TSTP Solution File: SYN918+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN918+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n016.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 Apr 30 18:11:08 EDT 2024

% Result   : Theorem 0.14s 3.09s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   56 (   1 unt;   0 def)
%            Number of atoms       :  237 (   0 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  292 ( 111   ~; 106   |;  44   &)
%                                         (   9 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   13 (  12 usr;  10 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   67 (  57   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f78,plain,
    $false,
    inference(avatar_sat_refutation,[],[f27,f32,f40,f44,f47,f49,f54,f56,f60,f64,f76]) ).

fof(f76,plain,
    ( ~ spl2_1
    | ~ spl2_7
    | ~ spl2_8 ),
    inference(avatar_contradiction_clause,[],[f75]) ).

fof(f75,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_7
    | ~ spl2_8 ),
    inference(resolution,[],[f73,f22]) ).

fof(f22,plain,
    ( ! [X4] : f(X4)
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f21]) ).

fof(f21,plain,
    ( spl2_1
  <=> ! [X4] : f(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f73,plain,
    ( ! [X0] : ~ f(X0)
    | ~ spl2_7
    | ~ spl2_8 ),
    inference(resolution,[],[f70,f59]) ).

fof(f59,plain,
    ( ! [X4] : g(X4)
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f58,plain,
    ( spl2_7
  <=> ! [X4] : g(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

fof(f70,plain,
    ( ! [X0] :
        ( ~ g(X0)
        | ~ f(X0) )
    | ~ spl2_8 ),
    inference(resolution,[],[f17,f63]) ).

fof(f63,plain,
    ( ! [X4] : ~ h(X4)
    | ~ spl2_8 ),
    inference(avatar_component_clause,[],[f62]) ).

fof(f62,plain,
    ( spl2_8
  <=> ! [X4] : ~ h(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

fof(f17,plain,
    ! [X0] :
      ( h(X0)
      | ~ g(X0)
      | ~ f(X0) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,plain,
    ( ! [X0] :
        ( h(X0)
        | ~ g(X0)
        | ~ f(X0) )
    & ! [X1] :
        ( g(X1)
        | ~ h(X1)
        | ~ f(X1) )
    & ( ! [X2] :
          ( h(X2)
          | ~ f(X2) )
      | ! [X3] :
          ( g(X3)
          | ~ f(X3) ) )
    & ! [X4] :
        ( ( ~ g(sK0)
          & f(sK0) )
        | ( ~ h(X4)
          & g(X4)
          & f(X4) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).

fof(f7,plain,
    ( ? [X5] :
        ( ~ g(X5)
        & f(X5) )
   => ( ~ g(sK0)
      & f(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f6,plain,
    ( ! [X0] :
        ( h(X0)
        | ~ g(X0)
        | ~ f(X0) )
    & ! [X1] :
        ( g(X1)
        | ~ h(X1)
        | ~ f(X1) )
    & ( ! [X2] :
          ( h(X2)
          | ~ f(X2) )
      | ! [X3] :
          ( g(X3)
          | ~ f(X3) ) )
    & ! [X4] :
        ( ? [X5] :
            ( ~ g(X5)
            & f(X5) )
        | ( ~ h(X4)
          & g(X4)
          & f(X4) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,plain,
    ( ! [X5] :
        ( h(X5)
        | ~ g(X5)
        | ~ f(X5) )
    & ! [X4] :
        ( g(X4)
        | ~ h(X4)
        | ~ f(X4) )
    & ( ! [X0] :
          ( h(X0)
          | ~ f(X0) )
      | ! [X1] :
          ( g(X1)
          | ~ f(X1) ) )
    & ! [X2] :
        ( ? [X3] :
            ( ~ g(X3)
            & f(X3) )
        | ( ~ h(X2)
          & g(X2)
          & f(X2) ) ) ),
    inference(flattening,[],[f4]) ).

