TSTP Solution File: SET712+4 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET712+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 : Fri May  3 03:01:19 EDT 2024

% Result   : Theorem 42.78s 6.68s
% Output   : CNFRefutation 42.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  114 (   7 unt;   0 def)
%            Number of atoms       :  488 (  46 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  600 ( 226   ~; 230   |; 100   &)
%                                         (  16 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-3 aty)
%            Number of variables   :  389 (   0 sgn 241   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,axiom,
    ! [X5,X0,X1] :
      ( maps(X5,X0,X1)
    <=> ( ! [X2,X6,X7] :
            ( ( member(X7,X1)
              & member(X6,X1)
              & member(X2,X0) )
           => ( ( apply(X5,X2,X7)
                & apply(X5,X2,X6) )
             => X6 = X7 ) )
        & ! [X2] :
            ( member(X2,X0)
           => ? [X4] :
                ( apply(X5,X2,X4)
                & member(X4,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).

fof(f17,axiom,
    ! [X5,X0,X1] :
      ( injective(X5,X0,X1)
    <=> ! [X12,X13,X4] :
          ( ( member(X4,X1)
            & member(X13,X0)
            & member(X12,X0) )
         => ( ( apply(X5,X13,X4)
              & apply(X5,X12,X4) )
           => X12 = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective) ).

fof(f18,axiom,
    ! [X5,X0,X1] :
      ( surjective(X5,X0,X1)
    <=> ! [X4] :
          ( member(X4,X1)
         => ? [X3] :
              ( apply(X5,X3,X4)
              & member(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).

fof(f19,axiom,
    ! [X5,X0,X1] :
      ( one_to_one(X5,X0,X1)
    <=> ( surjective(X5,X0,X1)
        & injective(X5,X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).

fof(f21,axiom,
    ! [X5,X0,X1,X2,X4] :
      ( ( member(X4,X1)
        & member(X2,X0) )
     => ( apply(X5,X2,X4)
      <=> apply(inverse_function(X5,X0,X1),X4,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).

fof(f29,conjecture,
    ! [X5,X0,X1] :
      ( ( one_to_one(X5,X0,X1)
        & maps(X5,X0,X1) )
     => maps(inverse_function(X5,X0,X1),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII03) ).

fof(f30,negated_conjecture,
    ~ ! [X5,X0,X1] :
        ( ( one_to_one(X5,X0,X1)
          & maps(X5,X0,X1) )
       => maps(inverse_function(X5,X0,X1),X1,X0) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
    <=> ( ! [X3,X4,X5] :
            ( ( member(X5,X2)
              & member(X4,X2)
              & member(X3,X1) )
           => ( ( apply(X0,X3,X5)
                & apply(X0,X3,X4) )
             => X4 = X5 ) )
        & ! [X6] :
            ( member(X6,X1)
           => ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) ) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( injective(X0,X1,X2)
    <=> ! [X3,X4,X5] :
          ( ( member(X5,X2)
            & member(X4,X1)
            & member(X3,X1) )
         => ( ( apply(X0,X4,X5)
              & apply(X0,X3,X5) )
           => X3 = X4 ) ) ),
    inference(rectify,[],[f17]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( surjective(X0,X1,X2)
    <=> ! [X3] :
          ( member(X3,X2)
         => ? [X4] :
              ( apply(X0,X4,X3)
              & member(X4,X1) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( one_to_one(X0,X1,X2)
    <=> ( surjective(X0,X1,X2)
        & injective(X0,X1,X2) ) ),
    inference(rectify,[],[f19]) ).

fof(f49,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( member(X4,X2)
        & member(X3,X1) )
     => ( apply(X0,X3,X4)
      <=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
    inference(rectify,[],[f21]) ).

