TSTP Solution File: SEU214+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU214+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 20:41:31 EDT 2024

% Result   : Theorem 1.73s 0.66s
% Output   : CNFRefutation 2.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   91 (  12 unt;   0 def)
%            Number of atoms       :  382 (  52 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  478 ( 187   ~; 193   |;  60   &)
%                                         (  23 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   16 (  14 usr;  12 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   4 con; 0-5 aty)
%            Number of variables   :  162 ( 138   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B,C] :
          ( ( in(B,relation_dom(A))
           => ( C = apply(A,B)
            <=> in(ordered_pair(B,C),A) ) )
          & ( ~ in(B,relation_dom(A))
           => ( C = apply(A,B)
            <=> C = empty_set ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f8,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( relation(B)
         => ! [C] :
              ( relation(C)
             => ( C = relation_composition(A,B)
              <=> ! [D,E] :
                    ( in(ordered_pair(D,E),C)
                  <=> ? [F] :
                        ( in(ordered_pair(D,F),A)
                        & in(ordered_pair(F,E),B) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [A,B] :
      ( ( relation(A)
        & relation(B) )
     => relation(relation_composition(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [A,B] :
      ( ( relation(A)
        & function(A)
        & relation(B)
        & function(B) )
     => ( relation(relation_composition(A,B))
        & function(relation_composition(A,B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,conjecture,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( in(A,relation_dom(relation_composition(C,B)))
           => apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ~ ! [A,B] :
        ( ( relation(B)
          & function(B) )
       => ! [C] :
            ( ( relation(C)
              & function(C) )
           => ( in(A,relation_dom(relation_composition(C,B)))
             => apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f36]) ).

fof(f49,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B,C] :
          ( ( ~ in(B,relation_dom(A))
            | ( C = apply(A,B)
            <=> in(ordered_pair(B,C),A) ) )
          & ( in(B,relation_dom(A))
            | ( C = apply(A,B)
            <=> C = empty_set ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f50,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B,C] :
          ( ( ~ in(B,relation_dom(A))
            | ( ( C != apply(A,B)
                | in(ordered_pair(B,C),A) )
              & ( C = apply(A,B)
                | ~ in(ordered_pair(B,C),A) ) ) )
          & ( in(B,relation_dom(A))
            | ( ( C != apply(A,B)
                | C = empty_set )
              & ( C = apply(A,B)
                | C != empty_set ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ( ! [B] :
            ( ~ in(B,relation_dom(A))
            | ( ! [C] :
                  ( C != apply(A,B)
                  | in(ordered_pair(B,C),A) )
              & ! [C] :
                  ( C = apply(A,B)
                  | ~ in(ordered_pair(B,C),A) ) ) )
        & ! [B] :
            ( in(B,relation_dom(A))
            | ( ! [C] :
                  ( C != apply(A,B)
                  | C = empty_set )
              & ! [C] :
                  ( C = apply(A,B)
                  | C != empty_set ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f50]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ in(X1,relation_dom(X0))
      | X2 != apply(X0,X1)
      | in(ordered_pair(X1,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ in(X1,relation_dom(X0))
      | X2 = apply(X0,X1)
      | ~ in(ordered_pair(X1,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f51]) ).

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)],[f6]) ).

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_0(C,B,A)),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ( ( ~ in(sk0_1(B,A),B)
                | ! [D] : ~ in(ordered_pair(sk0_1(B,A),D),A) )
              & ( in(sk0_1(B,A),B)
                | in(ordered_pair(sk0_1(B,A),sk0_2(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f58]) ).

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(f65,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( C = relation_composition(A,B)
              <=> ! [D,E] :
                    ( in(ordered_pair(D,E),C)
                  <=> ? [F] :
                        ( in(ordered_pair(D,F),A)
                        & in(ordered_pair(F,E),B) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

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

fof(f67,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ( ! [D,E] :
                        ( ~ in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) )
                    & ! [D,E] :
                        ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ? [D,E] :
                      ( ( ~ in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) )
                      & ( in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f66]) ).

fof(f68,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ( ! [D,E] :
                        ( ~ in(ordered_pair(D,E),C)
                        | ( in(ordered_pair(D,sk0_3(E,D,C,B,A)),A)
                          & in(ordered_pair(sk0_3(E,D,C,B,A),E),B) ) )
                    & ! [D,E] :
                        ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ( ( ~ in(ordered_pair(sk0_4(C,B,A),sk0_5(C,B,A)),C)
                      | ! [F] :
                          ( ~ in(ordered_pair(sk0_4(C,B,A),F),A)
                          | ~ in(ordered_pair(F,sk0_5(C,B,A)),B) ) )
                    & ( in(ordered_pair(sk0_4(C,B,A),sk0_5(C,B,A)),C)
                      | ( in(ordered_pair(sk0_4(C,B,A),sk0_6(C,B,A)),A)
                        & in(ordered_pair(sk0_6(C,B,A),sk0_5(C,B,A)),B) ) ) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f67]) ).

