TSTP Solution File: SET951+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n023.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 0.12s 0.39s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   80 (  16 unt;   0 def)
%            Number of atoms       :  247 (  50 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  275 ( 108   ~; 107   |;  46   &)
%                                         (  13 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   7 prp; 0-5 aty)
%            Number of functors    :   14 (  14 usr;   5 con; 0-4 aty)
%            Number of variables   :  210 ( 184   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,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(f5,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [A,B,C,D,E] :
      ~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
        & ! [F,G] :
            ~ ( A = ordered_pair(F,G)
              & in(F,set_intersection2(B,D))
              & in(G,set_intersection2(C,E)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [A,B,C,D,E] :
        ~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
          & ! [F,G] :
              ~ ( A = ordered_pair(F,G)
                & in(F,set_intersection2(B,D))
                & in(G,set_intersection2(C,E)) ) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f13,axiom,
    ! [A,B,C,D] :
      ( ordered_pair(A,B) = ordered_pair(C,D)
     => ( A = C
        & B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,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,[f4]) ).

fof(f19,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)],[f4,f18]) ).

fof(f20,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)],[f19]) ).

fof(f21,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)],[f20]) ).

fof(f22,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)],[f21]) ).

fof(f23,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)],[f22]) ).

fof(f27,plain,
    ! [A,B,C] :
      ( ( C != set_intersection2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
            & ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
      & ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f28,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f27]) ).

fof(f29,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ( ( ~ in(sk0_5(C,B,A),C)
            | ~ in(sk0_5(C,B,A),A)
            | ~ in(sk0_5(C,B,A),B) )
          & ( in(sk0_5(C,B,A),C)
            | ( in(sk0_5(C,B,A),A)
              & in(sk0_5(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f28]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f31,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f44,plain,
    ? [A,B,C,D,E] :
      ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
      & ! [F,G] :
          ( A != ordered_pair(F,G)
          | ~ in(F,set_intersection2(B,D))
          | ~ in(G,set_intersection2(C,E)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f45,plain,
    ? [A,B,C,D,E] :
      ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
      & ! [G] :
          ( ! [F] :
              ( A != ordered_pair(F,G)
              | ~ in(F,set_intersection2(B,D)) )
          | ~ in(G,set_intersection2(C,E)) ) ),
    inference(miniscoping,[status(esa)],[f44]) ).

fof(f46,plain,
    ( in(sk0_8,set_intersection2(cartesian_product2(sk0_9,sk0_10),cartesian_product2(sk0_11,sk0_12)))
    & ! [G] :
        ( ! [F] :
            ( sk0_8 != ordered_pair(F,G)
            | ~ in(F,set_intersection2(sk0_9,sk0_11)) )
        | ~ in(G,set_intersection2(sk0_10,sk0_12)) ) ),
    inference(skolemization,[status(esa)],[f45]) ).

fof(f47,plain,
    in(sk0_8,set_intersection2(cartesian_product2(sk0_9,sk0_10),cartesian_product2(sk0_11,sk0_12))),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( sk0_8 != ordered_pair(X0,X1)
      | ~ in(X0,set_intersection2(sk0_9,sk0_11))
      | ~ in(X1,set_intersection2(sk0_10,sk0_12)) ),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f49,plain,
    ! [A,B,C,D] :
      ( ordered_pair(A,B) != ordered_pair(C,D)
      | ( A = C
        & B = D ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f50,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,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)],[f18]) ).

fof(f53,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)],[f52]) ).

fof(f54,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ pd0_0(X0,X1,X2,X3,X4)
      | in(X1,X4) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f55,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ pd0_0(X0,X1,X2,X3,X4)
      | in(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ pd0_0(X0,X1,X2,X3,X4)
      | X2 = ordered_pair(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f58,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)],[f23]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | in(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f30]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f31]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_intersection2(X1,X2))
      | ~ in(X0,X1)
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f32]) ).

fof(f66,plain,
    in(sk0_8,cartesian_product2(sk0_9,sk0_10)),
    inference(resolution,[status(thm)],[f60,f47]) ).

fof(f70,plain,
    in(sk0_8,cartesian_product2(sk0_11,sk0_12)),
    inference(resolution,[status(thm)],[f61,f47]) ).

fof(f127,plain,
    pd0_0(sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_8,sk0_12,sk0_11),
    inference(resolution,[status(thm)],[f58,f70]) ).

fof(f128,plain,
    pd0_0(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_8,sk0_10,sk0_9),
    inference(resolution,[status(thm)],[f58,f66]) ).

fof(f144,plain,
    sk0_8 = ordered_pair(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11)),
    inference(resolution,[status(thm)],[f127,f56]) ).

