TSTP Solution File: SET724+4 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET724+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 : Tue Apr 30 20:40:15 EDT 2024

% Result   : Theorem 19.33s 2.81s
% Output   : CNFRefutation 19.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   70 (   6 unt;   0 def)
%            Number of atoms       :  400 (  29 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  565 ( 235   ~; 240   |;  76   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (  10 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   2 prp; 0-4 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-7 aty)
%            Number of variables   :  313 ( 282   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f14,axiom,
    ! [G,F,A,B,C,X,Z] :
      ( ( member(X,A)
        & member(Z,C) )
     => ( apply(compose_function(G,F,A,B,C),X,Z)
      <=> ? [Y] :
            ( member(Y,B)
            & apply(F,X,Y)
            & apply(G,Y,Z) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [F,G,A,B] :
      ( equal_maps(F,G,A,B)
    <=> ! [X,Y1,Y2] :
          ( ( member(X,A)
            & member(Y1,B)
            & member(Y2,B) )
         => ( ( apply(F,X,Y1)
              & apply(G,X,Y2) )
           => Y1 = Y2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [F,A,B] :
      ( surjective(F,A,B)
    <=> ! [Y] :
          ( member(Y,B)
         => ? [E] :
              ( member(E,A)
              & apply(F,E,Y) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [F,A,Y] :
      ( member(Y,image2(F,A))
    <=> ? [X] :
          ( member(X,A)
          & apply(F,X,Y) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,conjecture,
    ! [F,G,H,A,B,C] :
      ( ( maps(F,A,B)
        & maps(G,B,C)
        & maps(H,B,C)
        & surjective(F,A,B)
        & equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C) )
     => equal_maps(G,H,B,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    ~ ! [F,G,H,A,B,C] :
        ( ( maps(F,A,B)
          & maps(G,B,C)
          & maps(H,B,C)
          & surjective(F,A,B)
          & equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C) )
       => equal_maps(G,H,B,C) ),
    inference(negated_conjecture,[status(cth)],[f29]) ).

fof(f111,plain,
    ! [G,F,A,B,C,X,Z] :
      ( ~ member(X,A)
      | ~ member(Z,C)
      | ( apply(compose_function(G,F,A,B,C),X,Z)
      <=> ? [Y] :
            ( member(Y,B)
            & apply(F,X,Y)
            & apply(G,Y,Z) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f112,plain,
    ! [G,F,A,B,C,X,Z] :
      ( ~ member(X,A)
      | ~ member(Z,C)
      | ( ( ~ apply(compose_function(G,F,A,B,C),X,Z)
          | ? [Y] :
              ( member(Y,B)
              & apply(F,X,Y)
              & apply(G,Y,Z) ) )
        & ( apply(compose_function(G,F,A,B,C),X,Z)
          | ! [Y] :
              ( ~ member(Y,B)
              | ~ apply(F,X,Y)
              | ~ apply(G,Y,Z) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f111]) ).

fof(f113,plain,
    ! [A,C,X,Z] :
      ( ~ member(X,A)
      | ~ member(Z,C)
      | ( ! [G,F,B] :
            ( ~ apply(compose_function(G,F,A,B,C),X,Z)
            | ? [Y] :
                ( member(Y,B)
                & apply(F,X,Y)
                & apply(G,Y,Z) ) )
        & ! [G,F,B] :
            ( apply(compose_function(G,F,A,B,C),X,Z)
            | ! [Y] :
                ( ~ member(Y,B)
                | ~ apply(F,X,Y)
                | ~ apply(G,Y,Z) ) ) ) ),
    inference(miniscoping,[status(esa)],[f112]) ).

fof(f114,plain,
    ! [A,C,X,Z] :
      ( ~ member(X,A)
      | ~ member(Z,C)
      | ( ! [G,F,B] :
            ( ~ apply(compose_function(G,F,A,B,C),X,Z)
            | ( member(sk0_11(B,F,G,Z,X,C,A),B)
              & apply(F,X,sk0_11(B,F,G,Z,X,C,A))
              & apply(G,sk0_11(B,F,G,Z,X,C,A),Z) ) )
        & ! [G,F,B] :
            ( apply(compose_function(G,F,A,B,C),X,Z)
            | ! [Y] :
                ( ~ member(Y,B)
                | ~ apply(F,X,Y)
                | ~ apply(G,Y,Z) ) ) ) ),
    inference(skolemization,[status(esa)],[f113]) ).

