TSTP Solution File: SET772+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET772+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 : Mon Jun 24 14:35:41 EDT 2024

% Result   : Theorem 81.37s 11.77s
% Output   : CNFRefutation 81.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  195 (  17 unt;   0 def)
%            Number of atoms       :  821 (  33 equ)
%            Maximal formula atoms :   24 (   4 avg)
%            Number of connectives :  943 ( 317   ~; 334   |; 212   &)
%                                         (  30 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;   4 con; 0-3 aty)
%            Number of variables   :  602 (  13 sgn 389   !;  78   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f3,axiom,
    ! [X2,X0] :
      ( member(X2,power_set(X0))
    <=> subset(X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).

fof(f8,axiom,
    ! [X2,X0] :
      ( member(X2,singleton(X0))
    <=> X0 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).

fof(f9,axiom,
    ! [X2,X0,X1] :
      ( member(X2,unordered_pair(X0,X1))
    <=> ( X1 = X2
        | X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).

fof(f10,axiom,
    ! [X2,X0] :
      ( member(X2,sum(X0))
    <=> ? [X4] :
          ( member(X2,X4)
          & member(X4,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).

fof(f11,axiom,
    ! [X2,X0] :
      ( member(X2,product(X0))
    <=> ! [X4] :
          ( member(X4,X0)
         => member(X2,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).

fof(f13,axiom,
    ! [X0,X3] :
      ( partition(X0,X3)
    <=> ( ! [X2,X4] :
            ( ( member(X4,X0)
              & member(X2,X0) )
           => ( ? [X5] :
                  ( member(X5,X4)
                  & member(X5,X2) )
             => X2 = X4 ) )
        & ! [X2] :
            ( member(X2,X3)
           => ? [X4] :
                ( member(X2,X4)
                & member(X4,X0) ) )
        & ! [X2] :
            ( member(X2,X0)
           => subset(X2,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).

fof(f14,axiom,
    ! [X0,X6] :
      ( equivalence(X6,X0)
    <=> ( ! [X2,X4,X5] :
            ( ( member(X5,X0)
              & member(X4,X0)
              & member(X2,X0) )
           => ( ( apply(X6,X4,X5)
                & apply(X6,X2,X4) )
             => apply(X6,X2,X5) ) )
        & ! [X2,X4] :
            ( ( member(X4,X0)
              & member(X2,X0) )
           => ( apply(X6,X2,X4)
             => apply(X6,X4,X2) ) )
        & ! [X2] :
            ( member(X2,X0)
           => apply(X6,X2,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).

fof(f15,axiom,
    ! [X6,X3,X0,X2] :
      ( member(X2,equivalence_class(X0,X3,X6))
    <=> ( apply(X6,X0,X2)
        & member(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).

fof(f17,conjecture,
    ! [X0,X3,X6] :
      ( partition(X0,X3)
     => ( ! [X2,X4] :
            ( ( member(X4,X3)
              & member(X2,X3) )
           => ( apply(X6,X2,X4)
            <=> ? [X5] :
                  ( member(X4,X5)
                  & member(X2,X5)
                  & member(X5,X0) ) ) )
       => equivalence(X6,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII08) ).

