TSTP Solution File: SEU181+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU181+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 31 12:36:09 EDT 2023

% Result   : Theorem 2.30s 0.66s
% Output   : CNFRefutation 2.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  102 (   6 unt;   0 def)
%            Number of atoms       :  366 (  53 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  443 ( 179   ~; 191   |;  42   &)
%                                         (  22 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   8 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   1 con; 0-3 aty)
%            Number of variables   :  214 (; 191   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] :
      ( A = B
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_dom(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( relation(B)
         => ( B = relation_inverse(A)
          <=> ! [C,D] :
                ( in(ordered_pair(C,D),B)
              <=> in(ordered_pair(D,C),A) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [A] :
      ( relation(A)
     => relation(relation_inverse(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [A] :
      ( relation(A)
     => relation_inverse(relation_inverse(A)) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,conjecture,
    ! [A] :
      ( relation(A)
     => ( relation_rng(A) = relation_dom(relation_inverse(A))
        & relation_dom(A) = relation_rng(relation_inverse(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( relation_rng(A) = relation_dom(relation_inverse(A))
          & relation_dom(A) = relation_rng(relation_inverse(A)) ) ),
    inference(negated_conjecture,[status(cth)],[f33]) ).

fof(f44,plain,
    ! [A,B] :
      ( ( A != B
        | ( subset(A,B)
          & subset(B,A) ) )
      & ( A = B
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f45,plain,
    ( ! [A,B] :
        ( A != B
        | ( subset(A,B)
          & subset(B,A) ) )
    & ! [A,B] :
        ( A = B
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(miniscoping,[status(esa)],[f44]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f49,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f50,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f50]) ).

fof(f52,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f51]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f56,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B = relation_dom(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f57,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ( B != relation_dom(A)
            | ! [C] :
                ( ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
          & ( B = relation_dom(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f56]) ).

fof(f58,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f57]) ).

fof(f59,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(C,sk0_1(C,B,A)),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ( ( ~ in(sk0_2(B,A),B)
                | ! [D] : ~ in(ordered_pair(sk0_2(B,A),D),A) )
              & ( in(sk0_2(B,A),B)
                | in(ordered_pair(sk0_2(B,A),sk0_3(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f58]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | X1 != relation_dom(X0)
      | ~ in(X2,X1)
      | in(ordered_pair(X2,sk0_1(X2,X1,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f61,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != relation_dom(X0)
      | in(X2,X1)
      | ~ in(ordered_pair(X2,X3),X0) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f64,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f65,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ( B != relation_rng(A)
            | ! [C] :
                ( ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
          & ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f65]) ).

fof(f67,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(sk0_4(C,B,A),C),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ( ( ~ in(sk0_5(B,A),B)
                | ! [D] : ~ in(ordered_pair(D,sk0_5(B,A)),A) )
              & ( in(sk0_5(B,A),B)
                | in(ordered_pair(sk0_6(B,A),sk0_5(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f66]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | X1 != relation_rng(X0)
      | ~ in(X2,X1)
      | in(ordered_pair(sk0_4(X2,X1,X0),X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f69,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != relation_rng(X0)
      | in(X2,X1)
      | ~ in(ordered_pair(X3,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f73,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ( B = relation_inverse(A)
          <=> ! [C,D] :
                ( in(ordered_pair(C,D),B)
              <=> in(ordered_pair(D,C),A) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f74,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ( ( B != relation_inverse(A)
              | ! [C,D] :
                  ( ( ~ in(ordered_pair(C,D),B)
                    | in(ordered_pair(D,C),A) )
                  & ( in(ordered_pair(C,D),B)
                    | ~ in(ordered_pair(D,C),A) ) ) )
            & ( B = relation_inverse(A)
              | ? [C,D] :
                  ( ( ~ in(ordered_pair(C,D),B)
                    | ~ in(ordered_pair(D,C),A) )
                  & ( in(ordered_pair(C,D),B)
                    | in(ordered_pair(D,C),A) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f73]) ).

fof(f75,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ( ( B != relation_inverse(A)
              | ( ! [C,D] :
                    ( ~ in(ordered_pair(C,D),B)
                    | in(ordered_pair(D,C),A) )
                & ! [C,D] :
                    ( in(ordered_pair(C,D),B)
                    | ~ in(ordered_pair(D,C),A) ) ) )
            & ( B = relation_inverse(A)
              | ? [C,D] :
                  ( ( ~ in(ordered_pair(C,D),B)
                    | ~ in(ordered_pair(D,C),A) )
                  & ( in(ordered_pair(C,D),B)
                    | in(ordered_pair(D,C),A) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f74]) ).

