TSTP Solution File: SYN070+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN070+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 12:08:47 EDT 2024

% Result   : Theorem 0.14s 0.36s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   70 (   4 unt;   0 def)
%            Number of atoms       :  232 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  273 ( 111   ~; 106   |;  32   &)
%                                         (  13 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   18 (  17 usr;  14 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   68 (  58   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f88,plain,
    $false,
    inference(avatar_sat_refutation,[],[f41,f49,f57,f58,f59,f63,f67,f77,f79,f85,f87]) ).

fof(f87,plain,
    ( ~ spl5_2
    | ~ spl5_10 ),
    inference(avatar_contradiction_clause,[],[f86]) ).

fof(f86,plain,
    ( $false
    | ~ spl5_2
    | ~ spl5_10 ),
    inference(resolution,[],[f84,f40]) ).

fof(f40,plain,
    ( ! [X1] : ~ big_g(X1)
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl5_2
  <=> ! [X1] : ~ big_g(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f84,plain,
    ( big_g(sK1)
    | ~ spl5_10 ),
    inference(avatar_component_clause,[],[f82]) ).

fof(f82,plain,
    ( spl5_10
  <=> big_g(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).

fof(f85,plain,
    ( ~ spl5_8
    | spl5_10
    | spl5_6
    | ~ spl5_9 ),
    inference(avatar_split_clause,[],[f80,f75,f55,f82,f71]) ).

fof(f71,plain,
    ( spl5_8
  <=> big_f(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

fof(f55,plain,
    ( spl5_6
  <=> ! [X2] :
        ( big_g(X2)
        | ~ big_f(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

fof(f75,plain,
    ( spl5_9
  <=> ! [X0] :
        ( ~ big_h(X0,sK1)
        | big_g(X0)
        | ~ big_f(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).

fof(f80,plain,
    ( ! [X0] :
        ( big_g(X0)
        | ~ big_f(X0)
        | big_g(sK1)
        | ~ big_f(sK1) )
    | ~ spl5_9 ),
    inference(resolution,[],[f76,f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( big_h(X1,X0)
      | big_g(X0)
      | ~ big_f(X0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( big_g(X0)
      | ( ~ big_g(X1)
        & big_h(X1,X0)
        & big_f(X1) )
      | ~ big_f(X0) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( big_g(X0)
      | ( ~ big_g(X1)
        & big_h(X1,X0)
        & big_f(X1) )
      | ~ big_f(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ( ( ( big_h(X1,X0)
            & big_f(X1) )
         => big_g(X1) )
        & big_f(X0) )
     => big_g(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46_1) ).

fof(f76,plain,
    ( ! [X0] :
        ( ~ big_h(X0,sK1)
        | big_g(X0)
        | ~ big_f(X0) )
    | ~ spl5_9 ),
    inference(avatar_component_clause,[],[f75]) ).

fof(f79,plain,
    ( ~ spl5_4
    | spl5_8 ),
    inference(avatar_contradiction_clause,[],[f78]) ).

fof(f78,plain,
    ( $false
    | ~ spl5_4
    | spl5_8 ),
    inference(resolution,[],[f73,f48]) ).

fof(f48,plain,
    ( ! [X1] : big_f(X1)
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f47,plain,
    ( spl5_4
  <=> ! [X1] : big_f(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f73,plain,
    ( ~ big_f(sK1)
    | spl5_8 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f77,plain,
    ( ~ spl5_8
    | spl5_9
    | ~ spl5_7 ),
    inference(avatar_split_clause,[],[f69,f65,f75,f71]) ).

fof(f65,plain,
    ( spl5_7
  <=> ! [X1] :
        ( big_j(sK1,X1)
        | ~ big_f(X1)
        | big_g(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f69,plain,
    ( ! [X0] :
        ( ~ big_h(X0,sK1)
        | ~ big_f(sK1)
        | ~ big_f(X0)
        | big_g(X0) )
    | ~ spl5_7 ),
    inference(duplicate_literal_removal,[],[f68]) ).