fof(f57,plain,
    ~ ! [X0,X1,X2] :
        ( ( one_to_one(X0,X1,X2)
          & maps(X0,X1,X2) )
       => maps(inverse_function(X0,X1,X2),X2,X1) ),
    inference(rectify,[],[f30]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( one_to_one(X0,X1,X2)
     => ( surjective(X0,X1,X2)
        & injective(X0,X1,X2) ) ),
    inference(unused_predicate_definition_removal,[],[f47]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( surjective(X0,X1,X2)
     => ! [X3] :
          ( member(X3,X2)
         => ? [X4] :
              ( apply(X0,X4,X3)
              & member(X4,X1) ) ) ),
    inference(unused_predicate_definition_removal,[],[f46]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( injective(X0,X1,X2)
     => ! [X3,X4,X5] :
          ( ( member(X5,X2)
            & member(X4,X1)
            & member(X3,X1) )
         => ( ( apply(X0,X4,X5)
              & apply(X0,X3,X5) )
           => X3 = X4 ) ) ),
    inference(unused_predicate_definition_removal,[],[f45]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
    <=> ( ! [X3,X4,X5] :
            ( X4 = X5
            | ~ apply(X0,X3,X5)
            | ~ apply(X0,X3,X4)
            | ~ member(X5,X2)
            | ~ member(X4,X2)
            | ~ member(X3,X1) )
        & ! [X6] :
            ( ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) )
            | ~ member(X6,X1) ) ) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
    <=> ( ! [X3,X4,X5] :
            ( X4 = X5
            | ~ apply(X0,X3,X5)
            | ~ apply(X0,X3,X4)
            | ~ member(X5,X2)
            | ~ member(X4,X2)
            | ~ member(X3,X1) )
        & ! [X6] :
            ( ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) )
            | ~ member(X6,X1) ) ) ),
    inference(flattening,[],[f63]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4,X5] :
          ( X3 = X4
          | ~ apply(X0,X4,X5)
          | ~ apply(X0,X3,X5)
          | ~ member(X5,X2)
          | ~ member(X4,X1)
          | ~ member(X3,X1) )
      | ~ injective(X0,X1,X2) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4,X5] :
          ( X3 = X4
          | ~ apply(X0,X4,X5)
          | ~ apply(X0,X3,X5)
          | ~ member(X5,X2)
          | ~ member(X4,X1)
          | ~ member(X3,X1) )
      | ~ injective(X0,X1,X2) ),
    inference(flattening,[],[f67]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ? [X4] :
              ( apply(X0,X4,X3)
              & member(X4,X1) )
          | ~ member(X3,X2) )
      | ~ surjective(X0,X1,X2) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ( surjective(X0,X1,X2)
        & injective(X0,X1,X2) )
      | ~ one_to_one(X0,X1,X2) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f71,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( apply(X0,X3,X4)
      <=> apply(inverse_function(X0,X1,X2),X4,X3) )
      | ~ member(X4,X2)
      | ~ member(X3,X1) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f72,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( apply(X0,X3,X4)
      <=> apply(inverse_function(X0,X1,X2),X4,X3) )
      | ~ member(X4,X2)
      | ~ member(X3,X1) ),
    inference(flattening,[],[f71]) ).

fof(f73,plain,
    ? [X0,X1,X2] :
      ( ~ maps(inverse_function(X0,X1,X2),X2,X1)
      & one_to_one(X0,X1,X2)
      & maps(X0,X1,X2) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f74,plain,
    ? [X0,X1,X2] :
      ( ~ maps(inverse_function(X0,X1,X2),X2,X1)
      & one_to_one(X0,X1,X2)
      & maps(X0,X1,X2) ),
    inference(flattening,[],[f73]) ).

fof(f75,plain,
    ! [X0,X2,X1] :
      ( sP0(X0,X2,X1)
    <=> ! [X3,X4,X5] :
          ( X4 = X5
          | ~ apply(X0,X3,X5)
          | ~ apply(X0,X3,X4)
          | ~ member(X5,X2)
          | ~ member(X4,X2)
          | ~ member(X3,X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( maps(X0,X1,X2)
    <=> ( sP0(X0,X2,X1)
        & ! [X6] :
            ( ? [X7] :
                ( apply(X0,X6,X7)
                & member(X7,X2) )
            | ~ member(X6,X1) ) ) ),
    inference(definition_folding,[],[f64,f75]) ).