fof(f76,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ( ( B != relation_inverse(A)
              | ( ! [C,D] :
                    ( ~ in(ordered_pair(C,D),B)
                    | in(ordered_pair(D,C),A) )
                & ! [C,D] :
                    ( in(ordered_pair(C,D),B)
                    | ~ in(ordered_pair(D,C),A) ) ) )
            & ( B = relation_inverse(A)
              | ( ( ~ in(ordered_pair(sk0_7(B,A),sk0_8(B,A)),B)
                  | ~ in(ordered_pair(sk0_8(B,A),sk0_7(B,A)),A) )
                & ( in(ordered_pair(sk0_7(B,A),sk0_8(B,A)),B)
                  | in(ordered_pair(sk0_8(B,A),sk0_7(B,A)),A) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f75]) ).

fof(f78,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | X1 != relation_inverse(X0)
      | in(ordered_pair(X2,X3),X1)
      | ~ in(ordered_pair(X3,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f76]) ).

fof(f81,plain,
    ! [A] :
      ( ~ relation(A)
      | relation(relation_inverse(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f82,plain,
    ! [X0] :
      ( ~ relation(X0)
      | relation(relation_inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f90,plain,
    ! [A] :
      ( ~ relation(A)
      | relation_inverse(relation_inverse(A)) = A ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f91,plain,
    ! [X0] :
      ( ~ relation(X0)
      | relation_inverse(relation_inverse(X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f90]) ).

fof(f112,plain,
    ? [A] :
      ( relation(A)
      & ( relation_rng(A) != relation_dom(relation_inverse(A))
        | relation_dom(A) != relation_rng(relation_inverse(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f34]) ).

fof(f113,plain,
    ( relation(sk0_15)
    & ( relation_rng(sk0_15) != relation_dom(relation_inverse(sk0_15))
      | relation_dom(sk0_15) != relation_rng(relation_inverse(sk0_15)) ) ),
    inference(skolemization,[status(esa)],[f112]) ).

fof(f114,plain,
    relation(sk0_15),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f115,plain,
    ( relation_rng(sk0_15) != relation_dom(relation_inverse(sk0_15))
    | relation_dom(sk0_15) != relation_rng(relation_inverse(sk0_15)) ),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f134,plain,
    ( spl0_0
  <=> relation_rng(sk0_15) = relation_dom(relation_inverse(sk0_15)) ),
    introduced(split_symbol_definition) ).

fof(f137,plain,
    ( spl0_1
  <=> relation_dom(sk0_15) = relation_rng(relation_inverse(sk0_15)) ),
    introduced(split_symbol_definition) ).

fof(f140,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f115,f134,f137]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ in(X1,relation_dom(X0))
      | in(ordered_pair(X1,sk0_1(X1,relation_dom(X0),X0)),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f60]) ).

fof(f144,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_dom(X0))
      | ~ in(ordered_pair(X1,X2),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f61]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ in(X1,relation_rng(X0))
      | in(ordered_pair(sk0_4(X1,relation_rng(X0),X0),X1),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f68]) ).

fof(f146,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_rng(X0))
      | ~ in(ordered_pair(X2,X1),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f69]) ).

fof(f149,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ relation(relation_inverse(X0))
      | in(ordered_pair(X1,X2),relation_inverse(X0))
      | ~ in(ordered_pair(X2,X1),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f78]) ).

fof(f150,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(ordered_pair(X1,X2),relation_inverse(X0))
      | ~ in(ordered_pair(X2,X1),X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f149,f82]) ).

fof(f153,plain,
    relation_inverse(relation_inverse(sk0_15)) = sk0_15,
    inference(resolution,[status(thm)],[f91,f114]) ).

fof(f154,plain,
    ( spl0_2
  <=> relation(relation_inverse(sk0_15)) ),
    introduced(split_symbol_definition) ).

fof(f155,plain,
    ( relation(relation_inverse(sk0_15))
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f154]) ).

fof(f156,plain,
    ( ~ relation(relation_inverse(sk0_15))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f154]) ).

fof(f162,plain,
    ! [X0,X1,X2] :
      ( in(X0,relation_dom(relation_inverse(X1)))
      | ~ in(ordered_pair(X0,X2),relation_inverse(X1))
      | ~ relation(X1) ),
    inference(resolution,[status(thm)],[f144,f82]) ).

fof(f164,plain,
    ! [X0,X1,X2] :
      ( in(X0,relation_rng(relation_inverse(X1)))
      | ~ in(ordered_pair(X2,X0),relation_inverse(X1))
      | ~ relation(X1) ),
    inference(resolution,[status(thm)],[f146,f82]) ).