fof(f4,plain,
    ( ! [X5] :
        ( h(X5)
        | ~ g(X5)
        | ~ f(X5) )
    & ! [X4] :
        ( g(X4)
        | ~ h(X4)
        | ~ f(X4) )
    & ( ! [X0] :
          ( h(X0)
          | ~ f(X0) )
      | ! [X1] :
          ( g(X1)
          | ~ f(X1) ) )
    & ! [X2] :
        ( ? [X3] :
            ( ~ g(X3)
            & f(X3) )
        | ( ~ h(X2)
          & g(X2)
          & f(X2) ) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
    ~ ( ( ( ! [X0] :
              ( f(X0)
             => h(X0) )
          | ! [X1] :
              ( f(X1)
             => g(X1) ) )
        & ! [X2] :
            ( ( ( g(X2)
                & f(X2) )
             => h(X2) )
           => ? [X3] :
                ( ~ g(X3)
                & f(X3) ) ) )
     => ( ! [X4] :
            ( ( h(X4)
              & f(X4) )
           => g(X4) )
       => ? [X5] :
            ( ~ h(X5)
            & g(X5)
            & f(X5) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ( ( ( ! [X3] :
              ( f(X3)
             => h(X3) )
          | ! [X2] :
              ( f(X2)
             => g(X2) ) )
        & ! [X0] :
            ( ( ( g(X0)
                & f(X0) )
             => h(X0) )
           => ? [X1] :
                ( ~ g(X1)
                & f(X1) ) ) )
     => ( ! [X4] :
            ( ( h(X4)
              & f(X4) )
           => g(X4) )
       => ? [X5] :
            ( ~ h(X5)
            & g(X5)
            & f(X5) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ( ( ! [X3] :
            ( f(X3)
           => h(X3) )
        | ! [X2] :
            ( f(X2)
           => g(X2) ) )
      & ! [X0] :
          ( ( ( g(X0)
              & f(X0) )
           => h(X0) )
         => ? [X1] :
              ( ~ g(X1)
              & f(X1) ) ) )
   => ( ! [X4] :
          ( ( h(X4)
            & f(X4) )
         => g(X4) )
     => ? [X5] :
          ( ~ h(X5)
          & g(X5)
          & f(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

fof(f64,plain,
    ( spl2_8
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f14,f29,f62]) ).

fof(f29,plain,
    ( spl2_3
  <=> g(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f14,plain,
    ! [X4] :
      ( ~ g(sK0)
      | ~ h(X4) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f60,plain,
    ( spl2_7
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f13,f29,f58]) ).

fof(f13,plain,
    ! [X4] :
      ( ~ g(sK0)
      | g(X4) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f56,plain,
    ( ~ spl2_2
    | spl2_3
    | ~ spl2_5 ),
    inference(avatar_contradiction_clause,[],[f55]) ).

fof(f55,plain,
    ( $false
    | ~ spl2_2
    | spl2_3
    | ~ spl2_5 ),
    inference(resolution,[],[f26,f52]) ).

fof(f52,plain,
    ( ~ f(sK0)
    | spl2_3
    | ~ spl2_5 ),
    inference(resolution,[],[f51,f31]) ).

fof(f31,plain,
    ( ~ g(sK0)
    | spl2_3 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f51,plain,
    ( ! [X0] :
        ( g(X0)
        | ~ f(X0) )
    | ~ spl2_5 ),
    inference(duplicate_literal_removal,[],[f50]) ).

fof(f50,plain,
    ( ! [X0] :
        ( g(X0)
        | ~ f(X0)
        | ~ f(X0) )
    | ~ spl2_5 ),
    inference(resolution,[],[f16,f39]) ).

fof(f39,plain,
    ( ! [X2] :
        ( h(X2)
        | ~ f(X2) )
    | ~ spl2_5 ),
    inference(avatar_component_clause,[],[f38]) ).

fof(f38,plain,
    ( spl2_5
  <=> ! [X2] :
        ( h(X2)
        | ~ f(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

fof(f16,plain,
    ! [X1] :
      ( ~ h(X1)
      | g(X1)
      | ~ f(X1) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f26,plain,
    ( f(sK0)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f24]) ).

fof(f24,plain,
    ( spl2_2
  <=> f(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f54,plain,
    ( ~ spl2_1
    | spl2_3
    | ~ spl2_5 ),
    inference(avatar_contradiction_clause,[],[f53]) ).

fof(f53,plain,
    ( $false
    | ~ spl2_1
    | spl2_3
    | ~ spl2_5 ),
    inference(resolution,[],[f52,f22]) ).

