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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : SEU293+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:20:02 PM UTC 2026

% Result   : Theorem 0.18s 0.59s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   82 (  18 unt;   1 def)
%            Number of atoms       :  313 (  68 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  360 ( 129   ~; 136   |;  67   &)
%                                         (  14 <=>;  13  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :  150 ( 132   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A,B,C] :
      ( element(C,powerset(cartesian_product2(A,B)))
     => relation(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] :
      ( ( function(A)
        & relation(A) )
     => ! [B,C] :
          ( C = relation_inverse_image(A,B)
        <=> ! [D] :
              ( in(D,C)
            <=> ( in(apply(A,D),B)
                & in(D,relation_dom(A)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
     => ( ( B = empty_set
         => ( ( quasi_total(C,A,B)
            <=> C = empty_set )
            | A = empty_set ) )
        & ( ( B = empty_set
           => A = empty_set )
         => ( quasi_total(C,A,B)
          <=> A = relation_dom_as_subset(A,B,C) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
     => element(C,powerset(cartesian_product2(A,B))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ? [A] :
      ( empty(A)
      & one_to_one(A)
      & function(A)
      & relation(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,axiom,
    ! [A,B,C] :
      ( relation_of2(C,A,B)
     => relation_dom_as_subset(A,B,C) = relation_dom(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f43,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
    <=> relation_of2(C,A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f48,conjecture,
    ! [A,B,C,D] :
      ( ( relation_of2_as_subset(D,A,B)
        & quasi_total(D,A,B)
        & function(D) )
     => ( B != empty_set
       => ! [E] :
            ( in(E,relation_inverse_image(D,C))
          <=> ( in(apply(D,E),C)
              & in(E,A) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f49,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( relation_of2_as_subset(D,A,B)
          & quasi_total(D,A,B)
          & function(D) )
       => ( B != empty_set
         => ! [E] :
              ( in(E,relation_inverse_image(D,C))
            <=> ( in(apply(D,E),C)
                & in(E,A) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f48]) ).

fof(f52,axiom,
    ! [A] :
      ( empty(A)
     => A = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f61,plain,
    ! [A,B,C] :
      ( relation(C)
      | ~ element(C,powerset(cartesian_product2(A,B))) ),
    inference(pre_NNF_transformation,[status(thm)],[f4]) ).

fof(f62,plain,
    ! [C] :
      ( relation(C)
      | ! [A,B] : ~ element(C,powerset(cartesian_product2(A,B))) ),
    inference(miniscoping,[status(thm)],[f61]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( relation(X0)
      | ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
    inference(cnf_transformation,[status(thm)],[f62]) ).

fof(f68,plain,
    ! [A] :
      ( ! [B,C] :
          ( C = relation_inverse_image(A,B)
        <=> ! [D] :
              ( in(D,C)
            <=> ( in(apply(A,D),B)
                & in(D,relation_dom(A)) ) ) )
      | ~ function(A)
      | ~ relation(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f6]) ).

fof(f69,plain,
    ! [A] :
      ( ! [B,C] :
          ( ( ? [D] :
                ( ( ( in(apply(A,D),B)
                    & in(D,relation_dom(A)) )
                  | in(D,C) )
                & ( ~ in(apply(A,D),B)
                  | ~ in(D,relation_dom(A))
                  | ~ in(D,C) ) )
            | C = relation_inverse_image(A,B) )
          & ( ! [D] :
                ( ( ~ in(apply(A,D),B)
                  | ~ in(D,relation_dom(A))
                  | in(D,C) )
                & ( ( in(apply(A,D),B)
                    & in(D,relation_dom(A)) )
                  | ~ in(D,C) ) )
            | C != relation_inverse_image(A,B) ) )
      | ~ function(A)
      | ~ relation(A) ),
    inference(NNF_transformation,[status(thm)],[f68]) ).

fof(f70,plain,
    ! [A] :
      ( ( ! [B,C] :
            ( ? [D] :
                ( ( ( in(apply(A,D),B)
                    & in(D,relation_dom(A)) )
                  | in(D,C) )
                & ( ~ in(apply(A,D),B)
                  | ~ in(D,relation_dom(A))
                  | ~ in(D,C) ) )
            | C = relation_inverse_image(A,B) )
        & ! [B,C] :
            ( ( ! [D] :
                  ( ~ in(apply(A,D),B)
                  | ~ in(D,relation_dom(A))
                  | in(D,C) )
              & ! [D] :
                  ( ( in(apply(A,D),B)
                    & in(D,relation_dom(A)) )
                  | ~ in(D,C) ) )
            | C != relation_inverse_image(A,B) ) )
      | ~ function(A)
      | ~ relation(A) ),
    inference(miniscoping,[status(thm)],[f69]) ).