fof(f171,plain,
    ! [X0,X1,X2] :
      ( in(X0,relation_dom(relation_inverse(X1)))
      | ~ relation(X1)
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X0),X1) ),
    inference(resolution,[status(thm)],[f162,f150]) ).

fof(f172,plain,
    ! [X0,X1,X2] :
      ( in(X0,relation_dom(relation_inverse(X1)))
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X0),X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f171]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( in(X0,relation_dom(relation_inverse(sk0_15)))
      | ~ in(ordered_pair(X1,X0),sk0_15) ),
    inference(resolution,[status(thm)],[f172,f114]) ).

fof(f180,plain,
    ! [X0,X1,X2] :
      ( in(X0,relation_rng(relation_inverse(X1)))
      | ~ relation(X1)
      | ~ relation(X1)
      | ~ in(ordered_pair(X0,X2),X1) ),
    inference(resolution,[status(thm)],[f164,f150]) ).

fof(f181,plain,
    ! [X0,X1,X2] :
      ( in(X0,relation_rng(relation_inverse(X1)))
      | ~ relation(X1)
      | ~ in(ordered_pair(X0,X2),X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f180]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( in(X0,relation_rng(relation_inverse(sk0_15)))
      | ~ in(ordered_pair(X0,X1),sk0_15) ),
    inference(resolution,[status(thm)],[f181,f114]) ).

fof(f250,plain,
    ( ~ relation(sk0_15)
    | spl0_2 ),
    inference(resolution,[status(thm)],[f156,f82]) ).

fof(f251,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f250,f114]) ).

fof(f252,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f251]) ).

fof(f262,plain,
    ! [X0,X1] :
      ( in(X0,relation_rng(relation_inverse(relation_inverse(sk0_15))))
      | ~ in(ordered_pair(X0,X1),relation_inverse(sk0_15))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f155,f181]) ).

fof(f263,plain,
    ! [X0,X1] :
      ( in(X0,relation_rng(sk0_15))
      | ~ in(ordered_pair(X0,X1),relation_inverse(sk0_15))
      | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f153,f262]) ).

fof(f264,plain,
    ! [X0,X1] :
      ( in(X0,relation_dom(relation_inverse(relation_inverse(sk0_15))))
      | ~ in(ordered_pair(X1,X0),relation_inverse(sk0_15))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f155,f172]) ).

fof(f265,plain,
    ! [X0,X1] :
      ( in(X0,relation_dom(sk0_15))
      | ~ in(ordered_pair(X1,X0),relation_inverse(sk0_15))
      | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f153,f264]) ).

fof(f857,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(relation_inverse(sk0_15)))
      | in(ordered_pair(X0,sk0_1(X0,relation_dom(relation_inverse(sk0_15)),relation_inverse(sk0_15))),relation_inverse(sk0_15))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f143,f155]) ).

fof(f859,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sk0_15))
      | in(ordered_pair(X0,sk0_1(X0,relation_dom(sk0_15),sk0_15)),sk0_15) ),
    inference(resolution,[status(thm)],[f143,f114]) ).

fof(f867,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(relation_inverse(sk0_15)))
      | in(X0,relation_rng(sk0_15))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f857,f263]) ).

fof(f957,plain,
    ! [X0] :
      ( in(sk0_0(X0,relation_dom(relation_inverse(sk0_15))),relation_rng(sk0_15))
      | subset(relation_dom(relation_inverse(sk0_15)),X0)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f867,f54]) ).

fof(f958,plain,
    ( spl0_67
  <=> subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15)) ),
    introduced(split_symbol_definition) ).

fof(f959,plain,
    ( subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15))
    | ~ spl0_67 ),
    inference(component_clause,[status(thm)],[f958]) ).

fof(f961,plain,
    ( subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15))
    | subset(relation_dom(relation_inverse(sk0_15)),relation_rng(sk0_15))
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f957,f55]) ).

fof(f962,plain,
    ( spl0_67
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f961,f958,f154]) ).

fof(f964,plain,
    ( spl0_68
  <=> subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15))) ),
    introduced(split_symbol_definition) ).

fof(f967,plain,
    ( relation_rng(sk0_15) = relation_dom(relation_inverse(sk0_15))
    | ~ subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15)))
    | ~ spl0_67 ),
    inference(resolution,[status(thm)],[f959,f48]) ).

fof(f968,plain,
    ( spl0_0
    | ~ spl0_68
    | ~ spl0_67 ),
    inference(split_clause,[status(thm)],[f967,f134,f964,f958]) ).

