TSTP Solution File: SEU002+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU002+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 12:35:41 EDT 2023

% Result   : Theorem 2.53s 0.71s
% Output   : CNFRefutation 2.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  112 (  19 unt;   0 def)
%            Number of atoms       :  389 (  39 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  457 ( 180   ~; 183   |;  59   &)
%                                         (  21 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   22 (  20 usr;  16 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :  104 (;  87   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] :
                  ( in(D,relation_dom(A))
                  & C = apply(A,D) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B] :
      ( ( relation(A)
        & relation(B) )
     => relation(relation_composition(A,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B] :
      ( ( relation(A)
        & function(A)
        & relation(B)
        & function(B) )
     => ( relation(relation_composition(A,B))
        & function(relation_composition(A,B)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ? [A] :
      ( relation(A)
      & function(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ? [A] :
      ( ~ empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ? [A] :
      ( relation(A)
      & relation_empty_yielding(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( in(A,relation_dom(relation_composition(C,B)))
          <=> ( in(A,relation_dom(C))
              & in(apply(C,A),relation_dom(B)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,axiom,
    ! [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/sandbox/benchmark/theBenchmark.p') ).

fof(f30,conjecture,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( in(A,relation_rng(relation_composition(C,B)))
           => in(A,relation_rng(B)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    ~ ! [A,B] :
        ( ( relation(B)
          & function(B) )
       => ! [C] :
            ( ( relation(C)
              & function(C) )
           => ( in(A,relation_rng(relation_composition(C,B)))
             => in(A,relation_rng(B)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f30]) ).

fof(f45,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] :
                  ( in(D,relation_dom(A))
                  & C = apply(A,D) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f46,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B] :
          ( ( B != relation_rng(A)
            | ! [C] :
                ( ( ~ in(C,B)
                  | ? [D] :
                      ( in(D,relation_dom(A))
                      & C = apply(A,D) ) )
                & ( in(C,B)
                  | ! [D] :
                      ( ~ in(D,relation_dom(A))
                      | C != apply(A,D) ) ) ) )
          & ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] :
                      ( ~ in(D,relation_dom(A))
                      | C != apply(A,D) ) )
                & ( in(C,B)
                  | ? [D] :
                      ( in(D,relation_dom(A))
                      & C = apply(A,D) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f45]) ).

fof(f47,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ? [D] :
                      ( in(D,relation_dom(A))
                      & C = apply(A,D) ) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] :
                      ( ~ in(D,relation_dom(A))
                      | C != apply(A,D) ) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] :
                      ( ~ in(D,relation_dom(A))
                      | C != apply(A,D) ) )
                & ( in(C,B)
                  | ? [D] :
                      ( in(D,relation_dom(A))
                      & C = apply(A,D) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f46]) ).

fof(f48,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ( in(sk0_0(C,B,A),relation_dom(A))
                    & C = apply(A,sk0_0(C,B,A)) ) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] :
                      ( ~ in(D,relation_dom(A))
                      | C != apply(A,D) ) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ( ( ~ in(sk0_1(B,A),B)
                | ! [D] :
                    ( ~ in(D,relation_dom(A))
                    | sk0_1(B,A) != apply(A,D) ) )
              & ( in(sk0_1(B,A),B)
                | ( in(sk0_2(B,A),relation_dom(A))
                  & sk0_1(B,A) = apply(A,sk0_2(B,A)) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | X1 != relation_rng(X0)
      | ~ in(X2,X1)
      | in(sk0_0(X2,X1,X0),relation_dom(X0)) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | X1 != relation_rng(X0)
      | ~ in(X2,X1)
      | X2 = apply(X0,sk0_0(X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ function(X0)
      | X1 != relation_rng(X0)
      | in(X2,X1)
      | ~ in(X3,relation_dom(X0))
      | X2 != apply(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f55,plain,
    ! [A,B] :
      ( ~ relation(A)
      | ~ relation(B)
      | relation(relation_composition(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | relation(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f65,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)],[f9]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | function(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f85,plain,
    ( relation(sk0_4)
    & function(sk0_4) ),
    inference(skolemization,[status(esa)],[f18]) ).