fof(f99,plain,
    ! [X0,X2,X1] :
      ( ( sP0(X0,X2,X1)
        | ? [X3,X4,X5] :
            ( X4 != X5
            & apply(X0,X3,X5)
            & apply(X0,X3,X4)
            & member(X5,X2)
            & member(X4,X2)
            & member(X3,X1) ) )
      & ( ! [X3,X4,X5] :
            ( X4 = X5
            | ~ apply(X0,X3,X5)
            | ~ apply(X0,X3,X4)
            | ~ member(X5,X2)
            | ~ member(X4,X2)
            | ~ member(X3,X1) )
        | ~ sP0(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3,X4,X5] :
            ( X4 != X5
            & apply(X0,X3,X5)
            & apply(X0,X3,X4)
            & member(X5,X1)
            & member(X4,X1)
            & member(X3,X2) ) )
      & ( ! [X6,X7,X8] :
            ( X7 = X8
            | ~ apply(X0,X6,X8)
            | ~ apply(X0,X6,X7)
            | ~ member(X8,X1)
            | ~ member(X7,X1)
            | ~ member(X6,X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f99]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( X4 != X5
          & apply(X0,X3,X5)
          & apply(X0,X3,X4)
          & member(X5,X1)
          & member(X4,X1)
          & member(X3,X2) )
     => ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
        & apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
        & apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
        & member(sK6(X0,X1,X2),X1)
        & member(sK5(X0,X1,X2),X1)
        & member(sK4(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
          & apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
          & apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
          & member(sK6(X0,X1,X2),X1)
          & member(sK5(X0,X1,X2),X1)
          & member(sK4(X0,X1,X2),X2) ) )
      & ( ! [X6,X7,X8] :
            ( X7 = X8
            | ~ apply(X0,X6,X8)
            | ~ apply(X0,X6,X7)
            | ~ member(X8,X1)
            | ~ member(X7,X1)
            | ~ member(X6,X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f100,f101]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ( maps(X0,X1,X2)
        | ~ sP0(X0,X2,X1)
        | ? [X6] :
            ( ! [X7] :
                ( ~ apply(X0,X6,X7)
                | ~ member(X7,X2) )
            & member(X6,X1) ) )
      & ( ( sP0(X0,X2,X1)
          & ! [X6] :
              ( ? [X7] :
                  ( apply(X0,X6,X7)
                  & member(X7,X2) )
              | ~ member(X6,X1) ) )
        | ~ maps(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ( maps(X0,X1,X2)
        | ~ sP0(X0,X2,X1)
        | ? [X6] :
            ( ! [X7] :
                ( ~ apply(X0,X6,X7)
                | ~ member(X7,X2) )
            & member(X6,X1) ) )
      & ( ( sP0(X0,X2,X1)
          & ! [X6] :
              ( ? [X7] :
                  ( apply(X0,X6,X7)
                  & member(X7,X2) )
              | ~ member(X6,X1) ) )
        | ~ maps(X0,X1,X2) ) ),
    inference(flattening,[],[f103]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( ( maps(X0,X1,X2)
        | ~ sP0(X0,X2,X1)
        | ? [X3] :
            ( ! [X4] :
                ( ~ apply(X0,X3,X4)
                | ~ member(X4,X2) )
            & member(X3,X1) ) )
      & ( ( sP0(X0,X2,X1)
          & ! [X5] :
              ( ? [X6] :
                  ( apply(X0,X5,X6)
                  & member(X6,X2) )
              | ~ member(X5,X1) ) )
        | ~ maps(X0,X1,X2) ) ),
    inference(rectify,[],[f104]) ).

fof(f106,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ! [X4] :
              ( ~ apply(X0,X3,X4)
              | ~ member(X4,X2) )
          & member(X3,X1) )
     => ( ! [X4] :
            ( ~ apply(X0,sK7(X0,X1,X2),X4)
            | ~ member(X4,X2) )
        & member(sK7(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0,X2,X5] :
      ( ? [X6] :
          ( apply(X0,X5,X6)
          & member(X6,X2) )
     => ( apply(X0,X5,sK8(X0,X2,X5))
        & member(sK8(X0,X2,X5),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ! [X0,X1,X2] :
      ( ( maps(X0,X1,X2)
        | ~ sP0(X0,X2,X1)
        | ( ! [X4] :
              ( ~ apply(X0,sK7(X0,X1,X2),X4)
              | ~ member(X4,X2) )
          & member(sK7(X0,X1,X2),X1) ) )
      & ( ( sP0(X0,X2,X1)
          & ! [X5] :
              ( ( apply(X0,X5,sK8(X0,X2,X5))
                & member(sK8(X0,X2,X5),X2) )
              | ~ member(X5,X1) ) )
        | ~ maps(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f105,f107,f106]) ).

fof(f113,plain,
    ! [X0,X1,X3] :
      ( ? [X4] :
          ( apply(X0,X4,X3)
          & member(X4,X1) )
     => ( apply(X0,sK10(X0,X1,X3),X3)
        & member(sK10(X0,X1,X3),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ( apply(X0,sK10(X0,X1,X3),X3)
            & member(sK10(X0,X1,X3),X1) )
          | ~ member(X3,X2) )
      | ~ surjective(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f69,f113]) ).