fof(f18,negated_conjecture,
    ~ ! [X0,X3,X6] :
        ( partition(X0,X3)
       => ( ! [X2,X4] :
              ( ( member(X4,X3)
                & member(X2,X3) )
             => ( apply(X6,X2,X4)
              <=> ? [X5] :
                    ( member(X4,X5)
                    & member(X2,X5)
                    & member(X5,X0) ) ) )
         => equivalence(X6,X3) ) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
    <=> subset(X0,X1) ),
    inference(rectify,[],[f3]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
    <=> ( member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f22,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
    <=> X0 = X1 ),
    inference(rectify,[],[f8]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( X0 = X2
        | X0 = X1 ) ),
    inference(rectify,[],[f9]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( member(X0,sum(X1))
    <=> ? [X2] :
          ( member(X0,X2)
          & member(X2,X1) ) ),
    inference(rectify,[],[f10]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( member(X0,product(X1))
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X0,X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( partition(X0,X1)
    <=> ( ! [X2,X3] :
            ( ( member(X3,X0)
              & member(X2,X0) )
           => ( ? [X4] :
                  ( member(X4,X3)
                  & member(X4,X2) )
             => X2 = X3 ) )
        & ! [X5] :
            ( member(X5,X1)
           => ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) ) )
        & ! [X7] :
            ( member(X7,X0)
           => subset(X7,X1) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
    <=> ( ! [X2,X3,X4] :
            ( ( member(X4,X0)
              & member(X3,X0)
              & member(X2,X0) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X2,X3) )
             => apply(X1,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X0)
              & member(X5,X0) )
           => ( apply(X1,X5,X6)
             => apply(X1,X6,X5) ) )
        & ! [X7] :
            ( member(X7,X0)
           => apply(X1,X7,X7) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( member(X3,equivalence_class(X2,X1,X0))
    <=> ( apply(X0,X2,X3)
        & member(X3,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f32,plain,
    ~ ! [X0,X1,X2] :
        ( partition(X0,X1)
       => ( ! [X3,X4] :
              ( ( member(X4,X1)
                & member(X3,X1) )
             => ( apply(X2,X3,X4)
              <=> ? [X5] :
                    ( member(X4,X5)
                    & member(X3,X5)
                    & member(X5,X0) ) ) )
         => equivalence(X2,X1) ) ),
    inference(rectify,[],[f18]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3,X4] :
            ( ( member(X4,X0)
              & member(X3,X0)
              & member(X2,X0) )
           => ( ( apply(X1,X3,X4)
                & apply(X1,X2,X3) )
             => apply(X1,X2,X4) ) )
        & ! [X5,X6] :
            ( ( member(X6,X0)
              & member(X5,X0) )
           => ( apply(X1,X5,X6)
             => apply(X1,X6,X5) ) )
        & ! [X7] :
            ( member(X7,X0)
           => apply(X1,X7,X7) ) )
     => equivalence(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f29]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( partition(X0,X1)
     => ( ! [X2,X3] :
            ( ( member(X3,X0)
              & member(X2,X0) )
           => ( ? [X4] :
                  ( member(X4,X3)
                  & member(X4,X2) )
             => X2 = X3 ) )
        & ! [X5] :
            ( member(X5,X1)
           => ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) ) )
        & ! [X7] :
            ( member(X7,X0)
           => subset(X7,X1) ) ) ),
    inference(unused_predicate_definition_removal,[],[f28]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( member(X0,product(X1))
    <=> ! [X2] :
          ( member(X0,X2)
          | ~ member(X2,X1) ) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3] :
            ( X2 = X3
            | ! [X4] :
                ( ~ member(X4,X3)
                | ~ member(X4,X2) )
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5] :
            ( ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) )
            | ~ member(X5,X1) )
        & ! [X7] :
            ( subset(X7,X1)
            | ~ member(X7,X0) ) )
      | ~ partition(X0,X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3] :
            ( X2 = X3
            | ! [X4] :
                ( ~ member(X4,X3)
                | ~ member(X4,X2) )
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5] :
            ( ? [X6] :
                ( member(X5,X6)
                & member(X6,X0) )
            | ~ member(X5,X1) )
        & ! [X7] :
            ( subset(X7,X1)
            | ~ member(X7,X0) ) )
      | ~ partition(X0,X1) ),
    inference(flattening,[],[f37]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | ? [X2,X3,X4] :
          ( ~ apply(X1,X2,X4)
          & apply(X1,X3,X4)
          & apply(X1,X2,X3)
          & member(X4,X0)
          & member(X3,X0)
          & member(X2,X0) )
      | ? [X5,X6] :
          ( ~ apply(X1,X6,X5)
          & apply(X1,X5,X6)
          & member(X6,X0)
          & member(X5,X0) )
      | ? [X7] :
          ( ~ apply(X1,X7,X7)
          & member(X7,X0) ) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | ? [X2,X3,X4] :
          ( ~ apply(X1,X2,X4)
          & apply(X1,X3,X4)
          & apply(X1,X2,X3)
          & member(X4,X0)
          & member(X3,X0)
          & member(X2,X0) )
      | ? [X5,X6] :
          ( ~ apply(X1,X6,X5)
          & apply(X1,X5,X6)
          & member(X6,X0)
          & member(X5,X0) )
      | ? [X7] :
          ( ~ apply(X1,X7,X7)
          & member(X7,X0) ) ),
    inference(flattening,[],[f39]) ).