fof(f118,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ member(X0,X1)
      | ~ member(X2,X3)
      | apply(compose_function(X4,X5,X1,X6,X3),X0,X2)
      | ~ member(X7,X6)
      | ~ apply(X5,X0,X7)
      | ~ apply(X4,X7,X2) ),
    inference(cnf_transformation,[status(esa)],[f114]) ).

fof(f119,plain,
    ! [F,G,A,B] :
      ( equal_maps(F,G,A,B)
    <=> ! [X,Y1,Y2] :
          ( ~ member(X,A)
          | ~ member(Y1,B)
          | ~ member(Y2,B)
          | ~ apply(F,X,Y1)
          | ~ apply(G,X,Y2)
          | Y1 = Y2 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f120,plain,
    ! [F,G,A,B] :
      ( ( ~ equal_maps(F,G,A,B)
        | ! [X,Y1,Y2] :
            ( ~ member(X,A)
            | ~ member(Y1,B)
            | ~ member(Y2,B)
            | ~ apply(F,X,Y1)
            | ~ apply(G,X,Y2)
            | Y1 = Y2 ) )
      & ( equal_maps(F,G,A,B)
        | ? [X,Y1,Y2] :
            ( member(X,A)
            & member(Y1,B)
            & member(Y2,B)
            & apply(F,X,Y1)
            & apply(G,X,Y2)
            & Y1 != Y2 ) ) ),
    inference(NNF_transformation,[status(esa)],[f119]) ).

fof(f121,plain,
    ( ! [F,G,A,B] :
        ( ~ equal_maps(F,G,A,B)
        | ! [X,Y1,Y2] :
            ( ~ member(X,A)
            | ~ member(Y1,B)
            | ~ member(Y2,B)
            | ~ apply(F,X,Y1)
            | ~ apply(G,X,Y2)
            | Y1 = Y2 ) )
    & ! [F,G,A,B] :
        ( equal_maps(F,G,A,B)
        | ? [X,Y1,Y2] :
            ( member(X,A)
            & member(Y1,B)
            & member(Y2,B)
            & apply(F,X,Y1)
            & apply(G,X,Y2)
            & Y1 != Y2 ) ) ),
    inference(miniscoping,[status(esa)],[f120]) ).

fof(f122,plain,
    ( ! [F,G,A,B] :
        ( ~ equal_maps(F,G,A,B)
        | ! [X,Y1,Y2] :
            ( ~ member(X,A)
            | ~ member(Y1,B)
            | ~ member(Y2,B)
            | ~ apply(F,X,Y1)
            | ~ apply(G,X,Y2)
            | Y1 = Y2 ) )
    & ! [F,G,A,B] :
        ( equal_maps(F,G,A,B)
        | ( member(sk0_12(B,A,G,F),A)
          & member(sk0_13(B,A,G,F),B)
          & member(sk0_14(B,A,G,F),B)
          & apply(F,sk0_12(B,A,G,F),sk0_13(B,A,G,F))
          & apply(G,sk0_12(B,A,G,F),sk0_14(B,A,G,F))
          & sk0_13(B,A,G,F) != sk0_14(B,A,G,F) ) ) ),
    inference(skolemization,[status(esa)],[f121]) ).

fof(f123,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ equal_maps(X0,X1,X2,X3)
      | ~ member(X4,X2)
      | ~ member(X5,X3)
      | ~ member(X6,X3)
      | ~ apply(X0,X4,X5)
      | ~ apply(X1,X4,X6)
      | X5 = X6 ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f124,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X0,X1,X2,X3)
      | member(sk0_12(X3,X2,X1,X0),X2) ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f125,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X0,X1,X2,X3)
      | member(sk0_13(X3,X2,X1,X0),X3) ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f126,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X0,X1,X2,X3)
      | member(sk0_14(X3,X2,X1,X0),X3) ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f127,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X0,X1,X2,X3)
      | apply(X0,sk0_12(X3,X2,X1,X0),sk0_13(X3,X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f128,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X0,X1,X2,X3)
      | apply(X1,sk0_12(X3,X2,X1,X0),sk0_14(X3,X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f129,plain,
    ! [X0,X1,X2,X3] :
      ( equal_maps(X0,X1,X2,X3)
      | sk0_13(X3,X2,X1,X0) != sk0_14(X3,X2,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f148,plain,
    ! [F,A,B] :
      ( surjective(F,A,B)
    <=> ! [Y] :
          ( ~ member(Y,B)
          | ? [E] :
              ( member(E,A)
              & apply(F,E,Y) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f149,plain,
    ! [F,A,B] :
      ( ( ~ surjective(F,A,B)
        | ! [Y] :
            ( ~ member(Y,B)
            | ? [E] :
                ( member(E,A)
                & apply(F,E,Y) ) ) )
      & ( surjective(F,A,B)
        | ? [Y] :
            ( member(Y,B)
            & ! [E] :
                ( ~ member(E,A)
                | ~ apply(F,E,Y) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f148]) ).