fof(f68,plain,
    ( ! [X0] :
        ( ~ big_h(X0,sK1)
        | ~ big_f(sK1)
        | ~ big_f(X0)
        | ~ big_f(X0)
        | big_g(X0) )
    | ~ spl5_7 ),
    inference(resolution,[],[f24,f66]) ).

fof(f66,plain,
    ( ! [X1] :
        ( big_j(sK1,X1)
        | ~ big_f(X1)
        | big_g(X1) )
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ big_j(X1,X0)
      | ~ big_h(X0,X1)
      | ~ big_f(X1)
      | ~ big_f(X0) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ~ big_j(X1,X0)
      | ~ big_h(X0,X1)
      | ~ big_f(X1)
      | ~ big_f(X0) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ big_j(X1,X0)
      | ~ big_h(X0,X1)
      | ~ big_f(X1)
      | ~ big_f(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ( big_h(X0,X1)
        & big_f(X1)
        & big_f(X0) )
     => ~ big_j(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46_3) ).

fof(f67,plain,
    ( ~ spl5_5
    | spl5_7 ),
    inference(avatar_split_clause,[],[f29,f65,f51]) ).

fof(f51,plain,
    ( spl5_5
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f29,plain,
    ! [X1] :
      ( big_j(sK1,X1)
      | big_g(X1)
      | ~ big_f(X1)
      | ~ sP2 ),
    inference(general_splitting,[],[f23,f28_D]) ).

fof(f28,plain,
    ! [X2] :
      ( big_g(X2)
      | ~ big_f(X2)
      | sP2 ),
    inference(cnf_transformation,[],[f28_D]) ).

fof(f28_D,plain,
    ( ! [X2] :
        ( big_g(X2)
        | ~ big_f(X2) )
  <=> ~ sP2 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).

fof(f23,plain,
    ! [X2,X1] :
      ( big_j(sK1,X1)
      | big_g(X1)
      | ~ big_f(X1)
      | big_g(X2)
      | ~ big_f(X2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( ! [X1] :
          ( big_j(sK1,X1)
          | big_g(X1)
          | ~ big_f(X1) )
      & ~ big_g(sK1)
      & big_f(sK1) )
    | ! [X2] :
        ( big_g(X2)
        | ~ big_f(X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( big_j(X0,X1)
            | big_g(X1)
            | ~ big_f(X1) )
        & ~ big_g(X0)
        & big_f(X0) )
   => ( ! [X1] :
          ( big_j(sK1,X1)
          | big_g(X1)
          | ~ big_f(X1) )
      & ~ big_g(sK1)
      & big_f(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( big_j(X0,X1)
            | big_g(X1)
            | ~ big_f(X1) )
        & ~ big_g(X0)
        & big_f(X0) )
    | ! [X2] :
        ( big_g(X2)
        | ~ big_f(X2) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ( ? [X1] :
        ( ! [X2] :
            ( big_j(X1,X2)
            | big_g(X2)
            | ~ big_f(X2) )
        & ~ big_g(X1)
        & big_f(X1) )
    | ! [X0] :
        ( big_g(X0)
        | ~ big_f(X0) ) ),
    inference(flattening,[],[f8]) ).

fof(f8,plain,
    ( ? [X1] :
        ( ! [X2] :
            ( big_j(X1,X2)
            | big_g(X2)
            | ~ big_f(X2) )
        & ~ big_g(X1)
        & big_f(X1) )
    | ! [X0] :
        ( big_g(X0)
        | ~ big_f(X0) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ( ? [X0] :
        ( ~ big_g(X0)
        & big_f(X0) )
   => ? [X1] :
        ( ! [X2] :
            ( ( ~ big_g(X2)
              & big_f(X2) )
           => big_j(X1,X2) )
        & ~ big_g(X1)
        & big_f(X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ( ? [X0] :
        ( ~ big_g(X0)
        & big_f(X0) )
   => ? [X2] :
        ( ! [X1] :
            ( ( ~ big_g(X1)
              & big_f(X1) )
           => big_j(X2,X1) )
        & ~ big_g(X2)
        & big_f(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46_2) ).