fof(f41,plain,
    ? [X0,X1,X2] :
      ( ~ equivalence(X2,X1)
      & ! [X3,X4] :
          ( ( apply(X2,X3,X4)
          <=> ? [X5] :
                ( member(X4,X5)
                & member(X3,X5)
                & member(X5,X0) ) )
          | ~ member(X4,X1)
          | ~ member(X3,X1) )
      & partition(X0,X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f42,plain,
    ? [X0,X1,X2] :
      ( ~ equivalence(X2,X1)
      & ! [X3,X4] :
          ( ( apply(X2,X3,X4)
          <=> ? [X5] :
                ( member(X4,X5)
                & member(X3,X5)
                & member(X5,X0) ) )
          | ~ member(X4,X1)
          | ~ member(X3,X1) )
      & partition(X0,X1) ),
    inference(flattening,[],[f41]) ).

fof(f43,plain,
    ! [X1,X0] :
      ( ? [X2,X3,X4] :
          ( ~ apply(X1,X2,X4)
          & apply(X1,X3,X4)
          & apply(X1,X2,X3)
          & member(X4,X0)
          & member(X3,X0)
          & member(X2,X0) )
      | ~ sP0(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | ? [X5,X6] :
          ( ~ apply(X1,X6,X5)
          & apply(X1,X5,X6)
          & member(X6,X0)
          & member(X5,X0) )
      | ? [X7] :
          ( ~ apply(X1,X7,X7)
          & member(X7,X0) ) ),
    inference(definition_folding,[],[f40,f43]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f45]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK1(X0,X1),X1)
          & member(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f46,f47]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ( member(X0,power_set(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ member(X0,power_set(X1)) ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(flattening,[],[f50]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f52]) ).

fof(f54,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f54]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( member(X0,singleton(X1))
        | X0 != X1 )
      & ( X0 = X1
        | ~ member(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f24]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 ) )
      & ( X0 = X2
        | X0 = X1
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 ) )
      & ( X0 = X2
        | X0 = X1
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f57]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ? [X2] :
            ( member(X0,X2)
            & member(X2,X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ? [X3] :
            ( member(X0,X3)
            & member(X3,X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(rectify,[],[f59]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X0,X3)
          & member(X3,X1) )
     => ( member(X0,sK2(X0,X1))
        & member(sK2(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X0,X2)
            | ~ member(X2,X1) ) )
      & ( ( member(X0,sK2(X0,X1))
          & member(sK2(X0,X1),X1) )
        | ~ member(X0,sum(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f60,f61]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( member(X0,product(X1))
        | ? [X2] :
            ( ~ member(X0,X2)
            & member(X2,X1) ) )
      & ( ! [X2] :
            ( member(X0,X2)
            | ~ member(X2,X1) )
        | ~ member(X0,product(X1)) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( member(X0,product(X1))
        | ? [X2] :
            ( ~ member(X0,X2)
            & member(X2,X1) ) )
      & ( ! [X3] :
            ( member(X0,X3)
            | ~ member(X3,X1) )
        | ~ member(X0,product(X1)) ) ),
    inference(rectify,[],[f63]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X0,X2)
          & member(X2,X1) )
     => ( ~ member(X0,sK3(X0,X1))
        & member(sK3(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ( member(X0,product(X1))
        | ( ~ member(X0,sK3(X0,X1))
          & member(sK3(X0,X1),X1) ) )
      & ( ! [X3] :
            ( member(X0,X3)
            | ~ member(X3,X1) )
        | ~ member(X0,product(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f64,f65]) ).

