TSTP Solution File: SET791+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET791+4 : 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 : 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 : Wed Aug 31 18:25:39 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   61 (   7 unt;   0 def)
%            Number of atoms       :  264 (  24 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  309 ( 106   ~; 101   |;  65   &)
%                                         (   8 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :  151 ( 135   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f113,plain,
    $false,
    inference(avatar_sat_refutation,[],[f94,f99,f112]) ).

fof(f112,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f111]) ).

fof(f111,plain,
    ( $false
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f110,f47]) ).

fof(f47,plain,
    ~ max(sK1,sK2,sK0),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ( greatest(sK1,sK2,sK0)
    & ~ max(sK1,sK2,sK0)
    & order(sK2,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f35,f36]) ).

fof(f36,plain,
    ( ? [X0,X1,X2] :
        ( greatest(X1,X2,X0)
        & ~ max(X1,X2,X0)
        & order(X2,X0) )
   => ( greatest(sK1,sK2,sK0)
      & ~ max(sK1,sK2,sK0)
      & order(sK2,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ? [X0,X1,X2] :
      ( greatest(X1,X2,X0)
      & ~ max(X1,X2,X0)
      & order(X2,X0) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ? [X2,X0,X1] :
      ( greatest(X0,X1,X2)
      & ~ max(X0,X1,X2)
      & order(X1,X2) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ? [X1,X0,X2] :
      ( ~ max(X0,X1,X2)
      & order(X1,X2)
      & greatest(X0,X1,X2) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X1,X0,X2] :
        ( ( order(X1,X2)
          & greatest(X0,X1,X2) )
       => max(X0,X1,X2) ),
    inference(rectify,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X5,X0,X1] :
        ( ( greatest(X5,X0,X1)
          & order(X0,X1) )
       => max(X5,X0,X1) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X5,X0,X1] :
      ( ( greatest(X5,X0,X1)
        & order(X0,X1) )
     => max(X5,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV3) ).

fof(f110,plain,
    ( max(sK1,sK2,sK0)
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f109,f52]) ).

fof(f52,plain,
    member(sK1,sK0),
    inference(resolution,[],[f44,f48]) ).

fof(f48,plain,
    greatest(sK1,sK2,sK0),
    inference(cnf_transformation,[],[f37]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ greatest(X0,X2,X1)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( apply(X2,X3,X0)
            | ~ member(X3,X1) )
        & member(X0,X1) )
      | ~ greatest(X0,X2,X1) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ( ! [X3] :
            ( apply(X1,X3,X2)
            | ~ member(X3,X0) )
        & member(X2,X0) )
      | ~ greatest(X2,X1,X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X2,X1,X0] :
      ( greatest(X2,X1,X0)
     => ( ! [X3] :
            ( member(X3,X0)
           => apply(X1,X3,X2) )
        & member(X2,X0) ) ),
    inference(unused_predicate_definition_removal,[],[f16]) ).

fof(f16,plain,
    ! [X2,X1,X0] :
      ( greatest(X2,X1,X0)
    <=> ( ! [X3] :
            ( member(X3,X0)
           => apply(X1,X3,X2) )
        & member(X2,X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0,X5] :
      ( ( member(X5,X1)
        & ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X5) ) )
    <=> greatest(X5,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest) ).

fof(f109,plain,
    ( ~ member(sK1,sK0)
    | max(sK1,sK2,sK0)
    | ~ spl4_1 ),
    inference(trivial_inequality_removal,[],[f108]) ).

fof(f108,plain,
    ( max(sK1,sK2,sK0)
    | sK1 != sK1
    | ~ member(sK1,sK0)
    | ~ spl4_1 ),
    inference(superposition,[],[f51,f90]) ).

fof(f90,plain,
    ( sK1 = sK3(sK0,sK2,sK1)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f88]) ).

fof(f88,plain,
    ( spl4_1
  <=> sK1 = sK3(sK0,sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( sK3(X0,X1,X2) != X2
      | max(X2,X1,X0)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ~ member(X2,X0)
      | max(X2,X1,X0)
      | ( sK3(X0,X1,X2) != X2
        & member(sK3(X0,X1,X2),X0)
        & apply(X1,X2,sK3(X0,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f38,f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( X2 != X3
          & member(X3,X0)
          & apply(X1,X2,X3) )
     => ( sK3(X0,X1,X2) != X2
        & member(sK3(X0,X1,X2),X0)
        & apply(X1,X2,sK3(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ~ member(X2,X0)
      | max(X2,X1,X0)
      | ? [X3] :
          ( X2 != X3
          & member(X3,X0)
          & apply(X1,X2,X3) ) ),
    inference(rectify,[],[f32]) ).

