TSTP Solution File: SET929+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n018.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 : Wed Aug 31 18:26:07 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   60 (   3 unt;   0 def)
%            Number of atoms       :  166 (  35 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  175 (  69   ~;  73   |;  21   &)
%                                         (  10 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   54 (  42   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f137,plain,
    $false,
    inference(avatar_sat_refutation,[],[f63,f64,f65,f108,f113,f118,f125,f136]) ).

fof(f136,plain,
    ( spl7_3
    | ~ spl7_4 ),
    inference(avatar_contradiction_clause,[],[f135]) ).

fof(f135,plain,
    ( $false
    | spl7_3
    | ~ spl7_4 ),
    inference(subsumption_resolution,[],[f129,f62]) ).

fof(f62,plain,
    ( empty_set != sF6
    | spl7_3 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl7_3
  <=> empty_set = sF6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).

fof(f129,plain,
    ( empty_set = sF6
    | ~ spl7_4 ),
    inference(superposition,[],[f128,f47]) ).

fof(f47,plain,
    sF6 = set_difference(sF5,sK4),
    introduced(function_definition,[]) ).

fof(f128,plain,
    ( empty_set = set_difference(sF5,sK4)
    | ~ spl7_4 ),
    inference(resolution,[],[f117,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | empty_set = set_difference(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | empty_set != set_difference(X0,X1) )
      & ( empty_set = set_difference(X0,X1)
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | empty_set != set_difference(X1,X0) )
      & ( empty_set = set_difference(X1,X0)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> empty_set = set_difference(X1,X0) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( empty_set = set_difference(X0,X1)
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(f117,plain,
    ( subset(sF5,sK4)
    | ~ spl7_4 ),
    inference(avatar_component_clause,[],[f115]) ).

fof(f115,plain,
    ( spl7_4
  <=> subset(sF5,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).

fof(f125,plain,
    ( spl7_4
    | ~ spl7_1
    | ~ spl7_2 ),
    inference(avatar_split_clause,[],[f124,f56,f52,f115]) ).

fof(f52,plain,
    ( spl7_1
  <=> in(sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f56,plain,
    ( spl7_2
  <=> in(sK2,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f124,plain,
    ( subset(sF5,sK4)
    | ~ spl7_1
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f121,f57]) ).

fof(f57,plain,
    ( in(sK2,sK4)
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f121,plain,
    ( ~ in(sK2,sK4)
    | subset(sF5,sK4)
    | ~ spl7_1 ),
    inference(resolution,[],[f92,f53]) ).

fof(f53,plain,
    ( in(sK3,sK4)
    | ~ spl7_1 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f92,plain,
    ! [X0] :
      ( ~ in(sK3,X0)
      | subset(sF5,X0)
      | ~ in(sK2,X0) ),
    inference(superposition,[],[f38,f46]) ).

fof(f46,plain,
    unordered_pair(sK2,sK3) = sF5,
    introduced(function_definition,[]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( subset(unordered_pair(X1,X2),X0)
      | ~ in(X2,X0)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X2,X0)
          & in(X1,X0) )
        | ~ subset(unordered_pair(X1,X2),X0) )
      & ( subset(unordered_pair(X1,X2),X0)
        | ~ in(X2,X0)
        | ~ in(X1,X0) ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X2,X0)
          & in(X1,X0) )
        | ~ subset(unordered_pair(X1,X2),X0) )
      & ( subset(unordered_pair(X1,X2),X0)
        | ~ in(X2,X0)
        | ~ in(X1,X0) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( ( in(X2,X0)
        & in(X1,X0) )
    <=> subset(unordered_pair(X1,X2),X0) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( subset(unordered_pair(X0,X1),X2)
    <=> ( in(X0,X2)
        & in(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

fof(f118,plain,
    ( spl7_4
    | ~ spl7_3 ),
    inference(avatar_split_clause,[],[f67,f60,f115]) ).

fof(f67,plain,
    ( empty_set != sF6
    | subset(sF5,sK4) ),
    inference(superposition,[],[f33,f47]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( empty_set != set_difference(X0,X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f113,plain,
    ( spl7_1
    | ~ spl7_3 ),
    inference(avatar_contradiction_clause,[],[f112]) ).

fof(f112,plain,
    ( $false
    | spl7_1
    | ~ spl7_3 ),
    inference(subsumption_resolution,[],[f110,f54]) ).

fof(f54,plain,
    ( ~ in(sK3,sK4)
    | spl7_1 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f110,plain,
    ( in(sK3,sK4)
    | ~ spl7_3 ),
    inference(resolution,[],[f81,f70]) ).

fof(f70,plain,
    ( subset(sF5,sK4)
    | ~ spl7_3 ),
    inference(subsumption_resolution,[],[f67,f61]) ).

