TSTP Solution File: SET955+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET955+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 20:40:47 EDT 2024

% Result   : Theorem 0.16s 0.37s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   69 (   4 unt;   0 def)
%            Number of atoms       :  233 (  64 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  248 (  84   ~; 116   |;  28   &)
%                                         (  16 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   8 prp; 0-5 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-4 aty)
%            Number of variables   :  171 ( 143   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B,C] :
      ( C = cartesian_product2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ? [E,F] :
              ( in(E,A)
              & in(F,B)
              & D = ordered_pair(E,F) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,conjecture,
    ! [A,B,C,D] :
      ( ! [E,F] :
          ( in(ordered_pair(E,F),cartesian_product2(A,B))
        <=> in(ordered_pair(E,F),cartesian_product2(C,D)) )
     => cartesian_product2(A,B) = cartesian_product2(C,D) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ! [E,F] :
            ( in(ordered_pair(E,F),cartesian_product2(A,B))
          <=> in(ordered_pair(E,F),cartesian_product2(C,D)) )
       => cartesian_product2(A,B) = cartesian_product2(C,D) ),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f10,axiom,
    ! [A,B] :
      ( ! [C] :
          ( in(C,A)
        <=> in(C,B) )
     => A = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,plain,
    ! [A,B,D,E,F] :
      ( pd0_0(F,E,D,B,A)
    <=> ( in(E,A)
        & in(F,B)
        & D = ordered_pair(E,F) ) ),
    introduced(predicate_definition,[f3]) ).

fof(f15,plain,
    ! [A,B,C] :
      ( C = cartesian_product2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ? [E,F] : pd0_0(F,E,D,B,A) ) ),
    inference(formula_renaming,[status(thm)],[f3,f14]) ).

fof(f16,plain,
    ! [A,B,C] :
      ( ( C != cartesian_product2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ? [E,F] : pd0_0(F,E,D,B,A) )
            & ( in(D,C)
              | ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
      & ( C = cartesian_product2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ! [E,F] : ~ pd0_0(F,E,D,B,A) )
            & ( in(D,C)
              | ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ( ! [A,B,C] :
        ( C != cartesian_product2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ? [E,F] : pd0_0(F,E,D,B,A) )
          & ! [D] :
              ( in(D,C)
              | ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
    & ! [A,B,C] :
        ( C = cartesian_product2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ! [E,F] : ~ pd0_0(F,E,D,B,A) )
            & ( in(D,C)
              | ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f18,plain,
    ( ! [A,B,C] :
        ( C != cartesian_product2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | pd0_0(sk0_1(D,C,B,A),sk0_0(D,C,B,A),D,B,A) )
          & ! [D] :
              ( in(D,C)
              | ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
    & ! [A,B,C] :
        ( C = cartesian_product2(A,B)
        | ( ( ~ in(sk0_2(C,B,A),C)
            | ! [E,F] : ~ pd0_0(F,E,sk0_2(C,B,A),B,A) )
          & ( in(sk0_2(C,B,A),C)
            | pd0_0(sk0_4(C,B,A),sk0_3(C,B,A),sk0_2(C,B,A),B,A) ) ) ) ),
    inference(skolemization,[status(esa)],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != cartesian_product2(X1,X2)
      | ~ in(X3,X0)
      | pd0_0(sk0_1(X3,X0,X2,X1),sk0_0(X3,X0,X2,X1),X3,X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f29,plain,
    ? [A,B,C,D] :
      ( ! [E,F] :
          ( in(ordered_pair(E,F),cartesian_product2(A,B))
        <=> in(ordered_pair(E,F),cartesian_product2(C,D)) )
      & cartesian_product2(A,B) != cartesian_product2(C,D) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f30,plain,
    ? [A,B,C,D] :
      ( ! [E,F] :
          ( ( ~ in(ordered_pair(E,F),cartesian_product2(A,B))
            | in(ordered_pair(E,F),cartesian_product2(C,D)) )
          & ( in(ordered_pair(E,F),cartesian_product2(A,B))
            | ~ in(ordered_pair(E,F),cartesian_product2(C,D)) ) )
      & cartesian_product2(A,B) != cartesian_product2(C,D) ),
    inference(NNF_transformation,[status(esa)],[f29]) ).