fof(f71,plain,
    ! [A] :
      ( ( ! [B,C] :
            ( ( ( ( in(apply(A,sK0_skl(C,B,A)),B)
                  & in(sK0_skl(C,B,A),relation_dom(A)) )
                | in(sK0_skl(C,B,A),C) )
              & ( ~ in(apply(A,sK0_skl(C,B,A)),B)
                | ~ in(sK0_skl(C,B,A),relation_dom(A))
                | ~ in(sK0_skl(C,B,A),C) ) )
            | C = relation_inverse_image(A,B) )
        & ! [B,C] :
            ( ( ! [D] :
                  ( ~ in(apply(A,D),B)
                  | ~ in(D,relation_dom(A))
                  | in(D,C) )
              & ! [D] :
                  ( ( in(apply(A,D),B)
                    & in(D,relation_dom(A)) )
                  | ~ in(D,C) ) )
            | C != relation_inverse_image(A,B) ) )
      | ~ function(A)
      | ~ relation(A) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f70]) ).

fof(f72,plain,
    ! [X0,X1,X2,X3] :
      ( in(X3,relation_dom(X0))
      | ~ in(X3,X1)
      | X1 != relation_inverse_image(X0,X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3] :
      ( in(apply(X0,X3),X2)
      | ~ in(X3,X1)
      | X1 != relation_inverse_image(X0,X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(apply(X0,X3),X2)
      | ~ in(X3,relation_dom(X0))
      | in(X3,X1)
      | X1 != relation_inverse_image(X0,X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f78,plain,
    ! [A,B,C] :
      ( ( ( ( quasi_total(C,A,B)
          <=> C = empty_set )
          | A = empty_set
          | B != empty_set )
        & ( ( quasi_total(C,A,B)
          <=> A = relation_dom_as_subset(A,B,C) )
          | ( A != empty_set
            & B = empty_set ) ) )
      | ~ relation_of2_as_subset(C,A,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f7]) ).

fof(f79,definition,
    ! [A,B] :
      ( sP0_prd(B,A)
    <=> ( A != empty_set
        & B = empty_set ) ),
    introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).

fof(f80,plain,
    ! [A,B,C] :
      ( ( ( ( quasi_total(C,A,B)
          <=> C = empty_set )
          | A = empty_set
          | B != empty_set )
        & ( ( quasi_total(C,A,B)
          <=> A = relation_dom_as_subset(A,B,C) )
          | sP0_prd(B,A) ) )
      | ~ relation_of2_as_subset(C,A,B) ),
    inference(formula_renaming,[status(thm)],[f78,f79]) ).

fof(f81,plain,
    ! [A,B,C] :
      ( ( ( ( ( C != empty_set
              | quasi_total(C,A,B) )
            & ( C = empty_set
              | ~ quasi_total(C,A,B) ) )
          | A = empty_set
          | B != empty_set )
        & ( ( ( A != relation_dom_as_subset(A,B,C)
              | quasi_total(C,A,B) )
            & ( A = relation_dom_as_subset(A,B,C)
              | ~ quasi_total(C,A,B) ) )
          | sP0_prd(B,A) ) )
      | ~ relation_of2_as_subset(C,A,B) ),
    inference(NNF_transformation,[status(thm)],[f80]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( X1 = relation_dom_as_subset(X1,X2,X0)
      | ~ quasi_total(X0,X1,X2)
      | sP0_prd(X2,X1)
      | ~ relation_of2_as_subset(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f81]) ).

fof(f88,plain,
    ! [A,B,C] :
      ( element(C,powerset(cartesian_product2(A,B)))
      | ~ relation_of2_as_subset(C,A,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f17]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( element(X0,powerset(cartesian_product2(X1,X2)))
      | ~ relation_of2_as_subset(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f88]) ).

fof(f118,plain,
    ( empty(sK6_skl)
    & one_to_one(sK6_skl)
    & function(sK6_skl)
    & relation(sK6_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f30]) ).

fof(f122,plain,
    empty(sK6_skl),
    inference(cnf_transformation,[status(thm)],[f118]) ).

