TSTP Solution File: SWV488+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV488+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 May  5 11:00:05 EDT 2024

% Result   : Theorem 0.14s 0.32s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   52 (  16 unt;   0 def)
%            Number of atoms       :  210 (  51 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  262 ( 104   ~;  86   |;  52   &)
%                                         (   3 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   61 (  55   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f445,plain,
    $false,
    inference(avatar_sat_refutation,[],[f284,f408,f411,f441,f444]) ).

fof(f444,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f443]) ).

fof(f443,plain,
    ( $false
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f442,f37]) ).

fof(f37,plain,
    int_leq(sK0,n),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ( real_zero = a(sK0,sK1)
    & sK0 = sK1
    & int_leq(sK0,n)
    & int_leq(sK1,sK0)
    & int_leq(int_one,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f26]) ).

fof(f26,plain,
    ( ? [X0,X1] :
        ( real_zero = a(X0,X1)
        & X0 = X1
        & int_leq(X0,n)
        & int_leq(X1,X0)
        & int_leq(int_one,X1) )
   => ( real_zero = a(sK0,sK1)
      & sK0 = sK1
      & int_leq(sK0,n)
      & int_leq(sK1,sK0)
      & int_leq(int_one,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1] :
      ( real_zero = a(X0,X1)
      & X0 = X1
      & int_leq(X0,n)
      & int_leq(X1,X0)
      & int_leq(int_one,X1) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ? [X0,X1] :
      ( real_zero = a(X0,X1)
      & X0 = X1
      & int_leq(X0,n)
      & int_leq(X1,X0)
      & int_leq(int_one,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( int_leq(X0,n)
          & int_leq(X1,X0)
          & int_leq(int_one,X1) )
       => ( X0 = X1
         => real_zero != a(X0,X1) ) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0,X1] :
      ( ( int_leq(X0,n)
        & int_leq(X1,X0)
        & int_leq(int_one,X1) )
     => ( X0 = X1
       => real_zero != a(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',uti) ).

fof(f442,plain,
    ( ~ int_leq(sK0,n)
    | ~ spl3_1 ),
    inference(forward_demodulation,[],[f420,f38]) ).

fof(f38,plain,
    sK0 = sK1,
    inference(cnf_transformation,[],[f27]) ).

fof(f420,plain,
    ( ~ int_leq(sK1,n)
    | ~ spl3_1 ),
    inference(resolution,[],[f280,f35]) ).

fof(f35,plain,
    int_leq(int_one,sK1),
    inference(cnf_transformation,[],[f27]) ).

fof(f280,plain,
    ( ! [X0] :
        ( ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f279]) ).

fof(f279,plain,
    ( spl3_1
  <=> ! [X0] :
        ( ~ int_leq(X0,n)
        | ~ int_leq(int_one,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f441,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f440]) ).

fof(f440,plain,
    ( $false
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f419,f37]) ).

fof(f419,plain,
    ( ~ int_leq(sK0,n)
    | ~ spl3_1 ),
    inference(resolution,[],[f280,f65]) ).

fof(f65,plain,
    int_leq(int_one,sK0),
    inference(superposition,[],[f35,f38]) ).

fof(f411,plain,
    ~ spl3_2,
    inference(avatar_contradiction_clause,[],[f410]) ).

fof(f410,plain,
    ( $false
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f409,f37]) ).

fof(f409,plain,
    ( ~ int_leq(sK0,n)
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f387,f65]) ).

fof(f387,plain,
    ( ~ int_leq(int_one,sK0)
    | ~ int_leq(sK0,n)
    | ~ spl3_2 ),
    inference(resolution,[],[f384,f63]) ).

fof(f63,plain,
    ! [X1] : int_leq(X1,X1),
    inference(equality_resolution,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( int_leq(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( int_leq(X0,X1)
        | ( X0 != X1
          & ~ int_less(X0,X1) ) )
      & ( X0 = X1
        | int_less(X0,X1)
        | ~ int_leq(X0,X1) ) ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( int_leq(X0,X1)
        | ( X0 != X1
          & ~ int_less(X0,X1) ) )
      & ( X0 = X1
        | int_less(X0,X1)
        | ~ int_leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( int_leq(X0,X1)
    <=> ( X0 = X1
        | int_less(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).

