TSTP Solution File: SET770+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET770+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --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 18:22:11 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  103 (  14 unt;   0 def)
%            Number of atoms       :  352 (   0 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  374 ( 125   ~; 129   |;  76   &)
%                                         (  16 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   7 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  176 ( 153   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f629,plain,
    $false,
    inference(avatar_sat_refutation,[],[f112,f289,f304,f393,f534,f591,f628]) ).

fof(f628,plain,
    ( spl6_2
    | ~ spl6_5
    | spl6_6 ),
    inference(avatar_contradiction_clause,[],[f627]) ).

fof(f627,plain,
    ( $false
    | spl6_2
    | ~ spl6_5
    | spl6_6 ),
    inference(subsumption_resolution,[],[f621,f581]) ).

fof(f581,plain,
    ( apply(sK2,sK5,sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)))
    | spl6_2 ),
    inference(resolution,[],[f478,f55]) ).

fof(f55,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X1,X3,X2)
      | ~ member(X2,equivalence_class(X3,X0,X1)) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( apply(X1,X3,X2)
          & member(X2,X0) )
        | ~ member(X2,equivalence_class(X3,X0,X1)) )
      & ( member(X2,equivalence_class(X3,X0,X1))
        | ~ apply(X1,X3,X2)
        | ~ member(X2,X0) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,plain,
    ! [X3,X0,X2,X1] :
      ( ( ( apply(X0,X1,X2)
          & member(X2,X3) )
        | ~ member(X2,equivalence_class(X1,X3,X0)) )
      & ( member(X2,equivalence_class(X1,X3,X0))
        | ~ apply(X0,X1,X2)
        | ~ member(X2,X3) ) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X3,X0,X2,X1] :
      ( ( ( apply(X0,X1,X2)
          & member(X2,X3) )
        | ~ member(X2,equivalence_class(X1,X3,X0)) )
      & ( member(X2,equivalence_class(X1,X3,X0))
        | ~ apply(X0,X1,X2)
        | ~ member(X2,X3) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X3,X0,X2,X1] :
      ( ( apply(X0,X1,X2)
        & member(X2,X3) )
    <=> member(X2,equivalence_class(X1,X3,X0)) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X6,X0,X2,X3] :
      ( ( member(X2,X3)
        & apply(X6,X0,X2) )
    <=> member(X2,equivalence_class(X0,X3,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_class) ).

fof(f478,plain,
    ( member(sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),equivalence_class(sK5,sK4,sK2))
    | spl6_2 ),
    inference(unit_resulting_resolution,[],[f111,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ( ~ member(sK0(X0,X1),X0)
        & member(sK0(X0,X1),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f31,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1) )
     => ( ~ member(sK0(X0,X1),X0)
        & member(sK0(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1) ) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) )
     => subset(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

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

fof(f111,plain,
    ( ~ subset(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2))
    | spl6_2 ),
    inference(avatar_component_clause,[],[f109]) ).

fof(f109,plain,
    ( spl6_2
  <=> subset(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f621,plain,
    ( ~ apply(sK2,sK5,sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)))
    | ~ spl6_5
    | spl6_6 ),
    inference(unit_resulting_resolution,[],[f59,f63,f339,f60,f528,f533,f57]) ).