fof(f1046,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sk0_15))
      | in(X0,relation_rng(relation_inverse(sk0_15))) ),
    inference(resolution,[status(thm)],[f859,f188]) ).

fof(f1050,plain,
    ! [X0] :
      ( ~ in(sk0_0(relation_rng(relation_inverse(sk0_15)),X0),relation_dom(sk0_15))
      | subset(X0,relation_rng(relation_inverse(sk0_15))) ),
    inference(resolution,[status(thm)],[f1046,f55]) ).

fof(f1060,plain,
    ( spl0_74
  <=> subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15))) ),
    introduced(split_symbol_definition) ).

fof(f1061,plain,
    ( subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15)))
    | ~ spl0_74 ),
    inference(component_clause,[status(thm)],[f1060]) ).

fof(f1063,plain,
    ( subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15)))
    | subset(relation_dom(sk0_15),relation_rng(relation_inverse(sk0_15))) ),
    inference(resolution,[status(thm)],[f1050,f54]) ).

fof(f1064,plain,
    spl0_74,
    inference(split_clause,[status(thm)],[f1063,f1060]) ).

fof(f1066,plain,
    ( spl0_75
  <=> subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15)) ),
    introduced(split_symbol_definition) ).

fof(f1069,plain,
    ( relation_rng(relation_inverse(sk0_15)) = relation_dom(sk0_15)
    | ~ subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15))
    | ~ spl0_74 ),
    inference(resolution,[status(thm)],[f1061,f48]) ).

fof(f1070,plain,
    ( spl0_1
    | ~ spl0_75
    | ~ spl0_74 ),
    inference(split_clause,[status(thm)],[f1069,f137,f1066,f1060]) ).

fof(f1629,plain,
    ! [X0] :
      ( ~ in(X0,relation_rng(relation_inverse(sk0_15)))
      | in(ordered_pair(sk0_4(X0,relation_rng(relation_inverse(sk0_15)),relation_inverse(sk0_15)),X0),relation_inverse(sk0_15))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f145,f155]) ).

fof(f1631,plain,
    ! [X0] :
      ( ~ in(X0,relation_rng(sk0_15))
      | in(ordered_pair(sk0_4(X0,relation_rng(sk0_15),sk0_15),X0),sk0_15) ),
    inference(resolution,[status(thm)],[f145,f114]) ).

fof(f1739,plain,
    ! [X0] :
      ( ~ in(X0,relation_rng(relation_inverse(sk0_15)))
      | in(X0,relation_dom(sk0_15))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f1629,f265]) ).

fof(f1832,plain,
    ! [X0] :
      ( in(sk0_0(X0,relation_rng(relation_inverse(sk0_15))),relation_dom(sk0_15))
      | subset(relation_rng(relation_inverse(sk0_15)),X0)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f1739,f54]) ).

fof(f1838,plain,
    ( subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15))
    | subset(relation_rng(relation_inverse(sk0_15)),relation_dom(sk0_15))
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f1832,f55]) ).

fof(f1839,plain,
    ( spl0_75
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f1838,f1066,f154]) ).

fof(f2084,plain,
    ! [X0] :
      ( ~ in(X0,relation_rng(sk0_15))
      | in(X0,relation_dom(relation_inverse(sk0_15))) ),
    inference(resolution,[status(thm)],[f1631,f179]) ).

fof(f2087,plain,
    ! [X0] :
      ( ~ in(sk0_0(relation_dom(relation_inverse(sk0_15)),X0),relation_rng(sk0_15))
      | subset(X0,relation_dom(relation_inverse(sk0_15))) ),
    inference(resolution,[status(thm)],[f2084,f55]) ).

fof(f2757,plain,
    ( subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15)))
    | subset(relation_rng(sk0_15),relation_dom(relation_inverse(sk0_15))) ),
    inference(resolution,[status(thm)],[f2087,f54]) ).

fof(f2758,plain,
    spl0_68,
    inference(split_clause,[status(thm)],[f2757,f964]) ).

fof(f2759,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f140,f252,f962,f968,f1064,f1070,f1839,f2758]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU181+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 09:10:23 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  % Drodi V3.5.1
% 2.30/0.66  % Refutation found
% 2.30/0.66  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.30/0.66  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.30/0.68  % Elapsed time: 0.346652 seconds
% 2.30/0.68  % CPU time: 2.644271 seconds
% 2.30/0.68  % Memory used: 99.213 MB
%------------------------------------------------------------------------------