fof(f159,plain,
    ! [A,B,C] :
      ( relation_dom_as_subset(A,B,C) = relation_dom(C)
      | ~ relation_of2(C,A,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f42]) ).

fof(f160,plain,
    ! [X0,X1,X2] :
      ( relation_dom_as_subset(X1,X2,X0) = relation_dom(X0)
      | ~ relation_of2(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f159]) ).

fof(f161,plain,
    ! [A,B,C] :
      ( ( ~ relation_of2(C,A,B)
        | relation_of2_as_subset(C,A,B) )
      & ( relation_of2(C,A,B)
        | ~ relation_of2_as_subset(C,A,B) ) ),
    inference(NNF_transformation,[status(thm)],[f43]) ).

fof(f162,plain,
    ( ! [A,B,C] :
        ( ~ relation_of2(C,A,B)
        | relation_of2_as_subset(C,A,B) )
    & ! [A,B,C] :
        ( relation_of2(C,A,B)
        | ~ relation_of2_as_subset(C,A,B) ) ),
    inference(miniscoping,[status(thm)],[f161]) ).

fof(f163,plain,
    ! [X0,X1,X2] :
      ( relation_of2(X0,X1,X2)
      | ~ relation_of2_as_subset(X0,X1,X2) ),
    inference(cnf_transformation,[status(thm)],[f162]) ).

fof(f175,plain,
    ? [A,B,C,D] :
      ( ? [E] :
          ( in(E,relation_inverse_image(D,C))
        <~> ( in(apply(D,E),C)
            & in(E,A) ) )
      & B != empty_set
      & relation_of2_as_subset(D,A,B)
      & quasi_total(D,A,B)
      & function(D) ),
    inference(pre_NNF_transformation,[status(thm)],[f49]) ).

fof(f176,plain,
    ? [A,B,C,D] :
      ( ? [E] :
          ( ( ~ in(apply(D,E),C)
            | ~ in(E,A)
            | ~ in(E,relation_inverse_image(D,C)) )
          & ( ( in(apply(D,E),C)
              & in(E,A) )
            | in(E,relation_inverse_image(D,C)) ) )
      & B != empty_set
      & relation_of2_as_subset(D,A,B)
      & quasi_total(D,A,B)
      & function(D) ),
    inference(NNF_transformation,[status(thm)],[f175]) ).

fof(f177,plain,
    ? [A,B,D] :
      ( ? [C,E] :
          ( ( ~ in(apply(D,E),C)
            | ~ in(E,A)
            | ~ in(E,relation_inverse_image(D,C)) )
          & ( ( in(apply(D,E),C)
              & in(E,A) )
            | in(E,relation_inverse_image(D,C)) ) )
      & B != empty_set
      & relation_of2_as_subset(D,A,B)
      & quasi_total(D,A,B)
      & function(D) ),
    inference(miniscoping,[status(thm)],[f176]) ).

fof(f178,plain,
    ( ( ~ in(apply(sK20_skl,sK22_skl),sK21_skl)
      | ~ in(sK22_skl,sK18_skl)
      | ~ in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) )
    & ( ( in(apply(sK20_skl,sK22_skl),sK21_skl)
        & in(sK22_skl,sK18_skl) )
      | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) )
    & sK19_skl != empty_set
    & relation_of2_as_subset(sK20_skl,sK18_skl,sK19_skl)
    & quasi_total(sK20_skl,sK18_skl,sK19_skl)
    & function(sK20_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl,sK21_skl,sK22_skl]),skolemize(A,sK18_skl),skolemize(B,sK19_skl),skolemize(D,sK20_skl),skolemize(C,sK21_skl),skolemize(E,sK22_skl)],[f177]) ).

fof(f179,plain,
    function(sK20_skl),
    inference(cnf_transformation,[status(thm)],[f178]) ).

fof(f180,plain,
    quasi_total(sK20_skl,sK18_skl,sK19_skl),
    inference(cnf_transformation,[status(thm)],[f178]) ).

fof(f181,plain,
    relation_of2_as_subset(sK20_skl,sK18_skl,sK19_skl),
    inference(cnf_transformation,[status(thm)],[f178]) ).

fof(f182,plain,
    sK19_skl != empty_set,
    inference(cnf_transformation,[status(thm)],[f178]) ).

fof(f183,plain,
    ( in(sK22_skl,sK18_skl)
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(cnf_transformation,[status(thm)],[f178]) ).