fof(f57,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ member(X5,X0)
      | apply(X1,X4,X5)
      | ~ member(X3,X0)
      | ~ member(X4,X0)
      | ~ apply(X1,X3,X5)
      | ~ apply(X1,X4,X3)
      | ~ equivalence(X1,X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ equivalence(X1,X0)
      | ( ! [X2] :
            ( apply(X1,X2,X2)
            | ~ member(X2,X0) )
        & ! [X3,X4,X5] :
            ( ~ member(X4,X0)
            | ~ member(X5,X0)
            | apply(X1,X4,X5)
            | ~ apply(X1,X4,X3)
            | ~ member(X3,X0)
            | ~ apply(X1,X3,X5) )
        & ! [X6,X7] :
            ( ~ apply(X1,X7,X6)
            | ~ member(X6,X0)
            | ~ member(X7,X0)
            | apply(X1,X6,X7) ) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ equivalence(X1,X0)
      | ( ! [X7] :
            ( apply(X1,X7,X7)
            | ~ member(X7,X0) )
        & ! [X4,X6,X5] :
            ( ~ member(X6,X0)
            | ~ member(X5,X0)
            | apply(X1,X6,X5)
            | ~ apply(X1,X6,X4)
            | ~ member(X4,X0)
            | ~ apply(X1,X4,X5) )
        & ! [X3,X2] :
            ( ~ apply(X1,X2,X3)
            | ~ member(X3,X0)
            | ~ member(X2,X0)
            | apply(X1,X3,X2) ) ) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X1,X0] :
      ( ( ! [X7] :
            ( apply(X1,X7,X7)
            | ~ member(X7,X0) )
        & ! [X2,X3] :
            ( apply(X1,X3,X2)
            | ~ apply(X1,X2,X3)
            | ~ member(X2,X0)
            | ~ member(X3,X0) )
        & ! [X5,X4,X6] :
            ( apply(X1,X6,X5)
            | ~ apply(X1,X6,X4)
            | ~ apply(X1,X4,X5)
            | ~ member(X5,X0)
            | ~ member(X4,X0)
            | ~ member(X6,X0) ) )
      | ~ equivalence(X1,X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
      ( equivalence(X1,X0)
     => ( ! [X7] :
            ( member(X7,X0)
           => apply(X1,X7,X7) )
        & ! [X2,X3] :
            ( ( member(X2,X0)
              & member(X3,X0) )
           => ( apply(X1,X2,X3)
             => apply(X1,X3,X2) ) )
        & ! [X5,X4,X6] :
            ( ( member(X5,X0)
              & member(X4,X0)
              & member(X6,X0) )
           => ( ( apply(X1,X6,X4)
                & apply(X1,X4,X5) )
             => apply(X1,X6,X5) ) ) ) ),
    inference(unused_predicate_definition_removal,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0] :
      ( ( ! [X7] :
            ( member(X7,X0)
           => apply(X1,X7,X7) )
        & ! [X2,X3] :
            ( ( member(X2,X0)
              & member(X3,X0) )
           => ( apply(X1,X2,X3)
             => apply(X1,X3,X2) ) )
        & ! [X5,X4,X6] :
            ( ( member(X5,X0)
              & member(X4,X0)
              & member(X6,X0) )
           => ( ( apply(X1,X6,X4)
                & apply(X1,X4,X5) )
             => apply(X1,X6,X5) ) ) )
    <=> equivalence(X1,X0) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X6] :
      ( equivalence(X6,X0)
    <=> ( ! [X2,X4] :
            ( ( member(X4,X0)
              & member(X2,X0) )
           => ( apply(X6,X2,X4)
             => apply(X6,X4,X2) ) )
        & ! [X4,X5,X2] :
            ( ( member(X4,X0)
              & member(X5,X0)
              & member(X2,X0) )
           => ( ( apply(X6,X4,X5)
                & apply(X6,X2,X4) )
             => apply(X6,X2,X5) ) )
        & ! [X2] :
            ( member(X2,X0)
           => apply(X6,X2,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence) ).

fof(f533,plain,
    ( ~ apply(sK2,sK3,sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)))
    | spl6_6 ),
    inference(avatar_component_clause,[],[f531]) ).

fof(f531,plain,
    ( spl6_6
  <=> apply(sK2,sK3,sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

fof(f528,plain,
    ( member(sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK4)
    | ~ spl6_5 ),
    inference(avatar_component_clause,[],[f527]) ).

fof(f527,plain,
    ( spl6_5
  <=> member(sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

fof(f60,plain,
    member(sK3,sK4),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ( member(sK5,sK4)
    & ~ equal_set(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2))
    & ~ disjoint(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2))
    & member(sK3,sK4)
    & equivalence(sK2,sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f45,f46]) ).

fof(f46,plain,
    ( ? [X0,X1,X2,X3] :
        ( member(X3,X2)
        & ~ equal_set(equivalence_class(X3,X2,X0),equivalence_class(X1,X2,X0))
        & ~ disjoint(equivalence_class(X3,X2,X0),equivalence_class(X1,X2,X0))
        & member(X1,X2)
        & equivalence(X0,X2) )
   => ( member(sK5,sK4)
      & ~ equal_set(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2))
      & ~ disjoint(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2))
      & member(sK3,sK4)
      & equivalence(sK2,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ? [X0,X1,X2,X3] :
      ( member(X3,X2)
      & ~ equal_set(equivalence_class(X3,X2,X0),equivalence_class(X1,X2,X0))
      & ~ disjoint(equivalence_class(X3,X2,X0),equivalence_class(X1,X2,X0))
      & member(X1,X2)
      & equivalence(X0,X2) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ? [X2,X0,X3,X1] :
      ( member(X1,X3)
      & ~ equal_set(equivalence_class(X1,X3,X2),equivalence_class(X0,X3,X2))
      & ~ disjoint(equivalence_class(X1,X3,X2),equivalence_class(X0,X3,X2))
      & member(X0,X3)
      & equivalence(X2,X3) ),
    inference(flattening,[],[f35]) ).