fof(f384,plain,
    ( ! [X0] :
        ( ~ int_leq(sK0,X0)
        | ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n) )
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f383,f38]) ).

fof(f383,plain,
    ( ! [X0] :
        ( ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n)
        | ~ int_leq(sK1,X0) )
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f382,f43]) ).

fof(f43,plain,
    real_zero != real_one,
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    real_zero != real_one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).

fof(f382,plain,
    ( ! [X0] :
        ( real_zero = real_one
        | ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n)
        | ~ int_leq(sK1,X0) )
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f381,f66]) ).

fof(f66,plain,
    real_zero = a(sK0,sK0),
    inference(forward_demodulation,[],[f39,f38]) ).

fof(f39,plain,
    real_zero = a(sK0,sK1),
    inference(cnf_transformation,[],[f27]) ).

fof(f381,plain,
    ( ! [X0] :
        ( real_one = a(sK0,sK0)
        | ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n)
        | ~ int_leq(sK1,X0) )
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f356,f38]) ).

fof(f356,plain,
    ( ! [X0] :
        ( ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n)
        | real_one = a(sK1,sK1)
        | ~ int_leq(sK1,X0) )
    | ~ spl3_2 ),
    inference(resolution,[],[f283,f35]) ).

fof(f283,plain,
    ( ! [X1,X4] :
        ( ~ int_leq(int_one,X4)
        | ~ int_leq(int_one,X1)
        | ~ int_leq(X1,n)
        | real_one = a(X4,X4)
        | ~ int_leq(X4,X1) )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f282,plain,
    ( spl3_2
  <=> ! [X4,X1] :
        ( real_one = a(X4,X4)
        | ~ int_leq(int_one,X1)
        | ~ int_leq(X1,n)
        | ~ int_leq(int_one,X4)
        | ~ int_leq(X4,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f408,plain,
    ~ spl3_2,
    inference(avatar_contradiction_clause,[],[f407]) ).

fof(f407,plain,
    ( $false
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f406,f37]) ).

fof(f406,plain,
    ( ~ int_leq(sK0,n)
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f386,f65]) ).

fof(f386,plain,
    ( ~ int_leq(int_one,sK0)
    | ~ int_leq(sK0,n)
    | ~ spl3_2 ),
    inference(resolution,[],[f384,f64]) ).

fof(f64,plain,
    int_leq(sK0,sK0),
    inference(superposition,[],[f36,f38]) ).

fof(f36,plain,
    int_leq(sK1,sK0),
    inference(cnf_transformation,[],[f27]) ).

fof(f284,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f41,f282,f279]) ).