fof(f67,plain,
    ! [X0,X5] :
      ( ? [X6] :
          ( member(X5,X6)
          & member(X6,X0) )
     => ( member(X5,sK4(X0,X5))
        & member(sK4(X0,X5),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( ! [X2,X3] :
            ( X2 = X3
            | ! [X4] :
                ( ~ member(X4,X3)
                | ~ member(X4,X2) )
            | ~ member(X3,X0)
            | ~ member(X2,X0) )
        & ! [X5] :
            ( ( member(X5,sK4(X0,X5))
              & member(sK4(X0,X5),X0) )
            | ~ member(X5,X1) )
        & ! [X7] :
            ( subset(X7,X1)
            | ~ member(X7,X0) ) )
      | ~ partition(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f38,f67]) ).

fof(f69,plain,
    ! [X1,X0] :
      ( ? [X2,X3,X4] :
          ( ~ apply(X1,X2,X4)
          & apply(X1,X3,X4)
          & apply(X1,X2,X3)
          & member(X4,X0)
          & member(X3,X0)
          & member(X2,X0) )
      | ~ sP0(X1,X0) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( ~ apply(X0,X2,X4)
          & apply(X0,X3,X4)
          & apply(X0,X2,X3)
          & member(X4,X1)
          & member(X3,X1)
          & member(X2,X1) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f69]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( ~ apply(X0,X2,X4)
          & apply(X0,X3,X4)
          & apply(X0,X2,X3)
          & member(X4,X1)
          & member(X3,X1)
          & member(X2,X1) )
     => ( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
        & apply(X0,sK6(X0,X1),sK7(X0,X1))
        & apply(X0,sK5(X0,X1),sK6(X0,X1))
        & member(sK7(X0,X1),X1)
        & member(sK6(X0,X1),X1)
        & member(sK5(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
        & apply(X0,sK6(X0,X1),sK7(X0,X1))
        & apply(X0,sK5(X0,X1),sK6(X0,X1))
        & member(sK7(X0,X1),X1)
        & member(sK6(X0,X1),X1)
        & member(sK5(X0,X1),X1) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f70,f71]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | ? [X2,X3] :
          ( ~ apply(X1,X3,X2)
          & apply(X1,X2,X3)
          & member(X3,X0)
          & member(X2,X0) )
      | ? [X4] :
          ( ~ apply(X1,X4,X4)
          & member(X4,X0) ) ),
    inference(rectify,[],[f44]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ~ apply(X1,X3,X2)
          & apply(X1,X2,X3)
          & member(X3,X0)
          & member(X2,X0) )
     => ( ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
        & apply(X1,sK8(X0,X1),sK9(X0,X1))
        & member(sK9(X0,X1),X0)
        & member(sK8(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ~ apply(X1,X4,X4)
          & member(X4,X0) )
     => ( ~ apply(X1,sK10(X0,X1),sK10(X0,X1))
        & member(sK10(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | ( ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
        & apply(X1,sK8(X0,X1),sK9(X0,X1))
        & member(sK9(X0,X1),X0)
        & member(sK8(X0,X1),X0) )
      | ( ~ apply(X1,sK10(X0,X1),sK10(X0,X1))
        & member(sK10(X0,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f73,f75,f74]) ).

fof(f77,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(X3,equivalence_class(X2,X1,X0))
        | ~ apply(X0,X2,X3)
        | ~ member(X3,X1) )
      & ( ( apply(X0,X2,X3)
          & member(X3,X1) )
        | ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f78,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(X3,equivalence_class(X2,X1,X0))
        | ~ apply(X0,X2,X3)
        | ~ member(X3,X1) )
      & ( ( apply(X0,X2,X3)
          & member(X3,X1) )
        | ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
    inference(flattening,[],[f77]) ).

fof(f79,plain,
    ? [X0,X1,X2] :
      ( ~ equivalence(X2,X1)
      & ! [X3,X4] :
          ( ( ( apply(X2,X3,X4)
              | ! [X5] :
                  ( ~ member(X4,X5)
                  | ~ member(X3,X5)
                  | ~ member(X5,X0) ) )
            & ( ? [X5] :
                  ( member(X4,X5)
                  & member(X3,X5)
                  & member(X5,X0) )
              | ~ apply(X2,X3,X4) ) )
          | ~ member(X4,X1)
          | ~ member(X3,X1) )
      & partition(X0,X1) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f80,plain,
    ? [X0,X1,X2] :
      ( ~ equivalence(X2,X1)
      & ! [X3,X4] :
          ( ( ( apply(X2,X3,X4)
              | ! [X5] :
                  ( ~ member(X4,X5)
                  | ~ member(X3,X5)
                  | ~ member(X5,X0) ) )
            & ( ? [X6] :
                  ( member(X4,X6)
                  & member(X3,X6)
                  & member(X6,X0) )
              | ~ apply(X2,X3,X4) ) )
          | ~ member(X4,X1)
          | ~ member(X3,X1) )
      & partition(X0,X1) ),
    inference(rectify,[],[f79]) ).