fof(f31,plain,
    ? [A,B,C,D] :
      ( ! [E,F] :
          ( ~ in(ordered_pair(E,F),cartesian_product2(A,B))
          | in(ordered_pair(E,F),cartesian_product2(C,D)) )
      & ! [E,F] :
          ( in(ordered_pair(E,F),cartesian_product2(A,B))
          | ~ in(ordered_pair(E,F),cartesian_product2(C,D)) )
      & cartesian_product2(A,B) != cartesian_product2(C,D) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f32,plain,
    ( ! [E,F] :
        ( ~ in(ordered_pair(E,F),cartesian_product2(sk0_7,sk0_8))
        | in(ordered_pair(E,F),cartesian_product2(sk0_9,sk0_10)) )
    & ! [E,F] :
        ( in(ordered_pair(E,F),cartesian_product2(sk0_7,sk0_8))
        | ~ in(ordered_pair(E,F),cartesian_product2(sk0_9,sk0_10)) )
    & cartesian_product2(sk0_7,sk0_8) != cartesian_product2(sk0_9,sk0_10) ),
    inference(skolemization,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(sk0_7,sk0_8))
      | in(ordered_pair(X0,X1),cartesian_product2(sk0_9,sk0_10)) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(sk0_7,sk0_8))
      | ~ in(ordered_pair(X0,X1),cartesian_product2(sk0_9,sk0_10)) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f35,plain,
    cartesian_product2(sk0_7,sk0_8) != cartesian_product2(sk0_9,sk0_10),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f36,plain,
    ! [A,B] :
      ( ? [C] :
          ( in(C,A)
        <~> in(C,B) )
      | A = B ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f37,plain,
    ! [A,B] :
      ( ? [C] :
          ( ( in(C,A)
            | in(C,B) )
          & ( ~ in(C,A)
            | ~ in(C,B) ) )
      | A = B ),
    inference(NNF_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    ! [A,B] :
      ( ( ( in(sk0_11(B,A),A)
          | in(sk0_11(B,A),B) )
        & ( ~ in(sk0_11(B,A),A)
          | ~ in(sk0_11(B,A),B) ) )
      | A = B ),
    inference(skolemization,[status(esa)],[f37]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( in(sk0_11(X0,X1),X1)
      | in(sk0_11(X0,X1),X0)
      | X1 = X0 ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ in(sk0_11(X0,X1),X1)
      | ~ in(sk0_11(X0,X1),X0)
      | X1 = X0 ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f41,plain,
    ! [A,B,D,E,F] :
      ( ( ~ pd0_0(F,E,D,B,A)
        | ( in(E,A)
          & in(F,B)
          & D = ordered_pair(E,F) ) )
      & ( pd0_0(F,E,D,B,A)
        | ~ in(E,A)
        | ~ in(F,B)
        | D != ordered_pair(E,F) ) ),
    inference(NNF_transformation,[status(esa)],[f14]) ).

fof(f42,plain,
    ( ! [A,B,D,E,F] :
        ( ~ pd0_0(F,E,D,B,A)
        | ( in(E,A)
          & in(F,B)
          & D = ordered_pair(E,F) ) )
    & ! [A,B,D,E,F] :
        ( pd0_0(F,E,D,B,A)
        | ~ in(E,A)
        | ~ in(F,B)
        | D != ordered_pair(E,F) ) ),
    inference(miniscoping,[status(esa)],[f41]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ pd0_0(X0,X1,X2,X3,X4)
      | X2 = ordered_pair(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,cartesian_product2(X1,X2))
      | pd0_0(sk0_1(X0,cartesian_product2(X1,X2),X2,X1),sk0_0(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f19]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,cartesian_product2(X1,X2))
      | X0 = ordered_pair(sk0_0(X0,cartesian_product2(X1,X2),X2,X1),sk0_1(X0,cartesian_product2(X1,X2),X2,X1)) ),
    inference(resolution,[status(thm)],[f47,f45]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( sk0_11(X0,cartesian_product2(X1,X2)) = ordered_pair(sk0_0(sk0_11(X0,cartesian_product2(X1,X2)),cartesian_product2(X1,X2),X2,X1),sk0_1(sk0_11(X0,cartesian_product2(X1,X2)),cartesian_product2(X1,X2),X2,X1))
      | in(sk0_11(X0,cartesian_product2(X1,X2)),X0)
      | cartesian_product2(X1,X2) = X0 ),
    inference(resolution,[status(thm)],[f62,f39]) ).

fof(f68,plain,
    ! [X0,X1,X2,X3] :
      ( sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2))
      | cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
    inference(resolution,[status(thm)],[f63,f62]) ).

fof(f76,plain,
    ! [X0,X1,X2,X3] :
      ( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_7,sk0_8))
      | ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2)),cartesian_product2(sk0_9,sk0_10))
      | cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
    inference(paramodulation,[status(thm)],[f68,f34]) ).

fof(f79,plain,
    ! [X0,X1,X2,X3] :
      ( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_7,sk0_8))
      | ~ in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_9,sk0_10))
      | cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0))
      | cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
    inference(paramodulation,[status(thm)],[f68,f76]) ).