fof(f86,plain,
    relation(sk0_4),
    inference(cnf_transformation,[status(esa)],[f85]) ).

fof(f87,plain,
    function(sk0_4),
    inference(cnf_transformation,[status(esa)],[f85]) ).

fof(f97,plain,
    ( ~ empty(sk0_8)
    & relation(sk0_8) ),
    inference(skolemization,[status(esa)],[f22]) ).

fof(f99,plain,
    relation(sk0_8),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f105,plain,
    ( relation(sk0_11)
    & relation_empty_yielding(sk0_11) ),
    inference(skolemization,[status(esa)],[f25]) ).

fof(f106,plain,
    relation(sk0_11),
    inference(cnf_transformation,[status(esa)],[f105]) ).

fof(f112,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( in(A,relation_dom(relation_composition(C,B)))
          <=> ( in(A,relation_dom(C))
              & in(apply(C,A),relation_dom(B)) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f113,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ( ~ in(A,relation_dom(relation_composition(C,B)))
              | ( in(A,relation_dom(C))
                & in(apply(C,A),relation_dom(B)) ) )
            & ( in(A,relation_dom(relation_composition(C,B)))
              | ~ in(A,relation_dom(C))
              | ~ in(apply(C,A),relation_dom(B)) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f112]) ).

fof(f114,plain,
    ! [B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ! [A] :
                ( ~ in(A,relation_dom(relation_composition(C,B)))
                | ( in(A,relation_dom(C))
                  & in(apply(C,A),relation_dom(B)) ) )
            & ! [A] :
                ( in(A,relation_dom(relation_composition(C,B)))
                | ~ in(A,relation_dom(C))
                | ~ in(apply(C,A),relation_dom(B)) ) ) ) ),
    inference(miniscoping,[status(esa)],[f113]) ).

fof(f116,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | ~ in(X2,relation_dom(relation_composition(X1,X0)))
      | in(apply(X1,X2),relation_dom(X0)) ),
    inference(cnf_transformation,[status(esa)],[f114]) ).

fof(f118,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)],[f29]) ).

fof(f119,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)],[f118]) ).

fof(f120,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | ~ in(X2,relation_dom(relation_composition(X1,X0)))
      | apply(relation_composition(X1,X0),X2) = apply(X0,apply(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f121,plain,
    ? [A,B] :
      ( relation(B)
      & function(B)
      & ? [C] :
          ( relation(C)
          & function(C)
          & in(A,relation_rng(relation_composition(C,B)))
          & ~ in(A,relation_rng(B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f122,plain,
    ? [B] :
      ( relation(B)
      & function(B)
      & ? [C] :
          ( relation(C)
          & function(C)
          & ? [A] :
              ( in(A,relation_rng(relation_composition(C,B)))
              & ~ in(A,relation_rng(B)) ) ) ),
    inference(miniscoping,[status(esa)],[f121]) ).

fof(f123,plain,
    ( relation(sk0_12)
    & function(sk0_12)
    & relation(sk0_13)
    & function(sk0_13)
    & in(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)))
    & ~ in(sk0_14,relation_rng(sk0_12)) ),
    inference(skolemization,[status(esa)],[f122]) ).

fof(f124,plain,
    relation(sk0_12),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f125,plain,
    function(sk0_12),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f126,plain,
    relation(sk0_13),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f127,plain,
    function(sk0_13),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f128,plain,
    in(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12))),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f129,plain,
    ~ in(sk0_14,relation_rng(sk0_12)),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ in(X1,relation_rng(X0))
      | in(sk0_0(X1,relation_rng(X0),X0),relation_dom(X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f49]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ in(X1,relation_rng(X0))
      | X1 = apply(X0,sk0_0(X1,relation_rng(X0),X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f50]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | in(apply(X0,X1),relation_rng(X0))
      | ~ in(X1,relation_dom(X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f51]) ).

