TSTP Solution File: SWW600_2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW600_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.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 : Fri May  3 03:25:36 EDT 2024

% Result   : Theorem 0.45s 1.14s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   33 (  24 unt;   0 typ;   0 def)
%            Number of atoms       :  227 (  67 equ)
%            Maximal formula atoms :   18 (   6 avg)
%            Number of connectives :  143 (  57   ~;   0   |;  72   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :  108 ( 108 fml;   0 var)
%            Number arithmetic     :  336 (  51 atm; 117 fun;  51 num; 117 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   :  138 (   6 sgn  73   !;  44   ?; 117   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f70,axiom,
    ! [X1: $int,X7: $int,X4: $int] : ( gcd(gcd(X1,X7),X4) = gcd(X1,gcd(X7,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assoc) ).

tff(f71,axiom,
    ! [X1: $int,X7: $int] : ( gcd(X1,X7) = gcd(X7,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',comm) ).

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/sandbox/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(f107,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_138,[]) ).

tff(f108,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_139,[]) ).

tff(f118,plain,
    ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
    introduced(theory_axiom_138,[]) ).

tff(f119,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
    introduced(theory_axiom_139,[]) ).

tff(f194,plain,
    ! [X0: $int,X1: $int,X2: $int] : ( gcd(gcd(X0,X1),X2) = gcd(X0,gcd(X1,X2)) ),
    inference(rectify,[],[f70]) ).

tff(f195,plain,
    ! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
    inference(rectify,[],[f71]) ).

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(f381,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( gcd(gcd(X0,X1),X2) = gcd(X0,gcd(X1,X2)) ),
    inference(cnf_transformation,[],[f194]) ).

tff(f382,plain,
    ! [X0: $int,X1: $int] : ( gcd(X0,X1) = gcd(X1,X0) ),
    inference(cnf_transformation,[],[f195]) ).

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_59,plain,
    $product_int($product_int(X0_3,X1_3),X2_3) = $product_int(X0_3,$product_int(X1_3,X2_3)),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_60,plain,
    $product_int(X0_3,X1_3) = $product_int(X1_3,X0_3),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_70,plain,
    $sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3)),
    inference(cnf_transformation,[],[f108]) ).

cnf(c_71,plain,
    $sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_153,plain,
    gcd(gcd(X0_3,X1_3),X2_3) = gcd(X0_3,gcd(X1_3,X2_3)),
    inference(cnf_transformation,[],[f381]) ).

cnf(c_154,plain,
    gcd(X0_3,X1_3) = gcd(X1_3,X0_3),
    inference(cnf_transformation,[],[f382]) ).

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_263,negated_conjecture,
    $sum_int($product_int(sK4,sK9),$product_int(sK5,sK8)) = sK11,
    inference(theory_normalisation,[status(thm)],[c_169,c_153,c_154,c_59,c_60,c_70,c_71]) ).

cnf(c_4397,plain,
    $sum_int($product_int(sK4,X0_3),$product_int(X1_3,sK5)) != sK11,
    inference(superposition,[status(thm)],[c_60,c_166]) ).

cnf(c_4477,plain,
    $sum_int($product_int(sK4,X0_3),$product_int(sK5,X1_3)) != sK11,
    inference(superposition,[status(thm)],[c_60,c_4397]) ).

cnf(c_4483,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_263,c_4477]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW600_2 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May  2 22:17:04 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  Running TFA theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.45/1.14  % SZS status Started for theBenchmark.p
% 0.45/1.14  % SZS status Theorem for theBenchmark.p
% 0.45/1.14  
% 0.45/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.14  
% 0.45/1.14  ------  iProver source info
% 0.45/1.14  
% 0.45/1.14  git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.14  git: non_committed_changes: false
% 0.45/1.14  
% 0.45/1.14  ------ Parsing...
% 0.45/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.45/1.14  
% 0.45/1.14  ------ Preprocessing... sup_sim: 2  sf_s  rm: 18 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 10 0s  sf_e  pe_s  pe_e 
% 0.45/1.14  
% 0.45/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.45/1.14  
% 0.45/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.45/1.14  ------ Proving...
% 0.45/1.14  ------ Problem Properties 
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  clauses                                 109
% 0.45/1.14  conjectures                             9
% 0.45/1.14  EPR                                     19
% 0.45/1.14  Horn                                    76
% 0.45/1.14  unary                                   41
% 0.45/1.14  binary                                  40
% 0.45/1.14  lits                                    214
% 0.45/1.14  lits eq                                 75
% 0.45/1.14  fd_pure                                 1
% 0.45/1.14  fd_pseudo                               0
% 0.45/1.14  fd_cond                                 15
% 0.45/1.14  fd_pseudo_cond                          6
% 0.45/1.14  AC symbols                              3
% 0.45/1.14  
% 0.45/1.14  ------ Input Options Time Limit: Unbounded
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  ------ 
% 0.45/1.14  Current options:
% 0.45/1.14  ------ 
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  ------ Proving...
% 0.45/1.14  
% 0.45/1.14  
% 0.45/1.14  % SZS status Theorem for theBenchmark.p
% 0.45/1.14  
% 0.45/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.14  
% 0.45/1.14  
%------------------------------------------------------------------------------