fof(f115,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( apply(X0,X3,X4)
          | ~ apply(inverse_function(X0,X1,X2),X4,X3) )
        & ( apply(inverse_function(X0,X1,X2),X4,X3)
          | ~ apply(X0,X3,X4) ) )
      | ~ member(X4,X2)
      | ~ member(X3,X1) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f134,plain,
    ( ? [X0,X1,X2] :
        ( ~ maps(inverse_function(X0,X1,X2),X2,X1)
        & one_to_one(X0,X1,X2)
        & maps(X0,X1,X2) )
   => ( ~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16)
      & one_to_one(sK15,sK16,sK17)
      & maps(sK15,sK16,sK17) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16)
    & one_to_one(sK15,sK16,sK17)
    & maps(sK15,sK16,sK17) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f74,f134]) ).

fof(f163,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | member(sK4(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f164,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | member(sK5(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f165,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | member(sK6(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f166,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f167,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f168,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | sK5(X0,X1,X2) != sK6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f172,plain,
    ! [X2,X0,X1] :
      ( maps(X0,X1,X2)
      | ~ sP0(X0,X2,X1)
      | member(sK7(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f173,plain,
    ! [X2,X0,X1,X4] :
      ( maps(X0,X1,X2)
      | ~ sP0(X0,X2,X1)
      | ~ apply(X0,sK7(X0,X1,X2),X4)
      | ~ member(X4,X2) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f178,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( X3 = X4
      | ~ apply(X0,X4,X5)
      | ~ apply(X0,X3,X5)
      | ~ member(X5,X2)
      | ~ member(X4,X1)
      | ~ member(X3,X1)
      | ~ injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f179,plain,
    ! [X2,X3,X0,X1] :
      ( member(sK10(X0,X1,X3),X1)
      | ~ member(X3,X2)
      | ~ surjective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f180,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X0,sK10(X0,X1,X3),X3)
      | ~ member(X3,X2)
      | ~ surjective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f181,plain,
    ! [X2,X0,X1] :
      ( injective(X0,X1,X2)
      | ~ one_to_one(X0,X1,X2) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f182,plain,
    ! [X2,X0,X1] :
      ( surjective(X0,X1,X2)
      | ~ one_to_one(X0,X1,X2) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f183,plain,
    ! [X2,X3,X0,X1,X4] :
      ( apply(inverse_function(X0,X1,X2),X4,X3)
      | ~ apply(X0,X3,X4)
      | ~ member(X4,X2)
      | ~ member(X3,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f184,plain,
    ! [X2,X3,X0,X1,X4] :
      ( apply(X0,X3,X4)
      | ~ apply(inverse_function(X0,X1,X2),X4,X3)
      | ~ member(X4,X2)
      | ~ member(X3,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f200,plain,
    one_to_one(sK15,sK16,sK17),
    inference(cnf_transformation,[],[f135]) ).

fof(f201,plain,
    ~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_75,plain,
    ( sK5(X0,X1,X2) != sK6(X0,X1,X2)
    | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_76,plain,
    ( apply(X0,sK4(X0,X1,X2),sK6(X0,X1,X2))
    | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_77,plain,
    ( apply(X0,sK4(X0,X1,X2),sK5(X0,X1,X2))
    | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_78,plain,
    ( member(sK6(X0,X1,X2),X1)
    | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_79,plain,
    ( member(sK5(X0,X1,X2),X1)
    | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_80,plain,
    ( member(sK4(X0,X1,X2),X2)
    | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_82,plain,
    ( ~ apply(X0,sK7(X0,X1,X2),X3)
    | ~ sP0(X0,X2,X1)
    | ~ member(X3,X2)
    | maps(X0,X1,X2) ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_83,plain,
    ( ~ sP0(X0,X1,X2)
    | member(sK7(X0,X2,X1),X2)
    | maps(X0,X2,X1) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_91,plain,
    ( ~ apply(X0,X1,X2)
    | ~ apply(X0,X3,X2)
    | ~ injective(X0,X4,X5)
    | ~ member(X1,X4)
    | ~ member(X2,X5)
    | ~ member(X3,X4)
    | X1 = X3 ),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_92,plain,
    ( ~ surjective(X0,X1,X2)
    | ~ member(X3,X2)
    | apply(X0,sK10(X0,X1,X3),X3) ),
    inference(cnf_transformation,[],[f180]) ).