fof(f909,plain,
    ( spl0_14
  <=> relation(relation_composition(sk0_13,sk0_12)) ),
    introduced(split_symbol_definition) ).

fof(f911,plain,
    ( ~ relation(relation_composition(sk0_13,sk0_12))
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f909]) ).

fof(f912,plain,
    ( spl0_15
  <=> function(relation_composition(sk0_13,sk0_12)) ),
    introduced(split_symbol_definition) ).

fof(f914,plain,
    ( ~ function(relation_composition(sk0_13,sk0_12))
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f912]) ).

fof(f915,plain,
    ( spl0_16
  <=> in(sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)),relation_dom(relation_composition(sk0_13,sk0_12))) ),
    introduced(split_symbol_definition) ).

fof(f916,plain,
    ( in(sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)),relation_dom(relation_composition(sk0_13,sk0_12)))
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f915]) ).

fof(f918,plain,
    ( ~ relation(relation_composition(sk0_13,sk0_12))
    | ~ function(relation_composition(sk0_13,sk0_12))
    | in(sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)),relation_dom(relation_composition(sk0_13,sk0_12))) ),
    inference(resolution,[status(thm)],[f150,f128]) ).

fof(f919,plain,
    ( ~ spl0_14
    | ~ spl0_15
    | spl0_16 ),
    inference(split_clause,[status(thm)],[f918,f909,f912,f915]) ).

fof(f928,plain,
    ( spl0_19
  <=> sk0_14 = apply(relation_composition(sk0_13,sk0_12),sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))) ),
    introduced(split_symbol_definition) ).

fof(f929,plain,
    ( sk0_14 = apply(relation_composition(sk0_13,sk0_12),sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)))
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f928]) ).

fof(f931,plain,
    ( ~ relation(relation_composition(sk0_13,sk0_12))
    | ~ function(relation_composition(sk0_13,sk0_12))
    | sk0_14 = apply(relation_composition(sk0_13,sk0_12),sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))) ),
    inference(resolution,[status(thm)],[f151,f128]) ).

fof(f932,plain,
    ( ~ spl0_14
    | ~ spl0_15
    | spl0_19 ),
    inference(split_clause,[status(thm)],[f931,f909,f912,f928]) ).

fof(f963,plain,
    ( spl0_21
  <=> relation(sk0_13) ),
    introduced(split_symbol_definition) ).

fof(f965,plain,
    ( ~ relation(sk0_13)
    | spl0_21 ),
    inference(component_clause,[status(thm)],[f963]) ).

fof(f966,plain,
    ( spl0_22
  <=> function(sk0_13) ),
    introduced(split_symbol_definition) ).

fof(f968,plain,
    ( ~ function(sk0_13)
    | spl0_22 ),
    inference(component_clause,[status(thm)],[f966]) ).

fof(f969,plain,
    ( spl0_23
  <=> relation(sk0_12) ),
    introduced(split_symbol_definition) ).

fof(f971,plain,
    ( ~ relation(sk0_12)
    | spl0_23 ),
    inference(component_clause,[status(thm)],[f969]) ).

fof(f972,plain,
    ( spl0_24
  <=> function(sk0_12) ),
    introduced(split_symbol_definition) ).

fof(f974,plain,
    ( ~ function(sk0_12)
    | spl0_24 ),
    inference(component_clause,[status(thm)],[f972]) ).

fof(f975,plain,
    ( ~ relation(sk0_13)
    | ~ function(sk0_13)
    | ~ relation(sk0_12)
    | ~ function(sk0_12)
    | spl0_15 ),
    inference(resolution,[status(thm)],[f914,f67]) ).

fof(f976,plain,
    ( ~ spl0_21
    | ~ spl0_22
    | ~ spl0_23
    | ~ spl0_24
    | spl0_15 ),
    inference(split_clause,[status(thm)],[f975,f963,f966,f969,f972,f912]) ).