fof(f35,plain,
    ? [X0,X1,X2,X3] :
      ( ~ equal_set(equivalence_class(X1,X3,X2),equivalence_class(X0,X3,X2))
      & ~ disjoint(equivalence_class(X1,X3,X2),equivalence_class(X0,X3,X2))
      & member(X1,X3)
      & member(X0,X3)
      & equivalence(X2,X3) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( member(X1,X3)
          & member(X0,X3)
          & equivalence(X2,X3) )
       => ( equal_set(equivalence_class(X1,X3,X2),equivalence_class(X0,X3,X2))
          | disjoint(equivalence_class(X1,X3,X2),equivalence_class(X0,X3,X2)) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X1,X0,X6,X3] :
        ( ( member(X1,X3)
          & equivalence(X6,X3)
          & member(X0,X3) )
       => ( disjoint(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
          | equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X1,X0,X6,X3] :
      ( ( member(X1,X3)
        & equivalence(X6,X3)
        & member(X0,X3) )
     => ( disjoint(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6))
        | equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII06) ).

fof(f339,plain,
    apply(sK2,sK3,sK5),
    inference(unit_resulting_resolution,[],[f63,f60,f183,f184,f264,f66]) ).

fof(f66,plain,
    ! [X3,X4,X5] :
      ( ~ apply(sK2,X5,X3)
      | ~ member(X5,sK4)
      | ~ member(X4,sK4)
      | ~ member(X3,sK4)
      | ~ apply(sK2,X4,X5)
      | apply(sK2,X4,X3) ),
    inference(resolution,[],[f59,f57]) ).

fof(f264,plain,
    apply(sK2,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK5),
    inference(unit_resulting_resolution,[],[f63,f184,f196,f65]) ).

fof(f65,plain,
    ! [X2,X1] :
      ( ~ apply(sK2,X2,X1)
      | ~ member(X1,sK4)
      | ~ member(X2,sK4)
      | apply(sK2,X1,X2) ),
    inference(resolution,[],[f59,f56]) ).

fof(f56,plain,
    ! [X0,X1,X6,X7] :
      ( ~ member(X6,X0)
      | apply(X1,X6,X7)
      | ~ apply(X1,X7,X6)
      | ~ equivalence(X1,X0)
      | ~ member(X7,X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f196,plain,
    apply(sK2,sK5,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2))),
    inference(resolution,[],[f92,f55]) ).

fof(f92,plain,
    member(sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),equivalence_class(sK5,sK4,sK2)),
    inference(unit_resulting_resolution,[],[f61,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X1)
      | disjoint(X1,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) )
      | disjoint(X1,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f32,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) )
     => ( member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) )
      | disjoint(X1,X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0] :
      ( ~ ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
     => disjoint(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ~ ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
    <=> disjoint(X1,X0) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X1,X0] :
      ( ~ ? [X2] :
            ( member(X2,X0)
            & member(X2,X1) )
    <=> disjoint(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint) ).

fof(f61,plain,
    ~ disjoint(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),
    inference(cnf_transformation,[],[f47]) ).

fof(f184,plain,
    member(sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK4),
    inference(unit_resulting_resolution,[],[f91,f54]) ).

fof(f54,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,equivalence_class(X3,X0,X1)) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f91,plain,
    member(sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),equivalence_class(sK3,sK4,sK2)),
    inference(unit_resulting_resolution,[],[f61,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | disjoint(X1,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f183,plain,
    apply(sK2,sK3,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2))),
    inference(unit_resulting_resolution,[],[f91,f55]) ).

fof(f63,plain,
    member(sK5,sK4),
    inference(cnf_transformation,[],[f47]) ).

fof(f59,plain,
    equivalence(sK2,sK4),
    inference(cnf_transformation,[],[f47]) ).

fof(f591,plain,
    ( spl6_2
    | spl6_5 ),
    inference(avatar_contradiction_clause,[],[f590]) ).

fof(f590,plain,
    ( $false
    | spl6_2
    | spl6_5 ),
    inference(subsumption_resolution,[],[f579,f529]) ).

fof(f529,plain,
    ( ~ member(sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK4)
    | spl6_5 ),
    inference(avatar_component_clause,[],[f527]) ).

fof(f579,plain,
    ( member(sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK4)
    | spl6_2 ),
    inference(unit_resulting_resolution,[],[f478,f54]) ).

fof(f534,plain,
    ( ~ spl6_5
    | ~ spl6_6
    | spl6_2 ),
    inference(avatar_split_clause,[],[f524,f109,f531,f527]) ).

fof(f524,plain,
    ( ~ apply(sK2,sK3,sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)))
    | ~ member(sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK4)
    | spl6_2 ),
    inference(resolution,[],[f477,f53]) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | member(X2,equivalence_class(X3,X0,X1))
      | ~ apply(X1,X3,X2) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f477,plain,
    ( ~ member(sK0(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),equivalence_class(sK3,sK4,sK2))
    | spl6_2 ),
    inference(unit_resulting_resolution,[],[f111,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f393,plain,
    ( spl6_1
    | ~ spl6_3
    | spl6_4 ),
    inference(avatar_contradiction_clause,[],[f392]) ).