fof(f32,plain,
    ! [X1,X2,X0] :
      ( ~ member(X0,X1)
      | max(X0,X2,X1)
      | ? [X3] :
          ( X0 != X3
          & member(X3,X1)
          & apply(X2,X0,X3) ) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( max(X0,X2,X1)
      | ? [X3] :
          ( X0 != X3
          & member(X3,X1)
          & apply(X2,X0,X3) )
      | ~ member(X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( member(X3,X1)
              & apply(X2,X0,X3) )
           => X0 = X3 )
        & member(X0,X1) )
     => max(X0,X2,X1) ),
    inference(unused_predicate_definition_removal,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( max(X0,X2,X1)
    <=> ( ! [X3] :
            ( ( member(X3,X1)
              & apply(X2,X0,X3) )
           => X0 = X3 )
        & member(X0,X1) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X5,X1,X0] :
      ( max(X5,X0,X1)
    <=> ( ! [X2] :
            ( ( member(X2,X1)
              & apply(X0,X5,X2) )
           => X2 = X5 )
        & member(X5,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',max) ).

fof(f99,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f98]) ).

fof(f98,plain,
    ( $false
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f97,f47]) ).

fof(f97,plain,
    ( max(sK1,sK2,sK0)
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f96,f52]) ).

fof(f96,plain,
    ( ~ member(sK1,sK0)
    | max(sK1,sK2,sK0)
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f95,f46]) ).

fof(f46,plain,
    order(sK2,sK0),
    inference(cnf_transformation,[],[f37]) ).

fof(f95,plain,
    ( ~ order(sK2,sK0)
    | ~ member(sK1,sK0)
    | max(sK1,sK2,sK0)
    | ~ spl4_2 ),
    inference(resolution,[],[f93,f57]) ).

fof(f57,plain,
    ! [X0] :
      ( member(sK3(sK0,X0,sK1),sK0)
      | max(sK1,X0,sK0) ),
    inference(resolution,[],[f50,f52]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X0)
      | max(X2,X1,X0)
      | member(sK3(X0,X1,X2),X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f93,plain,
    ( ! [X0] :
        ( ~ member(sK3(sK0,sK2,sK1),X0)
        | ~ member(sK1,X0)
        | ~ order(sK2,X0) )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f92]) ).

fof(f92,plain,
    ( spl4_2
  <=> ! [X0] :
        ( ~ member(sK1,X0)
        | ~ member(sK3(sK0,sK2,sK1),X0)
        | ~ order(sK2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f94,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f86,f92,f88]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ member(sK1,X0)
      | sK1 = sK3(sK0,sK2,sK1)
      | ~ order(sK2,X0)
      | ~ member(sK3(sK0,sK2,sK1),X0) ),
    inference(subsumption_resolution,[],[f85,f47]) ).

fof(f85,plain,
    ! [X0] :
      ( max(sK1,sK2,sK0)
      | ~ member(sK3(sK0,sK2,sK1),X0)
      | ~ order(sK2,X0)
      | ~ member(sK1,X0)
      | sK1 = sK3(sK0,sK2,sK1) ),
    inference(duplicate_literal_removal,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( sK1 = sK3(sK0,sK2,sK1)
      | max(sK1,sK2,sK0)
      | ~ member(sK1,X0)
      | ~ order(sK2,X0)
      | max(sK1,sK2,sK0)
      | ~ member(sK3(sK0,sK2,sK1),X0) ),
    inference(resolution,[],[f67,f58]) ).

fof(f58,plain,
    ! [X0] :
      ( apply(sK2,sK3(sK0,X0,sK1),sK1)
      | max(sK1,X0,sK0) ),
    inference(resolution,[],[f57,f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | apply(sK2,X0,sK1) ),
    inference(resolution,[],[f45,f48]) ).

fof(f45,plain,
    ! [X2,X3,X0,X1] :
      ( ~ greatest(X0,X2,X1)
      | ~ member(X3,X1)
      | apply(X2,X3,X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f67,plain,
    ! [X6,X5] :
      ( ~ apply(X5,sK3(sK0,X5,sK1),sK1)
      | ~ order(X5,X6)
      | ~ member(sK3(sK0,X5,sK1),X6)
      | max(sK1,X5,sK0)
      | ~ member(sK1,X6)
      | sK1 = sK3(sK0,X5,sK1) ),
    inference(resolution,[],[f41,f61]) ).