cnf(c_93,plain,
    ( ~ surjective(X0,X1,X2)
    | ~ member(X3,X2)
    | member(sK10(X0,X1,X3),X1) ),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_94,plain,
    ( ~ one_to_one(X0,X1,X2)
    | surjective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_95,plain,
    ( ~ one_to_one(X0,X1,X2)
    | injective(X0,X1,X2) ),
    inference(cnf_transformation,[],[f181]) ).

cnf(c_96,plain,
    ( ~ apply(inverse_function(X0,X1,X2),X3,X4)
    | ~ member(X3,X2)
    | ~ member(X4,X1)
    | apply(X0,X4,X3) ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_97,plain,
    ( ~ apply(X0,X1,X2)
    | ~ member(X1,X3)
    | ~ member(X2,X4)
    | apply(inverse_function(X0,X3,X4),X2,X1) ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_112,negated_conjecture,
    ~ maps(inverse_function(sK15,sK16,sK17),sK17,sK16),
    inference(cnf_transformation,[],[f201]) ).

cnf(c_113,negated_conjecture,
    one_to_one(sK15,sK16,sK17),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_238,plain,
    ( surjective(X0,X1,X2)
    | ~ one_to_one(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_94]) ).

cnf(c_239,plain,
    ( ~ one_to_one(X0,X1,X2)
    | surjective(X0,X1,X2) ),
    inference(renaming,[status(thm)],[c_238]) ).

cnf(c_242,plain,
    ( ~ one_to_one(X0,X1,X2)
    | injective(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_95]) ).

cnf(c_1085,plain,
    ( X0 != sK15
    | X1 != sK16
    | X2 != sK17
    | injective(X0,X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_242,c_113]) ).

cnf(c_1086,plain,
    injective(sK15,sK16,sK17),
    inference(unflattening,[status(thm)],[c_1085]) ).

cnf(c_1090,plain,
    ( X0 != sK15
    | X1 != sK16
    | X2 != sK17
    | surjective(X0,X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_239,c_113]) ).

cnf(c_1091,plain,
    surjective(sK15,sK16,sK17),
    inference(unflattening,[status(thm)],[c_1090]) ).

cnf(c_1097,plain,
    ( X0 != sK15
    | X1 != sK16
    | X2 != sK17
    | ~ member(X3,X2)
    | member(sK10(X0,X1,X3),X1) ),
    inference(resolution_lifted,[status(thm)],[c_93,c_1091]) ).

cnf(c_1098,plain,
    ( ~ member(X0,sK17)
    | member(sK10(sK15,sK16,X0),sK16) ),
    inference(unflattening,[status(thm)],[c_1097]) ).

cnf(c_1106,plain,
    ( X0 != sK15
    | X1 != sK16
    | X2 != sK17
    | ~ member(X3,X2)
    | apply(X0,sK10(X0,X1,X3),X3) ),
    inference(resolution_lifted,[status(thm)],[c_92,c_1091]) ).

cnf(c_1107,plain,
    ( ~ member(X0,sK17)
    | apply(sK15,sK10(sK15,sK16,X0),X0) ),
    inference(unflattening,[status(thm)],[c_1106]) ).

cnf(c_1119,plain,
    ( X0 != sK15
    | X1 != sK16
    | X2 != sK17
    | ~ apply(X0,X3,X4)
    | ~ apply(X0,X5,X4)
    | ~ member(X3,X1)
    | ~ member(X4,X2)
    | ~ member(X5,X1)
    | X3 = X5 ),
    inference(resolution_lifted,[status(thm)],[c_91,c_1086]) ).

cnf(c_1120,plain,
    ( ~ apply(sK15,X0,X1)
    | ~ apply(sK15,X2,X1)
    | ~ member(X0,sK16)
    | ~ member(X1,sK17)
    | ~ member(X2,sK16)
    | X0 = X2 ),
    inference(unflattening,[status(thm)],[c_1119]) ).

cnf(c_1317,plain,
    ( inverse_function(sK15,sK16,sK17) != X0
    | X1 != sK16
    | X2 != sK17
    | ~ sP0(X0,X1,X2)
    | member(sK7(X0,X2,X1),X2) ),
    inference(resolution_lifted,[status(thm)],[c_83,c_112]) ).