fof(f81,plain,
    ( ? [X0,X1,X2] :
        ( ~ equivalence(X2,X1)
        & ! [X3,X4] :
            ( ( ( apply(X2,X3,X4)
                | ! [X5] :
                    ( ~ member(X4,X5)
                    | ~ member(X3,X5)
                    | ~ member(X5,X0) ) )
              & ( ? [X6] :
                    ( member(X4,X6)
                    & member(X3,X6)
                    & member(X6,X0) )
                | ~ apply(X2,X3,X4) ) )
            | ~ member(X4,X1)
            | ~ member(X3,X1) )
        & partition(X0,X1) )
   => ( ~ equivalence(sK13,sK12)
      & ! [X4,X3] :
          ( ( ( apply(sK13,X3,X4)
              | ! [X5] :
                  ( ~ member(X4,X5)
                  | ~ member(X3,X5)
                  | ~ member(X5,sK11) ) )
            & ( ? [X6] :
                  ( member(X4,X6)
                  & member(X3,X6)
                  & member(X6,sK11) )
              | ~ apply(sK13,X3,X4) ) )
          | ~ member(X4,sK12)
          | ~ member(X3,sK12) )
      & partition(sK11,sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ! [X3,X4] :
      ( ? [X6] :
          ( member(X4,X6)
          & member(X3,X6)
          & member(X6,sK11) )
     => ( member(X4,sK14(X3,X4))
        & member(X3,sK14(X3,X4))
        & member(sK14(X3,X4),sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ( ~ equivalence(sK13,sK12)
    & ! [X3,X4] :
        ( ( ( apply(sK13,X3,X4)
            | ! [X5] :
                ( ~ member(X4,X5)
                | ~ member(X3,X5)
                | ~ member(X5,sK11) ) )
          & ( ( member(X4,sK14(X3,X4))
              & member(X3,sK14(X3,X4))
              & member(sK14(X3,X4),sK11) )
            | ~ apply(sK13,X3,X4) ) )
        | ~ member(X4,sK12)
        | ~ member(X3,sK12) )
    & partition(sK11,sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f80,f82,f81]) ).

fof(f84,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f89,plain,
    ! [X2,X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f92,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f93,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f94,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f95,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f22]) ).

fof(f96,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f97,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X1)
      | ~ member(X0,difference(X2,X1)) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f98,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(X0,singleton(X1)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f56]) ).

fof(f101,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | X0 = X1
      | ~ member(X0,unordered_pair(X1,X2)) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f102,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f58]) ).