fof(f41,plain,
    ! [X0,X1,X4] :
      ( real_one = a(X4,X4)
      | ~ int_leq(X4,X1)
      | ~ int_leq(int_one,X4)
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ! [X3] :
                ( real_zero = a(X3,plus(X3,X2))
                | ~ int_leq(X3,X0)
                | ~ int_leq(int_one,X3) )
            | plus(X0,X2) != X1
            | ~ int_less(int_zero,X2) )
        & ! [X4] :
            ( real_one = a(X4,X4)
            | ~ int_leq(X4,X1)
            | ~ int_leq(int_one,X4) )
        & ! [X5] :
            ( ! [X6] :
                ( real_zero = a(plus(X6,X5),X6)
                | ~ int_leq(X6,X1)
                | ~ int_leq(int_one,X6) )
            | plus(X1,X5) != X0
            | ~ int_less(int_zero,X5) ) )
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ! [X3] :
                ( real_zero = a(X3,plus(X3,X2))
                | ~ int_leq(X3,X0)
                | ~ int_leq(int_one,X3) )
            | plus(X0,X2) != X1
            | ~ int_less(int_zero,X2) )
        & ! [X4] :
            ( real_one = a(X4,X4)
            | ~ int_leq(X4,X1)
            | ~ int_leq(int_one,X4) )
        & ! [X5] :
            ( ! [X6] :
                ( real_zero = a(plus(X6,X5),X6)
                | ~ int_leq(X6,X1)
                | ~ int_leq(int_one,X6) )
            | plus(X1,X5) != X0
            | ~ int_less(int_zero,X5) ) )
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( int_leq(X1,n)
        & int_leq(int_one,X1)
        & int_leq(X0,n)
        & int_leq(int_one,X0) )
     => ( ! [X2] :
            ( ( plus(X0,X2) = X1
              & int_less(int_zero,X2) )
           => ! [X3] :
                ( ( int_leq(X3,X0)
                  & int_leq(int_one,X3) )
               => real_zero = a(X3,plus(X3,X2)) ) )
        & ! [X4] :
            ( ( int_leq(X4,X1)
              & int_leq(int_one,X4) )
           => real_one = a(X4,X4) )
        & ! [X5] :
            ( ( plus(X1,X5) = X0
              & int_less(int_zero,X5) )
           => ! [X6] :
                ( ( int_leq(X6,X1)
                  & int_leq(int_one,X6) )
               => real_zero = a(plus(X6,X5),X6) ) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( ( int_leq(X1,n)
        & int_leq(int_one,X1)
        & int_leq(X0,n)
        & int_leq(int_one,X0) )
     => ( ! [X7] :
            ( ( plus(X0,X7) = X1
              & int_less(int_zero,X7) )
           => ! [X2] :
                ( ( int_leq(X2,X0)
                  & int_leq(int_one,X2) )
               => real_zero = a(X2,plus(X2,X7)) ) )
        & ! [X2] :
            ( ( int_leq(X2,X1)
              & int_leq(int_one,X2) )
           => real_one = a(X2,X2) )
        & ! [X7] :
            ( ( plus(X1,X7) = X0
              & int_less(int_zero,X7) )
           => ! [X2] :
                ( ( int_leq(X2,X1)
                  & int_leq(int_one,X2) )
               => real_zero = a(plus(X2,X7),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qii) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : SWV488+3 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Fri May  3 21:15:22 EDT 2024
% 0.10/0.29  % CPUTime    : 
% 0.10/0.29  % (17765)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.30  % (17767)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.30  % (17769)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.30  TRYING [1]
% 0.10/0.30  TRYING [2]
% 0.10/0.30  TRYING [3]
% 0.10/0.31  % (17772)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.31  % (17768)WARNING: value z3 for option sas not known
% 0.10/0.31  % (17771)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.31  TRYING [4]
% 0.10/0.31  % (17766)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.31  % (17770)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.10/0.31  % (17768)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.31  TRYING [1]
% 0.10/0.31  TRYING [2]
% 0.10/0.31  TRYING [5]
% 0.10/0.31  TRYING [3]
% 0.14/0.31  TRYING [1]
% 0.14/0.31  TRYING [2]
% 0.14/0.31  TRYING [4]
% 0.14/0.32  TRYING [5]
% 0.14/0.32  % (17768)First to succeed.
% 0.14/0.32  % (17768)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17765"
% 0.14/0.32  % (17768)Refutation found. Thanks to Tanya!
% 0.14/0.32  % SZS status Theorem for theBenchmark
% 0.14/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.32  % (17768)------------------------------
% 0.14/0.32  % (17768)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.32  % (17768)Termination reason: Refutation
% 0.14/0.32  
% 0.14/0.32  % (17768)Memory used [KB]: 898
% 0.14/0.32  % (17768)Time elapsed: 0.015 s
% 0.14/0.32  % (17768)Instructions burned: 22 (million)
% 0.14/0.32  % (17765)Success in time 0.029 s
%------------------------------------------------------------------------------