: $int,X1: $int] :
      ( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
          ( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
          & ~ $less(0,X6)
          & ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
          & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
          & ( gcd(X0,X1) = gcd(X7,X6) )
          & ~ $less(X6,0)
          & ~ $less(X7,0) )
      & ~ $less(X1,0)
      & ~ $less(X0,0) ),
    inference(flattening,[],[f277]) ).

tff(f297,plain,
    ( ? [X0: $int,X1: $int] :
        ( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
            ( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
            & ~ $less(0,X6)
            & ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
            & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
            & ( gcd(X0,X1) = gcd(X7,X6) )
            & ~ $less(X6,0)
            & ~ $less(X7,0) )
        & ~ $less(X1,0)
        & ~ $less(X0,0) )
   => ( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
          ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != X7 )
          & ~ $less(0,X6)
          & ( $sum($product(X3,sK4),$product(X2,sK5)) = X6 )
          & ( $sum($product(X5,sK4),$product(X4,sK5)) = X7 )
          & ( gcd(X7,X6) = gcd(sK4,sK5) )
          & ~ $less(X6,0)
          & ~ $less(X7,0) )
      & ~ $less(sK5,0)
      & ~ $less(sK4,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f298,plain,
    ( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
        ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != X7 )
        & ~ $less(0,X6)
        & ( $sum($product(X3,sK4),$product(X2,sK5)) = X6 )
        & ( $sum($product(X5,sK4),$product(X4,sK5)) = X7 )
        & ( gcd(X7,X6) = gcd(sK4,sK5) )
        & ~ $less(X6,0)
        & ~ $less(X7,0) )
   => ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != sK11 )
      & ~ $less(0,sK10)
      & ( sK10 = $sum($product(sK7,sK4),$product(sK6,sK5)) )
      & ( sK11 = $sum($product(sK9,sK4),$product(sK8,sK5)) )
      & ( gcd(sK4,sK5) = gcd(sK11,sK10) )
      & ~ $less(sK10,0)
      & ~ $less(sK11,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f299,plain,
    ( ! [X8: $int,X9: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != sK11 )
    & ~ $less(0,sK10)
    & ( sK10 = $sum($product(sK7,sK4),$product(sK6,sK5)) )
    & ( sK11 = $sum($product(sK9,sK4),$product(sK8,sK5)) )
    & ( gcd(sK4,sK5) = gcd(sK11,sK10) )
    & ~ $less(sK10,0)
    & ~ $less(sK11,0)
    & ~ $less(sK5,0)
    & ~ $less(sK4,0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f278,f298,f297]) ).

tff(f399,plain,
    sK11 = $sum($product(sK9,sK4),$product(sK8,sK5)),
    inference(cnf_transformation,[],[f299]) ).

tff(f402,plain,
    ! [X8: $int,X9: $int] : ( $sum($product(X8,sK4),$product(X9,sK5)) != sK11 ),
    inference(cnf_transformation,[],[f299]) ).

cnf(c_166,negated_conjecture,
    $sum_int($product_int(X0_3,sK4),$product_int(X1_3,sK5)) != sK11,
    inference(cnf_transformation,[],[f402]) ).

cnf(c_169,negated_conjecture,
    $sum_int($product_int(sK9,sK4),$product_int(sK8,sK5)) = sK11,
    inference(cnf_transformation,[],[f399]) ).

cnf(c_669,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_169,c_166]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.12  % Command  : run_iprover %s %d THM
% 0.13/0.33  % Computer : n005.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 : Wed Jun 19 08:02:24 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.19/0.44  Running TFA theorem proving
% 0.19/0.44  Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.66/1.05  % SZS status Started for theBenchmark.p
% 3.66/1.05  % SZS status Theorem for theBenchmark.p
% 3.66/1.05  
% 3.66/1.05  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.66/1.05  
% 3.66/1.05  ------  iProver source info
% 3.66/1.05  
% 3.66/1.05  git: date: 2024-06-12 09:56:46 +0000
% 3.66/1.05  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 3.66/1.05  git: non_committed_changes: false
% 3.66/1.05  
% 3.66/1.05  ------ Parsing...
% 3.66/1.05  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.66/1.05  
% 3.66/1.05  ------ Preprocessing...
% 3.66/1.05  
% 3.66/1.05  % SZS status Theorem for theBenchmark.p
% 3.66/1.05  
% 3.66/1.05  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.66/1.05  
% 3.66/1.05  
%------------------------------------------------------------------------------