fof(f103,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X2 ),
    inference(cnf_transformation,[],[f58]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X1)
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( member(X0,sK2(X0,X1))
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( member(X0,sum(X1))
      | ~ member(X0,X2)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f107,plain,
    ! [X3,X0,X1] :
      ( member(X0,X3)
      | ~ member(X3,X1)
      | ~ member(X0,product(X1)) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( member(X0,product(X1))
      | member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( member(X0,product(X1))
      | ~ member(X0,sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f110,plain,
    ! [X0,X1,X7] :
      ( subset(X7,X1)
      | ~ member(X7,X0)
      | ~ partition(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f111,plain,
    ! [X0,X1,X5] :
      ( member(sK4(X0,X5),X0)
      | ~ member(X5,X1)
      | ~ partition(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f112,plain,
    ! [X0,X1,X5] :
      ( member(X5,sK4(X0,X5))
      | ~ member(X5,X1)
      | ~ partition(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f113,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X2 = X3
      | ~ member(X4,X3)
      | ~ member(X4,X2)
      | ~ member(X3,X0)
      | ~ member(X2,X0)
      | ~ partition(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( member(sK5(X0,X1),X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( member(sK6(X0,X1),X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( member(sK7(X0,X1),X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( apply(X0,sK5(X0,X1),sK6(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( apply(X0,sK6(X0,X1),sK7(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | member(sK8(X0,X1),X0)
      | member(sK10(X0,X1),X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | member(sK8(X0,X1),X0)
      | ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | member(sK9(X0,X1),X0)
      | member(sK10(X0,X1),X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | member(sK9(X0,X1),X0)
      | ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | apply(X1,sK8(X0,X1),sK9(X0,X1))
      | member(sK10(X0,X1),X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | apply(X1,sK8(X0,X1),sK9(X0,X1))
      | ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
      | member(sK10(X0,X1),X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( equivalence(X1,X0)
      | sP0(X1,X0)
      | ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
      | ~ apply(X1,sK10(X0,X1),sK10(X0,X1)) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f128,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,equivalence_class(X2,X1,X0)) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f129,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X0,X2,X3)
      | ~ member(X3,equivalence_class(X2,X1,X0)) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f130,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,equivalence_class(X2,X1,X0))
      | ~ apply(X0,X2,X3)
      | ~ member(X3,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f131,plain,
    partition(sK11,sK12),
    inference(cnf_transformation,[],[f83]) ).

fof(f132,plain,
    ! [X3,X4] :
      ( member(sK14(X3,X4),sK11)
      | ~ apply(sK13,X3,X4)
      | ~ member(X4,sK12)
      | ~ member(X3,sK12) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f133,plain,
    ! [X3,X4] :
      ( member(X3,sK14(X3,X4))
      | ~ apply(sK13,X3,X4)
      | ~ member(X4,sK12)
      | ~ member(X3,sK12) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f134,plain,
    ! [X3,X4] :
      ( member(X4,sK14(X3,X4))
      | ~ apply(sK13,X3,X4)
      | ~ member(X4,sK12)
      | ~ member(X3,sK12) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f135,plain,
    ! [X3,X4,X5] :
      ( apply(sK13,X3,X4)
      | ~ member(X4,X5)
      | ~ member(X3,X5)
      | ~ member(X5,sK11)
      | ~ member(X4,sK12)
      | ~ member(X3,sK12) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f136,plain,
    ~ equivalence(sK13,sK12),
    inference(cnf_transformation,[],[f83]) ).

fof(f137,plain,
    ! [X1] : member(X1,singleton(X1)),
    inference(equality_resolution,[],[f100]) ).

fof(f138,plain,
    ! [X2,X1] : member(X2,unordered_pair(X1,X2)),
    inference(equality_resolution,[],[f103]) ).

fof(f139,plain,
    ! [X2,X1] : member(X1,unordered_pair(X1,X2)),
    inference(equality_resolution,[],[f102]) ).

cnf(c_49,plain,
    ( ~ member(sK1(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_50,plain,
    ( member(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_53,plain,
    ( ~ member(X0,power_set(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_55,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_56,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

cnf(c_57,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_58,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_59,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_60,plain,
    ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_61,plain,
    ( ~ member(X0,X1)
    | member(X0,difference(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f98]) ).

cnf(c_62,plain,
    ( ~ member(X0,difference(X1,X2))
    | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_63,plain,
    ( ~ member(X0,difference(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_64,plain,
    member(X0,singleton(X0)),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_65,plain,
    ( ~ member(X0,singleton(X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_66,plain,
    member(X0,unordered_pair(X1,X0)),
    inference(cnf_transformation,[],[f138]) ).

cnf(c_67,plain,
    member(X0,unordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_68,plain,
    ( ~ member(X0,unordered_pair(X1,X2))
    | X0 = X1
    | X0 = X2 ),
    inference(cnf_transformation,[],[f101]) ).

cnf(c_69,plain,
    ( ~ member(X0,X1)
    | ~ member(X1,X2)
    | member(X0,sum(X2)) ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_70,plain,
    ( ~ member(X0,sum(X1))
    | member(X0,sK2(X0,X1)) ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_71,plain,
    ( ~ member(X0,sum(X1))
    | member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_72,plain,
    ( ~ member(X0,sK3(X0,X1))
    | member(X0,product(X1)) ),
    inference(cnf_transformation,[],[f109]) ).