fof(f978,plain,
    ( $false
    | spl0_24 ),
    inference(forward_subsumption_resolution,[status(thm)],[f974,f125]) ).

fof(f979,plain,
    spl0_24,
    inference(contradiction_clause,[status(thm)],[f978]) ).

fof(f980,plain,
    ( $false
    | spl0_23 ),
    inference(forward_subsumption_resolution,[status(thm)],[f971,f124]) ).

fof(f981,plain,
    spl0_23,
    inference(contradiction_clause,[status(thm)],[f980]) ).

fof(f982,plain,
    ( $false
    | spl0_22 ),
    inference(forward_subsumption_resolution,[status(thm)],[f968,f127]) ).

fof(f983,plain,
    spl0_22,
    inference(contradiction_clause,[status(thm)],[f982]) ).

fof(f984,plain,
    ( $false
    | spl0_21 ),
    inference(forward_subsumption_resolution,[status(thm)],[f965,f126]) ).

fof(f985,plain,
    spl0_21,
    inference(contradiction_clause,[status(thm)],[f984]) ).

fof(f996,plain,
    ( ~ relation(sk0_13)
    | ~ relation(sk0_12)
    | spl0_14 ),
    inference(resolution,[status(thm)],[f911,f56]) ).

fof(f997,plain,
    ( ~ spl0_21
    | ~ spl0_23
    | spl0_14 ),
    inference(split_clause,[status(thm)],[f996,f963,f969,f909]) ).

fof(f2725,plain,
    ( spl0_33
  <=> in(apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))),relation_dom(sk0_12)) ),
    introduced(split_symbol_definition) ).

fof(f2726,plain,
    ( in(apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))),relation_dom(sk0_12))
    | ~ spl0_33 ),
    inference(component_clause,[status(thm)],[f2725]) ).

fof(f2728,plain,
    ( ~ relation(sk0_12)
    | ~ function(sk0_12)
    | ~ relation(sk0_13)
    | ~ function(sk0_13)
    | in(apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))),relation_dom(sk0_12))
    | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f116,f916]) ).

fof(f2729,plain,
    ( ~ spl0_23
    | ~ spl0_24
    | ~ spl0_21
    | ~ spl0_22
    | spl0_33
    | ~ spl0_16 ),
    inference(split_clause,[status(thm)],[f2728,f969,f972,f963,f966,f2725,f915]) ).

fof(f2739,plain,
    ( spl0_35
  <=> apply(relation_composition(sk0_13,sk0_12),sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))) = apply(sk0_12,apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)))) ),
    introduced(split_symbol_definition) ).

fof(f2740,plain,
    ( apply(relation_composition(sk0_13,sk0_12),sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))) = apply(sk0_12,apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))))
    | ~ spl0_35 ),
    inference(component_clause,[status(thm)],[f2739]) ).

fof(f2742,plain,
    ( ~ relation(sk0_12)
    | ~ function(sk0_12)
    | ~ relation(sk0_13)
    | ~ function(sk0_13)
    | apply(relation_composition(sk0_13,sk0_12),sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))) = apply(sk0_12,apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))))
    | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f120,f916]) ).

fof(f2743,plain,
    ( ~ spl0_23
    | ~ spl0_24
    | ~ spl0_21
    | ~ spl0_22
    | spl0_35
    | ~ spl0_16 ),
    inference(split_clause,[status(thm)],[f2742,f969,f972,f963,f966,f2739,f915]) ).

fof(f2748,plain,
    ( sk0_14 = apply(sk0_12,apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12))))
    | ~ spl0_19
    | ~ spl0_35 ),
    inference(forward_demodulation,[status(thm)],[f929,f2740]) ).