fof(f80,plain,
    ! [X0,X1,X2,X3] :
      ( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_7,sk0_8))
      | ~ in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_9,sk0_10))
      | cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f79]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
      | cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0))
      | in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1))
      | cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1) ),
    inference(resolution,[status(thm)],[f80,f39]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
      | cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0))
      | in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1)) ),
    inference(duplicate_literals_removal,[status(esa)],[f83]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
      | cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f84,f62]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0))
      | sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) ),
    inference(resolution,[status(thm)],[f85,f62]) ).

fof(f143,plain,
    ( spl0_2
  <=> cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f144,plain,
    ( cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f143]) ).

fof(f146,plain,
    ( spl0_3
  <=> sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f148,plain,
    ( sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) != sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10))
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f146]) ).

fof(f149,plain,
    ( spl0_4
  <=> ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f150,plain,
    ( ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10))
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f149]) ).

fof(f152,plain,
    ( cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
    | sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) != sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10))
    | ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) ),
    inference(equality_factoring,[status(esa)],[f86]) ).

fof(f153,plain,
    ( spl0_2
    | ~ spl0_3
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f152,f143,f146,f149]) ).

fof(f154,plain,
    ( $false
    | spl0_3 ),
    inference(trivial_equality_resolution,[status(esa)],[f148]) ).

fof(f155,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f154]) ).

fof(f156,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f144,f35]) ).

fof(f157,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f156]) ).

fof(f165,plain,
    ( spl0_6
  <=> in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8)) ),
    introduced(split_symbol_definition) ).

fof(f166,plain,
    ( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f165]) ).

fof(f173,plain,
    ( spl0_8
  <=> in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f174,plain,
    ( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f173]) ).

fof(f183,plain,
    ( spl0_10
  <=> in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_7,sk0_8)) ),
    introduced(split_symbol_definition) ).

fof(f185,plain,
    ( ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_7,sk0_8))
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f183]) ).

fof(f191,plain,
    ( spl0_12
  <=> in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_9,sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f193,plain,
    ( ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_9,sk0_10))
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f191]) ).

fof(f196,plain,
    ( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
    | ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_9,sk0_10))
    | ~ spl0_4 ),
    inference(paramodulation,[status(thm)],[f150,f34]) ).

fof(f197,plain,
    ( spl0_6
    | ~ spl0_12
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f196,f165,f191,f149]) ).

fof(f198,plain,
    ( ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_7,sk0_8))
    | in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10))
    | ~ spl0_4 ),
    inference(paramodulation,[status(thm)],[f150,f33]) ).

fof(f199,plain,
    ( ~ spl0_10
    | spl0_8
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f198,f183,f173,f149]) ).

fof(f200,plain,
    ( ~ in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10))
    | ~ spl0_4
    | spl0_12 ),
    inference(forward_demodulation,[status(thm)],[f150,f193]) ).

fof(f201,plain,
    ( ~ in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
    | ~ spl0_4
    | spl0_10 ),
    inference(forward_demodulation,[status(thm)],[f150,f185]) ).

fof(f210,plain,
    ( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
    | cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
    | ~ spl0_4
    | spl0_12 ),
    inference(resolution,[status(thm)],[f200,f39]) ).

fof(f211,plain,
    ( spl0_6
    | spl0_2
    | ~ spl0_4
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f210,f165,f143,f149,f191]) ).

fof(f212,plain,
    ( $false
    | ~ spl0_4
    | spl0_10
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f166,f201]) ).

fof(f213,plain,
    ( ~ spl0_4
    | spl0_10
    | ~ spl0_6 ),
    inference(contradiction_clause,[status(thm)],[f212]) ).

fof(f231,plain,
    ( ~ in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
    | cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f174,f40]) ).

fof(f232,plain,
    ( ~ spl0_6
    | spl0_2
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f231,f165,f143,f173]) ).

fof(f234,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f153,f155,f157,f197,f199,f211,f213,f232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SET955+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.02/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33  % Computer : n003.cluster.edu
% 0.10/0.33  % Model    : x86_64 x86_64
% 0.10/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33  % Memory   : 8042.1875MB
% 0.10/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33  % CPULimit : 300
% 0.10/0.33  % WCLimit  : 300
% 0.10/0.33  % DateTime : Mon Apr 29 21:50:03 EDT 2024
% 0.10/0.33  % CPUTime  : 
% 0.10/0.34  % Drodi V3.6.0
% 0.16/0.37  % Refutation found
% 0.16/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.39  % Elapsed time: 0.053850 seconds
% 0.16/0.39  % CPU time: 0.280596 seconds
% 0.16/0.39  % Total memory used: 61.159 MB
% 0.16/0.39  % Net memory used: 61.003 MB
%------------------------------------------------------------------------------