fof(f150,plain,
    ( ! [F,A,B] :
        ( ~ surjective(F,A,B)
        | ! [Y] :
            ( ~ member(Y,B)
            | ? [E] :
                ( member(E,A)
                & apply(F,E,Y) ) ) )
    & ! [F,A,B] :
        ( surjective(F,A,B)
        | ? [Y] :
            ( member(Y,B)
            & ! [E] :
                ( ~ member(E,A)
                | ~ apply(F,E,Y) ) ) ) ),
    inference(miniscoping,[status(esa)],[f149]) ).

fof(f151,plain,
    ( ! [F,A,B] :
        ( ~ surjective(F,A,B)
        | ! [Y] :
            ( ~ member(Y,B)
            | ( member(sk0_19(Y,B,A,F),A)
              & apply(F,sk0_19(Y,B,A,F),Y) ) ) )
    & ! [F,A,B] :
        ( surjective(F,A,B)
        | ( member(sk0_20(B,A,F),B)
          & ! [E] :
              ( ~ member(E,A)
              | ~ apply(F,E,sk0_20(B,A,F)) ) ) ) ),
    inference(skolemization,[status(esa)],[f150]) ).

fof(f152,plain,
    ! [X0,X1,X2,X3] :
      ( ~ surjective(X0,X1,X2)
      | ~ member(X3,X2)
      | member(sk0_19(X3,X2,X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f153,plain,
    ! [X0,X1,X2,X3] :
      ( ~ surjective(X0,X1,X2)
      | ~ member(X3,X2)
      | apply(X0,sk0_19(X3,X2,X1,X0),X3) ),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f176,plain,
    ! [F,A,Y] :
      ( ( ~ member(Y,image2(F,A))
        | ? [X] :
            ( member(X,A)
            & apply(F,X,Y) ) )
      & ( member(Y,image2(F,A))
        | ! [X] :
            ( ~ member(X,A)
            | ~ apply(F,X,Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f22]) ).

fof(f177,plain,
    ( ! [F,A,Y] :
        ( ~ member(Y,image2(F,A))
        | ? [X] :
            ( member(X,A)
            & apply(F,X,Y) ) )
    & ! [F,A,Y] :
        ( member(Y,image2(F,A))
        | ! [X] :
            ( ~ member(X,A)
            | ~ apply(F,X,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f176]) ).

fof(f178,plain,
    ( ! [F,A,Y] :
        ( ~ member(Y,image2(F,A))
        | ( member(sk0_23(Y,A,F),A)
          & apply(F,sk0_23(Y,A,F),Y) ) )
    & ! [F,A,Y] :
        ( member(Y,image2(F,A))
        | ! [X] :
            ( ~ member(X,A)
            | ~ apply(F,X,Y) ) ) ),
    inference(skolemization,[status(esa)],[f177]) ).

fof(f179,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,image2(X1,X2))
      | member(sk0_23(X0,X2,X1),X2) ),
    inference(cnf_transformation,[status(esa)],[f178]) ).

fof(f180,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,image2(X1,X2))
      | apply(X1,sk0_23(X0,X2,X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f178]) ).

fof(f181,plain,
    ! [X0,X1,X2,X3] :
      ( member(X0,image2(X1,X2))
      | ~ member(X3,X2)
      | ~ apply(X1,X3,X0) ),
    inference(cnf_transformation,[status(esa)],[f178]) ).

fof(f244,plain,
    ? [F,G,H,A,B,C] :
      ( maps(F,A,B)
      & maps(G,B,C)
      & maps(H,B,C)
      & surjective(F,A,B)
      & equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C)
      & ~ equal_maps(G,H,B,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f245,plain,
    ? [G,H,B,C] :
      ( ? [F,A] :
          ( maps(F,A,B)
          & maps(G,B,C)
          & maps(H,B,C)
          & surjective(F,A,B)
          & equal_maps(compose_function(G,F,A,B,C),compose_function(H,F,A,B,C),A,C) )
      & ~ equal_maps(G,H,B,C) ),
    inference(miniscoping,[status(esa)],[f244]) ).