cnf(c_1318,plain,
    ( ~ sP0(inverse_function(sK15,sK16,sK17),sK16,sK17)
    | member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17) ),
    inference(unflattening,[status(thm)],[c_1317]) ).

cnf(c_1911,plain,
    ( ~ member(X0,sK17)
    | member(sK10(sK15,sK16,X0),sK16) ),
    inference(prop_impl_just,[status(thm)],[c_1098]) ).

cnf(c_1913,plain,
    ( ~ member(X0,sK17)
    | apply(sK15,sK10(sK15,sK16,X0),X0) ),
    inference(prop_impl_just,[status(thm)],[c_1107]) ).

cnf(c_4849,plain,
    ( apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK5(inverse_function(sK15,sK16,sK17),sK16,sK17))
    | sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_77]) ).

cnf(c_4850,plain,
    ( apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK6(inverse_function(sK15,sK16,sK17),sK16,sK17))
    | sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_76]) ).

cnf(c_4851,plain,
    ( sK5(inverse_function(sK15,sK16,sK17),sK16,sK17) != sK6(inverse_function(sK15,sK16,sK17),sK16,sK17)
    | sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_75]) ).

cnf(c_4852,plain,
    ( member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
    | sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_80]) ).

cnf(c_4853,plain,
    ( member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_4854,plain,
    ( member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | sP0(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_7075,plain,
    ( ~ apply(inverse_function(X0,X1,X2),sK4(inverse_function(X0,X1,X2),X3,X4),sK6(inverse_function(X0,X1,X2),X3,X4))
    | ~ member(sK6(inverse_function(X0,X1,X2),X3,X4),X1)
    | ~ member(sK4(inverse_function(X0,X1,X2),X3,X4),X2)
    | apply(X0,sK6(inverse_function(X0,X1,X2),X3,X4),sK4(inverse_function(X0,X1,X2),X3,X4)) ),
    inference(instantiation,[status(thm)],[c_96]) ).

cnf(c_7190,plain,
    ( ~ apply(inverse_function(X0,X1,X2),sK4(inverse_function(X0,X1,X2),X3,X4),sK5(inverse_function(X0,X1,X2),X3,X4))
    | ~ member(sK5(inverse_function(X0,X1,X2),X3,X4),X1)
    | ~ member(sK4(inverse_function(X0,X1,X2),X3,X4),X2)
    | apply(X0,sK5(inverse_function(X0,X1,X2),X3,X4),sK4(inverse_function(X0,X1,X2),X3,X4)) ),
    inference(instantiation,[status(thm)],[c_96]) ).

cnf(c_8104,plain,
    ( ~ apply(sK15,sK5(X0,X1,X2),X3)
    | ~ apply(sK15,sK6(X0,X1,X2),X3)
    | ~ member(sK5(X0,X1,X2),sK16)
    | ~ member(sK6(X0,X1,X2),sK16)
    | ~ member(X3,sK17)
    | sK5(X0,X1,X2) = sK6(X0,X1,X2) ),
    inference(instantiation,[status(thm)],[c_1120]) ).

cnf(c_8149,plain,
    ( ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
    | apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)) ),
    inference(instantiation,[status(thm)],[c_1913]) ).

cnf(c_8150,plain,
    ( ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
    | member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK16) ),
    inference(instantiation,[status(thm)],[c_1911]) ).

cnf(c_10169,plain,
    ( ~ apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))
    | ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),X0)
    | ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),X1)
    | apply(inverse_function(sK15,X0,X1),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))) ),
    inference(instantiation,[status(thm)],[c_97]) ).

cnf(c_12911,plain,
    ( ~ apply(sK15,sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),X0)
    | ~ apply(sK15,sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),X0)
    | ~ member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | ~ member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | ~ member(X0,sK17)
    | sK5(inverse_function(sK15,sK16,sK17),sK16,sK17) = sK6(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_8104]) ).

cnf(c_13849,plain,
    ( ~ apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK6(inverse_function(sK15,sK16,sK17),sK16,sK17))
    | ~ member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | ~ member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
    | apply(sK15,sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17)) ),
    inference(instantiation,[status(thm)],[c_7075]) ).