fof(f61,plain,
    ! [X0] :
      ( apply(X0,sK1,sK3(sK0,X0,sK1))
      | max(sK1,X0,sK0) ),
    inference(resolution,[],[f49,f52]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X0)
      | apply(X1,X2,sK3(X0,X1,X2))
      | max(X2,X1,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f41,plain,
    ! [X0,X1,X6,X7] :
      ( ~ apply(X1,X6,X7)
      | ~ member(X7,X0)
      | ~ apply(X1,X7,X6)
      | ~ member(X6,X0)
      | ~ order(X1,X0)
      | X6 = X7 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ order(X1,X0)
      | ( ! [X2,X3,X4] :
            ( ~ apply(X1,X3,X2)
            | ~ apply(X1,X2,X4)
            | apply(X1,X3,X4)
            | ~ member(X4,X0)
            | ~ member(X2,X0)
            | ~ member(X3,X0) )
        & ! [X5] :
            ( ~ member(X5,X0)
            | apply(X1,X5,X5) )
        & ! [X6,X7] :
            ( ~ apply(X1,X7,X6)
            | ~ apply(X1,X6,X7)
            | ~ member(X6,X0)
            | ~ member(X7,X0)
            | X6 = X7 ) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0] :
      ( ~ order(X0,X1)
      | ( ! [X3,X4,X5] :
            ( ~ apply(X0,X4,X3)
            | ~ apply(X0,X3,X5)
            | apply(X0,X4,X5)
            | ~ member(X5,X1)
            | ~ member(X3,X1)
            | ~ member(X4,X1) )
        & ! [X2] :
            ( ~ member(X2,X1)
            | apply(X0,X2,X2) )
        & ! [X7,X6] :
            ( ~ apply(X0,X6,X7)
            | ~ apply(X0,X7,X6)
            | ~ member(X7,X1)
            | ~ member(X6,X1)
            | X6 = X7 ) ) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | apply(X0,X2,X2) )
        & ! [X4,X5,X3] :
            ( apply(X0,X4,X5)
            | ~ apply(X0,X3,X5)
            | ~ apply(X0,X4,X3)
            | ~ member(X5,X1)
            | ~ member(X4,X1)
            | ~ member(X3,X1) )
        & ! [X6,X7] :
            ( X6 = X7
            | ~ apply(X0,X6,X7)
            | ~ apply(X0,X7,X6)
            | ~ member(X7,X1)
            | ~ member(X6,X1) ) )
      | ~ order(X0,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( order(X0,X1)
     => ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X2) )
        & ! [X4,X5,X3] :
            ( ( member(X5,X1)
              & member(X4,X1)
              & member(X3,X1) )
           => ( ( apply(X0,X3,X5)
                & apply(X0,X4,X3) )
             => apply(X0,X4,X5) ) )
        & ! [X6,X7] :
            ( ( member(X7,X1)
              & member(X6,X1) )
           => ( ( apply(X0,X6,X7)
                & apply(X0,X7,X6) )
             => X6 = X7 ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X2) )
        & ! [X4,X5,X3] :
            ( ( member(X5,X1)
              & member(X4,X1)
              & member(X3,X1) )
           => ( ( apply(X0,X3,X5)
                & apply(X0,X4,X3) )
             => apply(X0,X4,X5) ) )
        & ! [X6,X7] :
            ( ( member(X7,X1)
              & member(X6,X1) )
           => ( ( apply(X0,X6,X7)
                & apply(X0,X7,X6) )
             => X6 = X7 ) ) )
    <=> order(X0,X1) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X2) )
        & ! [X3,X2,X4] :
            ( ( member(X3,X1)
              & member(X2,X1)
              & member(X4,X1) )
           => ( ( apply(X0,X2,X3)
                & apply(X0,X3,X4) )
             => apply(X0,X2,X4) ) )
        & ! [X2,X3] :
            ( ( member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X2,X3)
                & apply(X0,X3,X2) )
             => X2 = X3 ) ) )
    <=> order(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 13:44:20 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.46  % (19122)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.48  % (19122)First to succeed.
% 0.20/0.49  % (19122)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (19122)------------------------------
% 0.20/0.49  % (19122)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (19122)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (19122)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (19122)Memory used [KB]: 5500
% 0.20/0.49  % (19122)Time elapsed: 0.109 s
% 0.20/0.49  % (19122)Instructions burned: 5 (million)
% 0.20/0.49  % (19122)------------------------------
% 0.20/0.49  % (19122)------------------------------
% 0.20/0.49  % (19117)Success in time 0.141 s
%------------------------------------------------------------------------------