cnf(c_73,plain,
    ( member(sK3(X0,X1),X1)
    | member(X0,product(X1)) ),
    inference(cnf_transformation,[],[f108]) ).

cnf(c_74,plain,
    ( ~ member(X0,product(X1))
    | ~ member(X2,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_75,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | ~ member(X3,X0)
    | ~ member(X3,X2)
    | ~ partition(X1,X4)
    | X0 = X2 ),
    inference(cnf_transformation,[],[f113]) ).

cnf(c_76,plain,
    ( ~ member(X0,X1)
    | ~ partition(X2,X1)
    | member(X0,sK4(X2,X0)) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_77,plain,
    ( ~ member(X0,X1)
    | ~ partition(X2,X1)
    | member(sK4(X2,X0),X2) ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_78,plain,
    ( ~ member(X0,X1)
    | ~ partition(X1,X2)
    | subset(X0,X2) ),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_79,plain,
    ( ~ apply(X0,sK5(X0,X1),sK7(X0,X1))
    | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_80,plain,
    ( ~ sP0(X0,X1)
    | apply(X0,sK6(X0,X1),sK7(X0,X1)) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_81,plain,
    ( ~ sP0(X0,X1)
    | apply(X0,sK5(X0,X1),sK6(X0,X1)) ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_82,plain,
    ( ~ sP0(X0,X1)
    | member(sK7(X0,X1),X1) ),
    inference(cnf_transformation,[],[f116]) ).

cnf(c_83,plain,
    ( ~ sP0(X0,X1)
    | member(sK6(X0,X1),X1) ),
    inference(cnf_transformation,[],[f115]) ).

cnf(c_84,plain,
    ( ~ sP0(X0,X1)
    | member(sK5(X0,X1),X1) ),
    inference(cnf_transformation,[],[f114]) ).

cnf(c_85,plain,
    ( ~ apply(X0,sK9(X1,X0),sK8(X1,X0))
    | ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
    | sP0(X0,X1)
    | equivalence(X0,X1) ),
    inference(cnf_transformation,[],[f127]) ).

cnf(c_86,plain,
    ( ~ apply(X0,sK9(X1,X0),sK8(X1,X0))
    | member(sK10(X1,X0),X1)
    | sP0(X0,X1)
    | equivalence(X0,X1) ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_87,plain,
    ( ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
    | apply(X0,sK8(X1,X0),sK9(X1,X0))
    | sP0(X0,X1)
    | equivalence(X0,X1) ),
    inference(cnf_transformation,[],[f125]) ).

cnf(c_88,plain,
    ( apply(X0,sK8(X1,X0),sK9(X1,X0))
    | member(sK10(X1,X0),X1)
    | sP0(X0,X1)
    | equivalence(X0,X1) ),
    inference(cnf_transformation,[],[f124]) ).

cnf(c_89,plain,
    ( ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
    | member(sK9(X1,X0),X1)
    | sP0(X0,X1)
    | equivalence(X0,X1) ),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_90,plain,
    ( member(sK9(X0,X1),X0)
    | member(sK10(X0,X1),X0)
    | sP0(X1,X0)
    | equivalence(X1,X0) ),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_91,plain,
    ( ~ apply(X0,sK10(X1,X0),sK10(X1,X0))
    | member(sK8(X1,X0),X1)
    | sP0(X0,X1)
    | equivalence(X0,X1) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_92,plain,
    ( member(sK8(X0,X1),X0)
    | member(sK10(X0,X1),X0)
    | sP0(X1,X0)
    | equivalence(X1,X0) ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_93,plain,
    ( ~ apply(X0,X1,X2)
    | ~ member(X2,X3)
    | member(X2,equivalence_class(X1,X3,X0)) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_94,plain,
    ( ~ member(X0,equivalence_class(X1,X2,X3))
    | apply(X3,X1,X0) ),
    inference(cnf_transformation,[],[f129]) ).

cnf(c_95,plain,
    ( ~ member(X0,equivalence_class(X1,X2,X3))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f128]) ).