cnf(c_13851,plain,
    ( ~ apply(inverse_function(sK15,sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK5(inverse_function(sK15,sK16,sK17),sK16,sK17))
    | ~ member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | ~ member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
    | apply(sK15,sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17)) ),
    inference(instantiation,[status(thm)],[c_7190]) ).

cnf(c_21499,plain,
    ( ~ apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))
    | ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),X0)
    | ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
    | apply(inverse_function(sK15,X0,sK17),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))) ),
    inference(instantiation,[status(thm)],[c_10169]) ).

cnf(c_21500,plain,
    ( ~ apply(sK15,sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))
    | ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK16)
    | ~ member(sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK17)
    | apply(inverse_function(sK15,sK16,sK17),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16))) ),
    inference(instantiation,[status(thm)],[c_21499]) ).

cnf(c_22311,plain,
    ( ~ apply(sK15,sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17))
    | ~ apply(sK15,sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK4(inverse_function(sK15,sK16,sK17),sK16,sK17))
    | ~ member(sK5(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | ~ member(sK6(inverse_function(sK15,sK16,sK17),sK16,sK17),sK16)
    | ~ member(sK4(inverse_function(sK15,sK16,sK17),sK16,sK17),sK17)
    | sK5(inverse_function(sK15,sK16,sK17),sK16,sK17) = sK6(inverse_function(sK15,sK16,sK17),sK16,sK17) ),
    inference(instantiation,[status(thm)],[c_12911]) ).

cnf(c_24649,plain,
    ( ~ apply(inverse_function(sK15,sK16,sK17),sK7(inverse_function(sK15,sK16,sK17),sK17,sK16),sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)))
    | ~ member(sK10(sK15,sK16,sK7(inverse_function(sK15,sK16,sK17),sK17,sK16)),sK16)
    | ~ sP0(inverse_function(sK15,sK16,sK17),sK16,sK17)
    | maps(inverse_function(sK15,sK16,sK17),sK17,sK16) ),
    inference(instantiation,[status(thm)],[c_82]) ).

cnf(c_24650,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_24649,c_22311,c_21500,c_13851,c_13849,c_8149,c_8150,c_4849,c_4850,c_4851,c_4852,c_4853,c_4854,c_1318,c_112]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET712+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.10/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n014.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 20:23:17 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.43  Running first-order theorem proving
% 0.16/0.43  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
% 42.78/6.68  % SZS status Started for theBenchmark.p
% 42.78/6.68  % SZS status Theorem for theBenchmark.p
% 42.78/6.68  
% 42.78/6.68  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 42.78/6.68  
% 42.78/6.68  ------  iProver source info
% 42.78/6.68  
% 42.78/6.68  git: date: 2024-05-02 19:28:25 +0000
% 42.78/6.68  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 42.78/6.68  git: non_committed_changes: false
% 42.78/6.68  
% 42.78/6.68  ------ Parsing...
% 42.78/6.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 42.78/6.68  
% 42.78/6.68  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 42.78/6.68  
% 42.78/6.68  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 42.78/6.68  
% 42.78/6.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 42.78/6.68  ------ Proving...
% 42.78/6.68  ------ Problem Properties 
% 42.78/6.68  
% 42.78/6.68  
% 42.78/6.68  clauses                                 63
% 42.78/6.68  conjectures                             2
% 42.78/6.68  EPR                                     6
% 42.78/6.68  Horn                                    52
% 42.78/6.68  unary                                   6
% 42.78/6.68  binary                                  34
% 42.78/6.68  lits                                    161
% 42.78/6.68  lits eq                                 6
% 42.78/6.68  fd_pure                                 0
% 42.78/6.68  fd_pseudo                               0
% 42.78/6.68  fd_cond                                 0
% 42.78/6.68  fd_pseudo_cond                          4
% 42.78/6.68  AC symbols                              0
% 42.78/6.68  
% 42.78/6.68  ------ Input Options Time Limit: Unbounded
% 42.78/6.68  
% 42.78/6.68  
% 42.78/6.68  ------ 
% 42.78/6.68  Current options:
% 42.78/6.68  ------ 
% 42.78/6.68  
% 42.78/6.68  
% 42.78/6.68  
% 42.78/6.68  
% 42.78/6.68  ------ Proving...
% 42.78/6.68  
% 42.78/6.68  
% 42.78/6.68  % SZS status Theorem for theBenchmark.p
% 42.78/6.68  
% 42.78/6.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 42.78/6.68  
% 42.78/6.68  
%------------------------------------------------------------------------------