fof(f184,plain,
    ( in(apply(sK20_skl,sK22_skl),sK21_skl)
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(cnf_transformation,[status(thm)],[f178]) ).

fof(f185,plain,
    ( ~ in(apply(sK20_skl,sK22_skl),sK21_skl)
    | ~ in(sK22_skl,sK18_skl)
    | ~ in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(cnf_transformation,[status(thm)],[f178]) ).

fof(f192,plain,
    ! [A] :
      ( A = empty_set
      | ~ empty(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f52]) ).

fof(f193,plain,
    ! [X0] :
      ( X0 = empty_set
      | ~ empty(X0) ),
    inference(cnf_transformation,[status(thm)],[f192]) ).

fof(f200,plain,
    ! [A,B] :
      ( ( A = empty_set
        | B != empty_set
        | sP0_prd(B,A) )
      & ( ( A != empty_set
          & B = empty_set )
        | ~ sP0_prd(B,A) ) ),
    inference(NNF_transformation,[status(thm)],[f79]) ).

fof(f201,plain,
    ( ! [A,B] :
        ( A = empty_set
        | B != empty_set
        | sP0_prd(B,A) )
    & ! [A,B] :
        ( ( A != empty_set
          & B = empty_set )
        | ~ sP0_prd(B,A) ) ),
    inference(miniscoping,[status(thm)],[f200]) ).

fof(f202,plain,
    ! [X0,X1] :
      ( X0 = empty_set
      | ~ sP0_prd(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f201]) ).

fof(f205,plain,
    ! [X0,X1,X2] :
      ( in(X1,relation_dom(X0))
      | ~ in(X1,relation_inverse_image(X0,X2))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(destructive_equality_resolution,[status(thm)],[f72]) ).

fof(f206,plain,
    ! [X0,X1,X2] :
      ( in(apply(X0,X1),X2)
      | ~ in(X1,relation_inverse_image(X0,X2))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(destructive_equality_resolution,[status(thm)],[f73]) ).

fof(f207,plain,
    ! [X0,X1,X2] :
      ( ~ in(apply(X0,X1),X2)
      | ~ in(X1,relation_dom(X0))
      | in(X1,relation_inverse_image(X0,X2))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(destructive_equality_resolution,[status(thm)],[f74]) ).

fof(f217,plain,
    ( in(sK22_skl,relation_dom(sK20_skl))
    | ~ function(sK20_skl)
    | ~ relation(sK20_skl)
    | in(sK22_skl,sK18_skl) ),
    inference(resolution,[status(thm)],[f183,f205]) ).

fof(f220,plain,
    ( in(sK22_skl,relation_dom(sK20_skl))
    | ~ relation(sK20_skl)
    | in(sK22_skl,sK18_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f217,f179]) ).

fof(f222,plain,
    ( ~ in(sK22_skl,relation_dom(sK20_skl))
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl))
    | ~ function(sK20_skl)
    | ~ relation(sK20_skl)
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(resolution,[status(thm)],[f184,f207]) ).

fof(f224,plain,
    ( ~ in(sK22_skl,relation_dom(sK20_skl))
    | ~ function(sK20_skl)
    | ~ relation(sK20_skl)
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(duplicate_literals_removal,[status(thm)],[f222]) ).

fof(f225,plain,
    ( ~ in(sK22_skl,relation_dom(sK20_skl))
    | ~ relation(sK20_skl)
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f224,f179]) ).

fof(f239,plain,
    ( sK18_skl = relation_dom_as_subset(sK18_skl,sK19_skl,sK20_skl)
    | sP0_prd(sK19_skl,sK18_skl)
    | ~ relation_of2_as_subset(sK20_skl,sK18_skl,sK19_skl) ),
    inference(resolution,[status(thm)],[f82,f180]) ).

fof(f240,plain,
    ( sK18_skl = relation_dom_as_subset(sK18_skl,sK19_skl,sK20_skl)
    | sP0_prd(sK19_skl,sK18_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f239,f181]) ).

fof(f241,plain,
    element(sK20_skl,powerset(cartesian_product2(sK18_skl,sK19_skl))),
    inference(resolution,[status(thm)],[f89,f181]) ).

fof(f252,plain,
    sK6_skl = empty_set,
    inference(resolution,[status(thm)],[f122,f193]) ).

fof(f260,plain,
    relation(sK20_skl),
    inference(resolution,[status(thm)],[f241,f63]) ).