cnf(c_96,negated_conjecture,
    ~ equivalence(sK13,sK12),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_97,negated_conjecture,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK11)
    | ~ member(X2,sK12)
    | apply(sK13,X0,X2) ),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_98,negated_conjecture,
    ( ~ apply(sK13,X0,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK12)
    | member(X1,sK14(X0,X1)) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_99,negated_conjecture,
    ( ~ apply(sK13,X0,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK12)
    | member(X0,sK14(X0,X1)) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_100,negated_conjecture,
    ( ~ apply(sK13,X0,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK12)
    | member(sK14(X0,X1),sK11) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_101,negated_conjecture,
    partition(sK11,sK12),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_428,negated_conjecture,
    partition(sK11,sK12),
    inference(demodulation,[status(thm)],[c_101]) ).

cnf(c_429,negated_conjecture,
    ( ~ apply(sK13,X0,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK12)
    | member(sK14(X0,X1),sK11) ),
    inference(demodulation,[status(thm)],[c_100]) ).

cnf(c_430,negated_conjecture,
    ( ~ apply(sK13,X0,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK12)
    | member(X0,sK14(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_99]) ).

cnf(c_431,negated_conjecture,
    ( ~ apply(sK13,X0,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK12)
    | member(X1,sK14(X0,X1)) ),
    inference(demodulation,[status(thm)],[c_98]) ).

cnf(c_432,negated_conjecture,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | ~ member(X0,sK12)
    | ~ member(X1,sK11)
    | ~ member(X2,sK12)
    | apply(sK13,X0,X2) ),
    inference(demodulation,[status(thm)],[c_97]) ).

cnf(c_433,negated_conjecture,
    ~ equivalence(sK13,sK12),
    inference(demodulation,[status(thm)],[c_96]) ).

cnf(c_60924,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_428,c_429,c_430,c_431,c_432,c_433,c_95,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_71,c_70,c_69,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET772+4 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.12  % Command  : run_iprover %s %d THM
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sun Jun 23 14:32:09 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 81.37/11.77  % SZS status Started for theBenchmark.p
% 81.37/11.77  % SZS status Theorem for theBenchmark.p
% 81.37/11.77  
% 81.37/11.77  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 81.37/11.77  
% 81.37/11.77  ------  iProver source info
% 81.37/11.77  
% 81.37/11.77  git: date: 2024-06-12 09:56:46 +0000
% 81.37/11.77  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 81.37/11.77  git: non_committed_changes: false
% 81.37/11.77  
% 81.37/11.77  ------ Parsing...
% 81.37/11.77  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 81.37/11.77  
% 81.37/11.77  ------ Preprocessing...
% 81.37/11.77  
% 81.37/11.77  ------ Preprocessing...
% 81.37/11.77  
% 81.37/11.77  ------ Preprocessing...
% 81.37/11.77  ------ Proving...
% 81.37/11.77  ------ Problem Properties 
% 81.37/11.77  
% 81.37/11.77  
% 81.37/11.77  clauses                                 53
% 81.37/11.77  conjectures                             6
% 81.37/11.77  EPR                                     7
% 81.37/11.77  Horn                                    40
% 81.37/11.77  unary                                   6
% 81.37/11.77  binary                                  23
% 81.37/11.77  lits                                    141
% 81.37/11.77  lits eq                                 4
% 81.37/11.77  fd_pure                                 0
% 81.37/11.77  fd_pseudo                               0
% 81.37/11.77  fd_cond                                 0
% 81.37/11.77  fd_pseudo_cond                          3
% 81.37/11.77  AC symbols                              0
% 81.37/11.77  
% 81.37/11.77  ------ Input Options Time Limit: Unbounded
% 81.37/11.77  
% 81.37/11.77  
% 81.37/11.77  ------ 
% 81.37/11.77  Current options:
% 81.37/11.77  ------ 
% 81.37/11.77  
% 81.37/11.77  
% 81.37/11.77  
% 81.37/11.77  
% 81.37/11.77  ------ Proving...
% 81.37/11.77  
% 81.37/11.77  
% 81.37/11.77  % SZS status Theorem for theBenchmark.p
% 81.37/11.77  
% 81.37/11.77  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 81.37/11.77  
% 81.37/11.77  
%------------------------------------------------------------------------------