fof(f392,plain,
    ( $false
    | spl6_1
    | ~ spl6_3
    | spl6_4 ),
    inference(subsumption_resolution,[],[f376,f364]) ).

fof(f364,plain,
    ( ~ apply(sK2,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)))
    | ~ spl6_3
    | spl6_4 ),
    inference(unit_resulting_resolution,[],[f59,f184,f196,f63,f283,f288,f57]) ).

fof(f288,plain,
    ( ~ apply(sK2,sK5,sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)))
    | spl6_4 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f286,plain,
    ( spl6_4
  <=> apply(sK2,sK5,sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).

fof(f283,plain,
    ( member(sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),sK4)
    | ~ spl6_3 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f282,plain,
    ( spl6_3
  <=> member(sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

fof(f376,plain,
    ( apply(sK2,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)))
    | spl6_1
    | ~ spl6_3 ),
    inference(unit_resulting_resolution,[],[f59,f184,f262,f60,f283,f291,f57]) ).

fof(f291,plain,
    ( apply(sK2,sK3,sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)))
    | spl6_1 ),
    inference(unit_resulting_resolution,[],[f134,f55]) ).

fof(f134,plain,
    ( member(sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),equivalence_class(sK3,sK4,sK2))
    | spl6_1 ),
    inference(unit_resulting_resolution,[],[f107,f48]) ).

fof(f107,plain,
    ( ~ subset(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2))
    | spl6_1 ),
    inference(avatar_component_clause,[],[f105]) ).

fof(f105,plain,
    ( spl6_1
  <=> subset(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f262,plain,
    apply(sK2,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK3),
    inference(subsumption_resolution,[],[f261,f60]) ).

fof(f261,plain,
    ( apply(sK2,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK3)
    | ~ member(sK3,sK4) ),
    inference(subsumption_resolution,[],[f254,f184]) ).

fof(f254,plain,
    ( ~ member(sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK4)
    | ~ member(sK3,sK4)
    | apply(sK2,sK1(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)),sK3) ),
    inference(resolution,[],[f183,f65]) ).

fof(f304,plain,
    ( spl6_1
    | spl6_3 ),
    inference(avatar_contradiction_clause,[],[f303]) ).

fof(f303,plain,
    ( $false
    | spl6_1
    | spl6_3 ),
    inference(subsumption_resolution,[],[f292,f284]) ).

fof(f284,plain,
    ( ~ member(sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),sK4)
    | spl6_3 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f292,plain,
    ( member(sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),sK4)
    | spl6_1 ),
    inference(unit_resulting_resolution,[],[f134,f54]) ).

fof(f289,plain,
    ( ~ spl6_3
    | ~ spl6_4
    | spl6_1 ),
    inference(avatar_split_clause,[],[f279,f105,f286,f282]) ).

fof(f279,plain,
    ( ~ apply(sK2,sK5,sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)))
    | ~ member(sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),sK4)
    | spl6_1 ),
    inference(resolution,[],[f133,f53]) ).

fof(f133,plain,
    ( ~ member(sK0(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),equivalence_class(sK5,sK4,sK2))
    | spl6_1 ),
    inference(unit_resulting_resolution,[],[f107,f49]) ).

fof(f112,plain,
    ( ~ spl6_1
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f103,f109,f105]) ).

fof(f103,plain,
    ( ~ subset(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2))
    | ~ subset(equivalence_class(sK3,sK4,sK2),equivalence_class(sK5,sK4,sK2)) ),
    inference(resolution,[],[f62,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | equal_set(X1,X0)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( equal_set(X1,X0)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( equal_set(X1,X0)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
     => equal_set(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> equal_set(X1,X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).

fof(f62,plain,
    ~ equal_set(equivalence_class(sK5,sK4,sK2),equivalence_class(sK3,sK4,sK2)),
    inference(cnf_transformation,[],[f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET770+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:20:55 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  % (17233)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.49  % (17249)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.52  % (17233)First to succeed.
% 0.20/0.52  % (17233)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  % (17233)------------------------------
% 0.20/0.52  % (17233)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (17233)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (17233)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (17233)Memory used [KB]: 6140
% 0.20/0.52  % (17233)Time elapsed: 0.082 s
% 0.20/0.52  % (17233)Instructions burned: 24 (million)
% 0.20/0.52  % (17233)------------------------------
% 0.20/0.52  % (17233)------------------------------
% 0.20/0.52  % (17225)Success in time 0.167 s
%------------------------------------------------------------------------------