fof(f266,plain,
    sK19_skl != sK6_skl,
    inference(backward_demodulation,[status(thm)],[f252,f182]) ).

fof(f277,plain,
    ( ~ in(sK22_skl,relation_dom(sK20_skl))
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f225,f260]) ).

fof(f280,plain,
    ( in(sK22_skl,relation_dom(sK20_skl))
    | in(sK22_skl,sK18_skl) ),
    inference(backward_subsumption_resolution,[status(thm)],[f220,f260]) ).

fof(f443,plain,
    relation_of2(sK20_skl,sK18_skl,sK19_skl),
    inference(resolution,[status(thm)],[f163,f181]) ).

fof(f479,plain,
    relation_dom_as_subset(sK18_skl,sK19_skl,sK20_skl) = relation_dom(sK20_skl),
    inference(resolution,[status(thm)],[f443,f160]) ).

fof(f521,plain,
    ! [X0,X1] :
      ( X0 = sK6_skl
      | ~ sP0_prd(X0,X1) ),
    inference(forward_demodulation,[status(thm)],[f252,f202]) ).

fof(f522,plain,
    ( sK18_skl = relation_dom_as_subset(sK18_skl,sK19_skl,sK20_skl)
    | sK19_skl = sK6_skl ),
    inference(resolution,[status(thm)],[f521,f240]) ).

fof(f523,plain,
    sK18_skl = relation_dom_as_subset(sK18_skl,sK19_skl,sK20_skl),
    inference(forward_subsumption_resolution,[status(thm)],[f522,f266]) ).

fof(f872,plain,
    ( ~ in(sK22_skl,sK18_skl)
    | in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)) ),
    inference(backward_demodulation,[status(thm)],[f874,f277]) ).

fof(f873,plain,
    ( in(sK22_skl,sK18_skl)
    | in(sK22_skl,sK18_skl) ),
    inference(backward_demodulation,[status(thm)],[f874,f280]) ).

fof(f874,plain,
    sK18_skl = relation_dom(sK20_skl),
    inference(forward_demodulation,[status(thm)],[f523,f479]) ).

fof(f878,plain,
    in(sK22_skl,relation_inverse_image(sK20_skl,sK21_skl)),
    inference(forward_subsumption_resolution,[status(thm)],[f872,f183]) ).

fof(f879,plain,
    in(sK22_skl,sK18_skl),
    inference(duplicate_literals_removal,[status(thm)],[f873]) ).

fof(f895,plain,
    ( ~ in(apply(sK20_skl,sK22_skl),sK21_skl)
    | ~ in(sK22_skl,sK18_skl) ),
    inference(backward_subsumption_resolution,[status(thm)],[f185,f878]) ).

fof(f897,plain,
    ( in(apply(sK20_skl,sK22_skl),sK21_skl)
    | ~ function(sK20_skl)
    | ~ relation(sK20_skl) ),
    inference(resolution,[status(thm)],[f878,f206]) ).

fof(f903,plain,
    ( in(apply(sK20_skl,sK22_skl),sK21_skl)
    | ~ function(sK20_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f897,f260]) ).

fof(f905,plain,
    ~ in(apply(sK20_skl,sK22_skl),sK21_skl),
    inference(backward_subsumption_resolution,[status(thm)],[f895,f879]) ).

fof(f2116,plain,
    in(apply(sK20_skl,sK22_skl),sK21_skl),
    inference(forward_subsumption_resolution,[status(thm)],[f903,f179]) ).

fof(f2117,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f905,f2116]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : SEU293+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45  % Computer : n006.cluster.edu
% 0.18/0.45  % Model    : x86_64 x86_64
% 0.18/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45  % Memory   : 8046.5625MB
% 0.18/0.45  % OS       : Linux 6.8.0-71-generic
% 0.18/0.45  % CPULimit : 300
% 0.18/0.45  % WCLimit  : 300
% 0.18/0.45  % DateTime : Mon Sep 21 06:08:12 UTC 2026
% 0.18/0.45  % CPUTime  : 
% 0.18/0.47  % Drodi V4.1.1
% 0.18/0.59  % Refutation found
% 0.18/0.59  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.59  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.65  % Elapsed time: 0.184771 seconds
% 0.18/0.65  % CPU time: 0.930819 seconds
% 0.18/0.65  % Total memory used: 95.265 MB
% 0.18/0.65  % Net memory used: 93.890 MB
%------------------------------------------------------------------------------