fof(f69,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(X2)
      | X2 != relation_composition(X0,X1)
      | ~ in(ordered_pair(X3,X4),X2)
      | in(ordered_pair(X3,sk0_3(X4,X3,X2,X1,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f70,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(X2)
      | X2 != relation_composition(X0,X1)
      | ~ in(ordered_pair(X3,X4),X2)
      | in(ordered_pair(sk0_3(X4,X3,X2,X1,X0),X4),X1) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f75,plain,
    ! [A,B] :
      ( ~ relation(A)
      | ~ relation(B)
      | relation(relation_composition(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | relation(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f75]) ).

fof(f85,plain,
    ! [A,B] :
      ( ~ relation(A)
      | ~ function(A)
      | ~ relation(B)
      | ~ function(B)
      | ( relation(relation_composition(A,B))
        & function(relation_composition(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | function(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f85]) ).

fof(f120,plain,
    ? [A,B] :
      ( relation(B)
      & function(B)
      & ? [C] :
          ( relation(C)
          & function(C)
          & in(A,relation_dom(relation_composition(C,B)))
          & apply(relation_composition(C,B),A) != apply(B,apply(C,A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f121,plain,
    ? [B] :
      ( relation(B)
      & function(B)
      & ? [C] :
          ( relation(C)
          & function(C)
          & ? [A] :
              ( in(A,relation_dom(relation_composition(C,B)))
              & apply(relation_composition(C,B),A) != apply(B,apply(C,A)) ) ) ),
    inference(miniscoping,[status(esa)],[f120]) ).

fof(f122,plain,
    ( relation(sk0_14)
    & function(sk0_14)
    & relation(sk0_15)
    & function(sk0_15)
    & in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))
    & apply(relation_composition(sk0_15,sk0_14),sk0_16) != apply(sk0_14,apply(sk0_15,sk0_16)) ),
    inference(skolemization,[status(esa)],[f121]) ).

fof(f123,plain,
    relation(sk0_14),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f124,plain,
    function(sk0_14),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f125,plain,
    relation(sk0_15),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f126,plain,
    function(sk0_15),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f127,plain,
    in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14))),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f128,plain,
    apply(relation_composition(sk0_15,sk0_14),sk0_16) != apply(sk0_14,apply(sk0_15,sk0_16)),
    inference(cnf_transformation,[status(esa)],[f122]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ in(X1,relation_dom(X0))
      | in(ordered_pair(X1,apply(X0,X1)),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f52]) ).

fof(f143,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(f144,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(relation_composition(X0,X1))
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(X2,sk0_3(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f69]) ).

fof(f145,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(relation_composition(X0,X1))
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(sk0_3(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f70]) ).

fof(f148,plain,
    ( spl0_0
  <=> relation(relation_composition(sk0_15,sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f150,plain,
    ( ~ relation(relation_composition(sk0_15,sk0_14))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f148]) ).

fof(f151,plain,
    ( spl0_1
  <=> function(relation_composition(sk0_15,sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f153,plain,
    ( ~ function(relation_composition(sk0_15,sk0_14))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f151]) ).

fof(f154,plain,
    ( spl0_2
  <=> in(ordered_pair(sk0_16,apply(relation_composition(sk0_15,sk0_14),sk0_16)),relation_composition(sk0_15,sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f155,plain,
    ( in(ordered_pair(sk0_16,apply(relation_composition(sk0_15,sk0_14),sk0_16)),relation_composition(sk0_15,sk0_14))
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f154]) ).

fof(f157,plain,
    ( ~ relation(relation_composition(sk0_15,sk0_14))
    | ~ function(relation_composition(sk0_15,sk0_14))
    | in(ordered_pair(sk0_16,apply(relation_composition(sk0_15,sk0_14),sk0_16)),relation_composition(sk0_15,sk0_14)) ),
    inference(resolution,[status(thm)],[f139,f127]) ).

fof(f158,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f157,f148,f151,f154]) ).

fof(f168,plain,
    ( spl0_5
  <=> relation(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f170,plain,
    ( ~ relation(sk0_14)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f168]) ).

fof(f176,plain,
    ( spl0_7
  <=> relation(sk0_15) ),
    introduced(split_symbol_definition) ).

fof(f178,plain,
    ( ~ relation(sk0_15)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f176]) ).

fof(f181,plain,
    ( ~ relation(sk0_15)
    | ~ relation(sk0_14)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f150,f76]) ).

fof(f182,plain,
    ( ~ spl0_7
    | ~ spl0_5
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f181,f176,f168,f148]) ).

fof(f183,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f170,f123]) ).

fof(f184,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f183]) ).

fof(f185,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f178,f125]) ).

fof(f186,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f185]) ).

fof(f204,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | X1 = apply(X0,X2)
      | ~ in(ordered_pair(X2,X1),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f53,f143]) ).

fof(f235,plain,
    ( spl0_17
  <=> function(sk0_15) ),
    introduced(split_symbol_definition) ).

fof(f237,plain,
    ( ~ function(sk0_15)
    | spl0_17 ),
    inference(component_clause,[status(thm)],[f235]) ).