fof(f2808,plain,
    ( spl0_38
  <=> relation(sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f2810,plain,
    ( ~ relation(sk0_4)
    | spl0_38 ),
    inference(component_clause,[status(thm)],[f2808]) ).

fof(f2867,plain,
    ( $false
    | spl0_38 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2810,f86]) ).

fof(f2868,plain,
    spl0_38,
    inference(contradiction_clause,[status(thm)],[f2867]) ).

fof(f2879,plain,
    ( spl0_52
  <=> function(sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f2881,plain,
    ( ~ function(sk0_4)
    | spl0_52 ),
    inference(component_clause,[status(thm)],[f2879]) ).

fof(f2885,plain,
    ( $false
    | spl0_52 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2881,f87]) ).

fof(f2886,plain,
    spl0_52,
    inference(contradiction_clause,[status(thm)],[f2885]) ).

fof(f2889,plain,
    ( spl0_53
  <=> in(apply(sk0_12,apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)))),relation_rng(sk0_12)) ),
    introduced(split_symbol_definition) ).

fof(f2890,plain,
    ( in(apply(sk0_12,apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)))),relation_rng(sk0_12))
    | ~ spl0_53 ),
    inference(component_clause,[status(thm)],[f2889]) ).

fof(f2892,plain,
    ( ~ relation(sk0_12)
    | ~ function(sk0_12)
    | in(apply(sk0_12,apply(sk0_13,sk0_0(sk0_14,relation_rng(relation_composition(sk0_13,sk0_12)),relation_composition(sk0_13,sk0_12)))),relation_rng(sk0_12))
    | ~ spl0_33 ),
    inference(resolution,[status(thm)],[f2726,f152]) ).

fof(f2893,plain,
    ( ~ spl0_23
    | ~ spl0_24
    | spl0_53
    | ~ spl0_33 ),
    inference(split_clause,[status(thm)],[f2892,f969,f972,f2889,f2725]) ).

fof(f2895,plain,
    ( spl0_54
  <=> relation(sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f2897,plain,
    ( ~ relation(sk0_8)
    | spl0_54 ),
    inference(component_clause,[status(thm)],[f2895]) ).

fof(f2936,plain,
    ( $false
    | spl0_54 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2897,f99]) ).

fof(f2937,plain,
    spl0_54,
    inference(contradiction_clause,[status(thm)],[f2936]) ).

fof(f2958,plain,
    ( spl0_63
  <=> relation(sk0_11) ),
    introduced(split_symbol_definition) ).

fof(f2960,plain,
    ( ~ relation(sk0_11)
    | spl0_63 ),
    inference(component_clause,[status(thm)],[f2958]) ).

fof(f2999,plain,
    ( $false
    | spl0_63 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2960,f106]) ).

fof(f3000,plain,
    spl0_63,
    inference(contradiction_clause,[status(thm)],[f2999]) ).

fof(f3271,plain,
    ( in(sk0_14,relation_rng(sk0_12))
    | ~ spl0_19
    | ~ spl0_35
    | ~ spl0_53 ),
    inference(forward_demodulation,[status(thm)],[f2748,f2890]) ).

fof(f3272,plain,
    ( $false
    | ~ spl0_19
    | ~ spl0_35
    | ~ spl0_53 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3271,f129]) ).

fof(f3273,plain,
    ( ~ spl0_19
    | ~ spl0_35
    | ~ spl0_53 ),
    inference(contradiction_clause,[status(thm)],[f3272]) ).

fof(f3274,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f919,f932,f976,f979,f981,f983,f985,f997,f2729,f2743,f2868,f2886,f2893,f2937,f3000,f3273]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU002+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue May 30 09:09:25 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.5.1
% 2.53/0.71  % Refutation found
% 2.53/0.71  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.53/0.71  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.53/0.73  % Elapsed time: 0.373702 seconds
% 2.53/0.73  % CPU time: 2.842506 seconds
% 2.53/0.73  % Memory used: 82.426 MB
%------------------------------------------------------------------------------