fof(f246,plain,
    ( maps(sk0_43,sk0_44,sk0_41)
    & maps(sk0_39,sk0_41,sk0_42)
    & maps(sk0_40,sk0_41,sk0_42)
    & surjective(sk0_43,sk0_44,sk0_41)
    & equal_maps(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),compose_function(sk0_40,sk0_43,sk0_44,sk0_41,sk0_42),sk0_44,sk0_42)
    & ~ equal_maps(sk0_39,sk0_40,sk0_41,sk0_42) ),
    inference(skolemization,[status(esa)],[f245]) ).

fof(f250,plain,
    surjective(sk0_43,sk0_44,sk0_41),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f251,plain,
    equal_maps(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),compose_function(sk0_40,sk0_43,sk0_44,sk0_41,sk0_42),sk0_44,sk0_42),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f252,plain,
    ~ equal_maps(sk0_39,sk0_40,sk0_41,sk0_42),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f269,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,sk0_44)
      | ~ member(X1,sk0_42)
      | ~ member(X2,sk0_42)
      | ~ apply(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),X0,X1)
      | ~ apply(compose_function(sk0_40,sk0_43,sk0_44,sk0_41,sk0_42),X0,X2)
      | X1 = X2 ),
    inference(resolution,[status(thm)],[f123,f251]) ).

fof(f270,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,sk0_44)
      | ~ member(X1,sk0_42)
      | ~ member(X2,sk0_41)
      | ~ apply(sk0_43,X0,X2)
      | ~ apply(sk0_40,X2,X1)
      | ~ member(X0,sk0_44)
      | ~ member(X3,sk0_42)
      | ~ member(X1,sk0_42)
      | ~ apply(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),X0,X3)
      | X3 = X1 ),
    inference(resolution,[status(thm)],[f118,f269]) ).

fof(f271,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,sk0_44)
      | ~ member(X1,sk0_42)
      | ~ member(X2,sk0_41)
      | ~ apply(sk0_43,X0,X2)
      | ~ apply(sk0_40,X2,X1)
      | ~ member(X3,sk0_42)
      | ~ apply(compose_function(sk0_39,sk0_43,sk0_44,sk0_41,sk0_42),X0,X3)
      | X3 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f270]) ).

fof(f274,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ member(X0,sk0_44)
      | ~ member(X1,sk0_42)
      | ~ member(X2,sk0_41)
      | ~ apply(sk0_43,X0,X2)
      | ~ apply(sk0_40,X2,X1)
      | ~ member(X3,sk0_42)
      | X3 = X1
      | ~ member(X0,sk0_44)
      | ~ member(X3,sk0_42)
      | ~ member(X4,sk0_41)
      | ~ apply(sk0_43,X0,X4)
      | ~ apply(sk0_39,X4,X3) ),
    inference(resolution,[status(thm)],[f271,f118]) ).

fof(f275,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ member(X0,sk0_44)
      | ~ member(X1,sk0_42)
      | ~ member(X2,sk0_41)
      | ~ apply(sk0_43,X0,X2)
      | ~ apply(sk0_40,X2,X1)
      | ~ member(X3,sk0_42)
      | X3 = X1
      | ~ member(X4,sk0_41)
      | ~ apply(sk0_43,X0,X4)
      | ~ apply(sk0_39,X4,X3) ),
    inference(duplicate_literals_removal,[status(esa)],[f274]) ).

fof(f2493,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ member(X0,image2(sk0_43,X1))
      | ~ member(sk0_23(X0,X1,sk0_43),sk0_44)
      | ~ member(X2,sk0_42)
      | ~ member(X3,sk0_41)
      | ~ apply(sk0_43,sk0_23(X0,X1,sk0_43),X3)
      | ~ apply(sk0_40,X3,X2)
      | ~ member(X4,sk0_42)
      | X4 = X2
      | ~ member(X0,sk0_41)
      | ~ apply(sk0_39,X0,X4) ),
    inference(resolution,[status(thm)],[f180,f275]) ).

fof(f2528,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,image2(sk0_43,X1))
      | ~ member(sk0_23(X0,X1,sk0_43),sk0_44)
      | ~ member(X2,sk0_42)
      | ~ member(X0,sk0_41)
      | ~ apply(sk0_40,X0,X2)
      | ~ member(X3,sk0_42)
      | X3 = X2
      | ~ member(X0,sk0_41)
      | ~ apply(sk0_39,X0,X3)
      | ~ member(X0,image2(sk0_43,X1)) ),
    inference(resolution,[status(thm)],[f2493,f180]) ).