fof(f238,plain,
    ( spl0_18
  <=> function(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f240,plain,
    ( ~ function(sk0_14)
    | spl0_18 ),
    inference(component_clause,[status(thm)],[f238]) ).

fof(f241,plain,
    ( ~ relation(sk0_15)
    | ~ function(sk0_15)
    | ~ relation(sk0_14)
    | ~ function(sk0_14)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f87,f153]) ).

fof(f242,plain,
    ( ~ spl0_7
    | ~ spl0_17
    | ~ spl0_5
    | ~ spl0_18
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f241,f176,f235,f168,f238,f151]) ).

fof(f243,plain,
    ( $false
    | spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f237,f126]) ).

fof(f244,plain,
    spl0_17,
    inference(contradiction_clause,[status(thm)],[f243]) ).

fof(f245,plain,
    ( $false
    | spl0_18 ),
    inference(forward_subsumption_resolution,[status(thm)],[f240,f124]) ).

fof(f246,plain,
    spl0_18,
    inference(contradiction_clause,[status(thm)],[f245]) ).

fof(f642,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(X2,sk0_3(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f144,f76]) ).

fof(f643,plain,
    ( spl0_30
  <=> in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15) ),
    introduced(split_symbol_definition) ).

fof(f644,plain,
    ( in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)
    | ~ spl0_30 ),
    inference(component_clause,[status(thm)],[f643]) ).

fof(f646,plain,
    ( ~ relation(sk0_15)
    | ~ relation(sk0_14)
    | in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f642,f155]) ).

fof(f647,plain,
    ( ~ spl0_7
    | ~ spl0_5
    | spl0_30
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f646,f176,f168,f643,f154]) ).

fof(f648,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(sk0_3(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f145,f76]) ).

fof(f649,plain,
    ( spl0_31
  <=> in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f650,plain,
    ( in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)
    | ~ spl0_31 ),
    inference(component_clause,[status(thm)],[f649]) ).

fof(f652,plain,
    ( ~ relation(sk0_15)
    | ~ relation(sk0_14)
    | in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f648,f155]) ).

fof(f653,plain,
    ( ~ spl0_7
    | ~ spl0_5
    | spl0_31
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f652,f176,f168,f649,f154]) ).

fof(f782,plain,
    ( spl0_39
  <=> sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15) = apply(sk0_15,sk0_16) ),
    introduced(split_symbol_definition) ).

fof(f783,plain,
    ( sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15) = apply(sk0_15,sk0_16)
    | ~ spl0_39 ),
    inference(component_clause,[status(thm)],[f782]) ).

fof(f785,plain,
    ( ~ relation(sk0_15)
    | ~ function(sk0_15)
    | sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15) = apply(sk0_15,sk0_16)
    | ~ spl0_30 ),
    inference(resolution,[status(thm)],[f644,f204]) ).

fof(f786,plain,
    ( ~ spl0_7
    | ~ spl0_17
    | spl0_39
    | ~ spl0_30 ),
    inference(split_clause,[status(thm)],[f785,f176,f235,f782,f643]) ).

fof(f830,plain,
    ( in(ordered_pair(apply(sk0_15,sk0_16),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)
    | ~ spl0_39
    | ~ spl0_31 ),
    inference(forward_demodulation,[status(thm)],[f783,f650]) ).

fof(f836,plain,
    ( spl0_48
  <=> apply(relation_composition(sk0_15,sk0_14),sk0_16) = apply(sk0_14,apply(sk0_15,sk0_16)) ),
    introduced(split_symbol_definition) ).

fof(f837,plain,
    ( apply(relation_composition(sk0_15,sk0_14),sk0_16) = apply(sk0_14,apply(sk0_15,sk0_16))
    | ~ spl0_48 ),
    inference(component_clause,[status(thm)],[f836]) ).

fof(f839,plain,
    ( ~ relation(sk0_14)
    | ~ function(sk0_14)
    | apply(relation_composition(sk0_15,sk0_14),sk0_16) = apply(sk0_14,apply(sk0_15,sk0_16))
    | ~ spl0_39
    | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f830,f204]) ).

fof(f840,plain,
    ( ~ spl0_5
    | ~ spl0_18
    | spl0_48
    | ~ spl0_39
    | ~ spl0_31 ),
    inference(split_clause,[status(thm)],[f839,f168,f238,f836,f782,f649]) ).

fof(f847,plain,
    ( $false
    | ~ spl0_48 ),
    inference(forward_subsumption_resolution,[status(thm)],[f837,f128]) ).

fof(f848,plain,
    ~ spl0_48,
    inference(contradiction_clause,[status(thm)],[f847]) ).

fof(f849,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f158,f182,f184,f186,f242,f244,f246,f647,f653,f786,f840,f848]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SEU214+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 20:09:14 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 1.73/0.66  % Refutation found
% 1.73/0.66  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.73/0.66  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.37/0.69  % Elapsed time: 0.323775 seconds
% 2.37/0.69  % CPU time: 2.390651 seconds
% 2.37/0.69  % Total memory used: 85.842 MB
% 2.37/0.69  % Net memory used: 85.005 MB
%------------------------------------------------------------------------------