fof(f63,plain,
    ~ spl5_6,
    inference(avatar_contradiction_clause,[],[f62]) ).

fof(f62,plain,
    ( $false
    | ~ spl5_6 ),
    inference(resolution,[],[f60,f19]) ).

fof(f19,plain,
    big_f(sK0),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( ~ big_g(sK0)
    & big_f(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f14]) ).

fof(f14,plain,
    ( ? [X0] :
        ( ~ big_g(X0)
        & big_f(X0) )
   => ( ~ big_g(sK0)
      & big_f(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f7,plain,
    ? [X0] :
      ( ~ big_g(X0)
      & big_f(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ! [X0] :
        ( big_f(X0)
       => big_g(X0) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ! [X0] :
      ( big_f(X0)
     => big_g(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel46) ).

fof(f60,plain,
    ( ~ big_f(sK0)
    | ~ spl5_6 ),
    inference(resolution,[],[f56,f20]) ).

fof(f20,plain,
    ~ big_g(sK0),
    inference(cnf_transformation,[],[f15]) ).

fof(f56,plain,
    ( ! [X2] :
        ( big_g(X2)
        | ~ big_f(X2) )
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f59,plain,
    ( spl5_3
    | spl5_6 ),
    inference(avatar_split_clause,[],[f32,f55,f43]) ).

fof(f43,plain,
    ( spl5_3
  <=> sP4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f32,plain,
    ! [X0] :
      ( big_g(X0)
      | ~ big_f(X0)
      | sP4 ),
    inference(cnf_transformation,[],[f32_D]) ).

fof(f32_D,plain,
    ( ! [X0] :
        ( big_g(X0)
        | ~ big_f(X0) )
  <=> ~ sP4 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).

fof(f58,plain,
    ( spl5_1
    | spl5_6 ),
    inference(avatar_split_clause,[],[f30,f55,f35]) ).

fof(f35,plain,
    ( spl5_1
  <=> sP3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f30,plain,
    ! [X0] :
      ( big_g(X0)
      | ~ big_f(X0)
      | sP3 ),
    inference(cnf_transformation,[],[f30_D]) ).

fof(f30_D,plain,
    ( ! [X0] :
        ( big_g(X0)
        | ~ big_f(X0) )
  <=> ~ sP3 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).

fof(f57,plain,
    ( spl5_5
    | spl5_6 ),
    inference(avatar_split_clause,[],[f28,f55,f51]) ).

fof(f49,plain,
    ( ~ spl5_3
    | spl5_4 ),
    inference(avatar_split_clause,[],[f33,f47,f43]) ).

fof(f33,plain,
    ! [X1] :
      ( big_f(X1)
      | ~ sP4 ),
    inference(general_splitting,[],[f25,f32_D]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( big_g(X0)
      | big_f(X1)
      | ~ big_f(X0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f41,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f31,f39,f35]) ).

fof(f31,plain,
    ! [X1] :
      ( ~ big_g(X1)
      | ~ sP3 ),
    inference(general_splitting,[],[f27,f30_D]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( big_g(X0)
      | ~ big_g(X1)
      | ~ big_f(X0) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SYN070+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri May  3 17:22:38 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (30331)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (30334)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)
% 0.14/0.36  % (30334)First to succeed.
% 0.14/0.36  % (30334)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30331"
% 0.14/0.36  % (30334)Refutation found. Thanks to Tanya!
% 0.14/0.36  % SZS status Theorem for theBenchmark
% 0.14/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.36  % (30334)------------------------------
% 0.14/0.36  % (30334)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.36  % (30334)Termination reason: Refutation
% 0.14/0.36  
% 0.14/0.36  % (30334)Memory used [KB]: 775
% 0.14/0.36  % (30334)Time elapsed: 0.003 s
% 0.14/0.36  % (30334)Instructions burned: 4 (million)
% 0.14/0.36  % (30331)Success in time 0.002 s
%------------------------------------------------------------------------------