fof(f2529,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,image2(sk0_43,X1))
      | ~ member(sk0_23(X0,X1,sk0_43),sk0_44)
      | ~ member(X2,sk0_42)
      | ~ member(X0,sk0_41)
      | ~ apply(sk0_40,X0,X2)
      | ~ member(X3,sk0_42)
      | X3 = X2
      | ~ apply(sk0_39,X0,X3) ),
    inference(duplicate_literals_removal,[status(esa)],[f2528]) ).

fof(f2532,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,image2(sk0_43,sk0_44))
      | ~ member(X1,sk0_42)
      | ~ member(X0,sk0_41)
      | ~ apply(sk0_40,X0,X1)
      | ~ member(X2,sk0_42)
      | X2 = X1
      | ~ apply(sk0_39,X0,X2)
      | ~ member(X0,image2(sk0_43,sk0_44)) ),
    inference(resolution,[status(thm)],[f2529,f179]) ).

fof(f2533,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,image2(sk0_43,sk0_44))
      | ~ member(X1,sk0_42)
      | ~ member(X0,sk0_41)
      | ~ apply(sk0_40,X0,X1)
      | ~ member(X2,sk0_42)
      | X2 = X1
      | ~ apply(sk0_39,X0,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f2532]) ).

fof(f2555,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,sk0_42)
      | ~ member(X1,sk0_41)
      | ~ apply(sk0_40,X1,X0)
      | ~ member(X2,sk0_42)
      | X2 = X0
      | ~ apply(sk0_39,X1,X2)
      | ~ member(X3,sk0_44)
      | ~ apply(sk0_43,X3,X1) ),
    inference(resolution,[status(thm)],[f2533,f181]) ).

fof(f2559,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ member(X0,sk0_42)
      | ~ member(X1,sk0_41)
      | ~ apply(sk0_40,X1,X0)
      | ~ member(X2,sk0_42)
      | X2 = X0
      | ~ apply(sk0_39,X1,X2)
      | ~ member(sk0_19(X1,X3,X4,sk0_43),sk0_44)
      | ~ surjective(sk0_43,X4,X3)
      | ~ member(X1,X3) ),
    inference(resolution,[status(thm)],[f2555,f153]) ).

fof(f2748,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,sk0_42)
      | ~ member(X1,sk0_41)
      | ~ apply(sk0_40,X1,X0)
      | ~ member(X2,sk0_42)
      | X2 = X0
      | ~ apply(sk0_39,X1,X2)
      | ~ surjective(sk0_43,sk0_44,X3)
      | ~ member(X1,X3)
      | ~ surjective(sk0_43,sk0_44,X3)
      | ~ member(X1,X3) ),
    inference(resolution,[status(thm)],[f2559,f152]) ).

fof(f2749,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,sk0_42)
      | ~ member(X1,sk0_41)
      | ~ apply(sk0_40,X1,X0)
      | ~ member(X2,sk0_42)
      | X2 = X0
      | ~ apply(sk0_39,X1,X2)
      | ~ surjective(sk0_43,sk0_44,X3)
      | ~ member(X1,X3) ),
    inference(duplicate_literals_removal,[status(esa)],[f2748]) ).

fof(f2751,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,sk0_42)
      | ~ member(X1,sk0_41)
      | ~ apply(sk0_40,X1,X0)
      | ~ member(X2,sk0_42)
      | X2 = X0
      | ~ apply(sk0_39,X1,X2)
      | ~ member(X1,sk0_41) ),
    inference(resolution,[status(thm)],[f2749,f250]) ).

fof(f2752,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,sk0_42)
      | ~ member(X1,sk0_41)
      | ~ apply(sk0_40,X1,X0)
      | ~ member(X2,sk0_42)
      | X2 = X0
      | ~ apply(sk0_39,X1,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f2751]) ).

fof(f2765,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(sk0_14(X0,X1,sk0_40,X2),sk0_42)
      | ~ member(sk0_12(X0,X1,sk0_40,X2),sk0_41)
      | ~ member(X3,sk0_42)
      | X3 = sk0_14(X0,X1,sk0_40,X2)
      | ~ apply(sk0_39,sk0_12(X0,X1,sk0_40,X2),X3)
      | equal_maps(X2,sk0_40,X1,X0) ),
    inference(resolution,[status(thm)],[f2752,f128]) ).