fof(f49,plain,
    ( ~ spl2_1
    | spl2_3
    | ~ spl2_6 ),
    inference(avatar_contradiction_clause,[],[f48]) ).

fof(f48,plain,
    ( $false
    | ~ spl2_1
    | spl2_3
    | ~ spl2_6 ),
    inference(resolution,[],[f22,f45]) ).

fof(f45,plain,
    ( ~ f(sK0)
    | spl2_3
    | ~ spl2_6 ),
    inference(resolution,[],[f43,f31]) ).

fof(f43,plain,
    ( ! [X3] :
        ( g(X3)
        | ~ f(X3) )
    | ~ spl2_6 ),
    inference(avatar_component_clause,[],[f42]) ).

fof(f42,plain,
    ( spl2_6
  <=> ! [X3] :
        ( g(X3)
        | ~ f(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

fof(f47,plain,
    ( ~ spl2_2
    | spl2_3
    | ~ spl2_6 ),
    inference(avatar_contradiction_clause,[],[f46]) ).

fof(f46,plain,
    ( $false
    | ~ spl2_2
    | spl2_3
    | ~ spl2_6 ),
    inference(resolution,[],[f45,f26]) ).

fof(f44,plain,
    ( ~ spl2_4
    | spl2_6 ),
    inference(avatar_split_clause,[],[f19,f42,f34]) ).

fof(f34,plain,
    ( spl2_4
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

fof(f19,plain,
    ! [X3] :
      ( g(X3)
      | ~ f(X3)
      | ~ sP1 ),
    inference(general_splitting,[],[f15,f18_D]) ).

fof(f18,plain,
    ! [X2] :
      ( h(X2)
      | ~ f(X2)
      | sP1 ),
    inference(cnf_transformation,[],[f18_D]) ).

fof(f18_D,plain,
    ( ! [X2] :
        ( h(X2)
        | ~ f(X2) )
  <=> ~ sP1 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f15,plain,
    ! [X2,X3] :
      ( h(X2)
      | ~ f(X2)
      | g(X3)
      | ~ f(X3) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f40,plain,
    ( spl2_4
    | spl2_5 ),
    inference(avatar_split_clause,[],[f18,f38,f34]) ).

fof(f32,plain,
    ( spl2_1
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f12,f29,f21]) ).

fof(f12,plain,
    ! [X4] :
      ( ~ g(sK0)
      | f(X4) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f27,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f9,f24,f21]) ).

fof(f9,plain,
    ! [X4] :
      ( f(sK0)
      | f(X4) ),
    inference(cnf_transformation,[],[f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/2.84  % Problem    : SYN918+1 : TPTP v8.1.2. Released v3.1.0.
% 0.14/2.86  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/3.07  % Computer : n016.cluster.edu
% 0.14/3.07  % Model    : x86_64 x86_64
% 0.14/3.07  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/3.07  % Memory   : 8042.1875MB
% 0.14/3.07  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/3.07  % CPULimit   : 300
% 0.14/3.07  % WCLimit    : 300
% 0.14/3.07  % DateTime   : Tue Apr 30 02:25:30 EDT 2024
% 0.14/3.07  % CPUTime    : 
% 0.14/3.08  % (26489)Running in auto input_syntax mode. Trying TPTP
% 0.14/3.09  % (26492)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/3.09  % (26492)First to succeed.
% 0.14/3.09  % (26492)Refutation found. Thanks to Tanya!
% 0.14/3.09  % SZS status Theorem for theBenchmark
% 0.14/3.09  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/3.09  % (26492)------------------------------
% 0.14/3.09  % (26492)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/3.09  % (26492)Termination reason: Refutation
% 0.14/3.09  
% 0.14/3.09  % (26492)Memory used [KB]: 761
% 0.14/3.09  % (26492)Time elapsed: 0.003 s
% 0.14/3.09  % (26492)Instructions burned: 4 (million)
% 0.14/3.09  % (26492)------------------------------
% 0.14/3.09  % (26492)------------------------------
% 0.14/3.09  % (26489)Success in time 0.011 s
%------------------------------------------------------------------------------