fof(f61,plain,
    ( empty_set = sF6
    | ~ spl7_3 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ subset(sF5,X0)
      | in(sK3,X0) ),
    inference(superposition,[],[f40,f46]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( ~ subset(unordered_pair(X1,X2),X0)
      | in(X2,X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f108,plain,
    ( spl7_2
    | ~ spl7_3 ),
    inference(avatar_split_clause,[],[f106,f60,f56]) ).

fof(f106,plain,
    ( in(sK2,sK4)
    | ~ spl7_3 ),
    inference(resolution,[],[f72,f70]) ).

fof(f72,plain,
    ! [X0] :
      ( ~ subset(sF5,X0)
      | in(sK2,X0) ),
    inference(superposition,[],[f39,f46]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( ~ subset(unordered_pair(X1,X2),X0)
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f65,plain,
    ( spl7_1
    | spl7_3 ),
    inference(avatar_split_clause,[],[f50,f60,f52]) ).

fof(f50,plain,
    ( empty_set = sF6
    | in(sK3,sK4) ),
    inference(definition_folding,[],[f43,f47,f46]) ).

fof(f43,plain,
    ( in(sK3,sK4)
    | empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( ( ~ in(sK2,sK4)
      | ~ in(sK3,sK4)
      | empty_set != set_difference(unordered_pair(sK2,sK3),sK4) )
    & ( ( in(sK2,sK4)
        & in(sK3,sK4) )
      | empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f29,f30]) ).

fof(f30,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ in(X0,X2)
          | ~ in(X1,X2)
          | empty_set != set_difference(unordered_pair(X0,X1),X2) )
        & ( ( in(X0,X2)
            & in(X1,X2) )
          | empty_set = set_difference(unordered_pair(X0,X1),X2) ) )
   => ( ( ~ in(sK2,sK4)
        | ~ in(sK3,sK4)
        | empty_set != set_difference(unordered_pair(sK2,sK3),sK4) )
      & ( ( in(sK2,sK4)
          & in(sK3,sK4) )
        | empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ? [X0,X1,X2] :
      ( ( ~ in(X0,X2)
        | ~ in(X1,X2)
        | empty_set != set_difference(unordered_pair(X0,X1),X2) )
      & ( ( in(X0,X2)
          & in(X1,X2) )
        | empty_set = set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ? [X0,X1,X2] :
      ( ( ~ in(X0,X2)
        | ~ in(X1,X2)
        | empty_set != set_difference(unordered_pair(X0,X1),X2) )
      & ( ( in(X0,X2)
          & in(X1,X2) )
        | empty_set = set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( empty_set = set_difference(unordered_pair(X0,X1),X2)
    <~> ( in(X0,X2)
        & in(X1,X2) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( ( in(X0,X2)
          & in(X1,X2) )
      <=> empty_set = set_difference(unordered_pair(X0,X1),X2) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X1,X2,X0] :
      ( ( in(X0,X2)
        & in(X1,X2) )
    <=> empty_set = set_difference(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).

fof(f64,plain,
    ( spl7_2
    | spl7_3 ),
    inference(avatar_split_clause,[],[f49,f60,f56]) ).

fof(f49,plain,
    ( empty_set = sF6
    | in(sK2,sK4) ),
    inference(definition_folding,[],[f44,f47,f46]) ).

fof(f44,plain,
    ( in(sK2,sK4)
    | empty_set = set_difference(unordered_pair(sK2,sK3),sK4) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f63,plain,
    ( ~ spl7_1
    | ~ spl7_2
    | ~ spl7_3 ),
    inference(avatar_split_clause,[],[f48,f60,f56,f52]) ).

fof(f48,plain,
    ( empty_set != sF6
    | ~ in(sK2,sK4)
    | ~ in(sK3,sK4) ),
    inference(definition_folding,[],[f45,f47,f46]) ).

fof(f45,plain,
    ( ~ in(sK2,sK4)
    | ~ in(sK3,sK4)
    | empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ),
    inference(cnf_transformation,[],[f31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:35:10 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  % (31179)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.51  % (31171)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.51  TRYING [1]
% 0.20/0.51  % (31179)First to succeed.
% 0.20/0.51  TRYING [2]
% 0.20/0.51  TRYING [3]
% 0.20/0.52  TRYING [4]
% 0.20/0.52  TRYING [5]
% 0.20/0.52  % (31179)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (31179)------------------------------
% 0.20/0.52  % (31179)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (31179)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (31179)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (31179)Memory used [KB]: 5500
% 0.20/0.52  % (31179)Time elapsed: 0.085 s
% 0.20/0.52  % (31179)Instructions burned: 4 (million)
% 0.20/0.52  % (31179)------------------------------
% 0.20/0.52  % (31179)------------------------------
% 0.20/0.52  % (31153)Success in time 0.165 s
%------------------------------------------------------------------------------