fof(f2797,plain,
    ! [X0,X1] :
      ( ~ member(sk0_14(X0,X1,sk0_40,sk0_39),sk0_42)
      | ~ member(sk0_12(X0,X1,sk0_40,sk0_39),sk0_41)
      | ~ member(sk0_13(X0,X1,sk0_40,sk0_39),sk0_42)
      | sk0_13(X0,X1,sk0_40,sk0_39) = sk0_14(X0,X1,sk0_40,sk0_39)
      | equal_maps(sk0_39,sk0_40,X1,X0)
      | equal_maps(sk0_39,sk0_40,X1,X0) ),
    inference(resolution,[status(thm)],[f2765,f127]) ).

fof(f2798,plain,
    ! [X0,X1] :
      ( ~ member(sk0_14(X0,X1,sk0_40,sk0_39),sk0_42)
      | ~ member(sk0_12(X0,X1,sk0_40,sk0_39),sk0_41)
      | ~ member(sk0_13(X0,X1,sk0_40,sk0_39),sk0_42)
      | sk0_13(X0,X1,sk0_40,sk0_39) = sk0_14(X0,X1,sk0_40,sk0_39)
      | equal_maps(sk0_39,sk0_40,X1,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f2797]) ).

fof(f2799,plain,
    ! [X0,X1] :
      ( ~ member(sk0_14(X0,X1,sk0_40,sk0_39),sk0_42)
      | ~ member(sk0_12(X0,X1,sk0_40,sk0_39),sk0_41)
      | ~ member(sk0_13(X0,X1,sk0_40,sk0_39),sk0_42)
      | equal_maps(sk0_39,sk0_40,X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2798,f129]) ).

fof(f2802,plain,
    ! [X0] :
      ( ~ member(sk0_12(sk0_42,X0,sk0_40,sk0_39),sk0_41)
      | ~ member(sk0_13(sk0_42,X0,sk0_40,sk0_39),sk0_42)
      | equal_maps(sk0_39,sk0_40,X0,sk0_42)
      | equal_maps(sk0_39,sk0_40,X0,sk0_42) ),
    inference(resolution,[status(thm)],[f2799,f126]) ).

fof(f2803,plain,
    ! [X0] :
      ( ~ member(sk0_12(sk0_42,X0,sk0_40,sk0_39),sk0_41)
      | ~ member(sk0_13(sk0_42,X0,sk0_40,sk0_39),sk0_42)
      | equal_maps(sk0_39,sk0_40,X0,sk0_42) ),
    inference(duplicate_literals_removal,[status(esa)],[f2802]) ).

fof(f2804,plain,
    ! [X0] :
      ( ~ member(sk0_12(sk0_42,X0,sk0_40,sk0_39),sk0_41)
      | equal_maps(sk0_39,sk0_40,X0,sk0_42) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2803,f125]) ).

fof(f2806,plain,
    ( spl0_51
  <=> equal_maps(sk0_39,sk0_40,sk0_41,sk0_42) ),
    introduced(split_symbol_definition) ).

fof(f2807,plain,
    ( equal_maps(sk0_39,sk0_40,sk0_41,sk0_42)
    | ~ spl0_51 ),
    inference(component_clause,[status(thm)],[f2806]) ).

fof(f2809,plain,
    ( equal_maps(sk0_39,sk0_40,sk0_41,sk0_42)
    | equal_maps(sk0_39,sk0_40,sk0_41,sk0_42) ),
    inference(resolution,[status(thm)],[f2804,f124]) ).

fof(f2810,plain,
    spl0_51,
    inference(split_clause,[status(thm)],[f2809,f2806]) ).

fof(f2812,plain,
    ( $false
    | ~ spl0_51 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2807,f252]) ).

fof(f2813,plain,
    ~ spl0_51,
    inference(contradiction_clause,[status(thm)],[f2812]) ).

fof(f2814,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2810,f2813]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SET724+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.05/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Mon Apr 29 21:36:05 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.14/0.32  % Drodi V3.6.0
% 19.33/2.81  % Refutation found
% 19.33/2.81  % SZS status Theorem for theBenchmark: Theorem is valid
% 19.33/2.81  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.33/2.86  % Elapsed time: 2.536492 seconds
% 19.33/2.86  % CPU time: 19.936518 seconds
% 19.33/2.86  % Total memory used: 150.386 MB
% 19.33/2.86  % Net memory used: 146.298 MB
%------------------------------------------------------------------------------