fof(f145,plain,
    ( spl0_0
  <=> in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),set_intersection2(sk0_9,sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f147,plain,
    ( ~ in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),set_intersection2(sk0_9,sk0_11))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f145]) ).

fof(f148,plain,
    ( spl0_1
  <=> in(sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),set_intersection2(sk0_10,sk0_12)) ),
    introduced(split_symbol_definition) ).

fof(f150,plain,
    ( ~ in(sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),set_intersection2(sk0_10,sk0_12))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f148]) ).

fof(f151,plain,
    ( ~ in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),set_intersection2(sk0_9,sk0_11))
    | ~ in(sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),set_intersection2(sk0_10,sk0_12)) ),
    inference(resolution,[status(thm)],[f144,f48]) ).

fof(f152,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f151,f145,f148]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ordered_pair(X0,X1) != sk0_8
      | X1 = sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11) ),
    inference(paramodulation,[status(thm)],[f144,f51]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ordered_pair(X0,X1) != sk0_8
      | X0 = sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11) ),
    inference(paramodulation,[status(thm)],[f144,f50]) ).

fof(f163,plain,
    ( spl0_3
  <=> in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f165,plain,
    ( ~ in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_9)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f163]) ).

fof(f166,plain,
    ( spl0_4
  <=> in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_11) ),
    introduced(split_symbol_definition) ).

fof(f168,plain,
    ( ~ in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_11)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f166]) ).

fof(f169,plain,
    ( ~ in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_9)
    | ~ in(sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_11)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f147,f62]) ).

fof(f170,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f169,f163,f166,f145]) ).

fof(f174,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),X1,X2,sk0_9)
      | spl0_3 ),
    inference(resolution,[status(thm)],[f165,f54]) ).

fof(f187,plain,
    sk0_8 = ordered_pair(sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9)),
    inference(resolution,[status(thm)],[f128,f56]) ).

fof(f196,plain,
    sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9) = sk0_0(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),
    inference(resolution,[status(thm)],[f187,f156]) ).

fof(f197,plain,
    sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9) = sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),
    inference(resolution,[status(thm)],[f187,f154]) ).

fof(f217,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),X1,X2,sk0_9)
      | spl0_3 ),
    inference(backward_demodulation,[status(thm)],[f196,f174]) ).

fof(f224,plain,
    pd0_0(sk0_1(sk0_8,cartesian_product2(sk0_11,sk0_12),sk0_12,sk0_11),sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_8,sk0_12,sk0_11),
    inference(backward_demodulation,[status(thm)],[f196,f127]) ).

fof(f225,plain,
    pd0_0(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_8,sk0_12,sk0_11),
    inference(forward_demodulation,[status(thm)],[f197,f224]) ).

fof(f227,plain,
    ( $false
    | spl0_3 ),
    inference(backward_subsumption_resolution,[status(thm)],[f128,f217]) ).

fof(f228,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f227]) ).

fof(f229,plain,
    ( ~ in(sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_11)
    | spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f196,f168]) ).

fof(f232,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,sk0_0(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),X1,X2,sk0_11)
      | spl0_4 ),
    inference(resolution,[status(thm)],[f229,f54]) ).

fof(f233,plain,
    ( $false
    | spl0_4 ),
    inference(backward_subsumption_resolution,[status(thm)],[f225,f232]) ).

fof(f234,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f233]) ).

fof(f235,plain,
    ( ~ in(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),set_intersection2(sk0_10,sk0_12))
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f197,f150]) ).

fof(f240,plain,
    ( spl0_11
  <=> in(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_10) ),
    introduced(split_symbol_definition) ).

fof(f242,plain,
    ( ~ in(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_10)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f240]) ).

fof(f243,plain,
    ( spl0_12
  <=> in(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_12) ),
    introduced(split_symbol_definition) ).

fof(f245,plain,
    ( ~ in(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_12)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f243]) ).

fof(f246,plain,
    ( ~ in(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_10)
    | ~ in(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),sk0_12)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f235,f62]) ).

fof(f247,plain,
    ( ~ spl0_11
    | ~ spl0_12
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f246,f240,f243,f148]) ).

fof(f259,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),X0,X1,sk0_10,X2)
      | spl0_11 ),
    inference(resolution,[status(thm)],[f242,f55]) ).

fof(f261,plain,
    ( $false
    | spl0_11 ),
    inference(backward_subsumption_resolution,[status(thm)],[f128,f259]) ).

fof(f262,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f261]) ).

fof(f267,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(sk0_1(sk0_8,cartesian_product2(sk0_9,sk0_10),sk0_10,sk0_9),X0,X1,sk0_12,X2)
      | spl0_12 ),
    inference(resolution,[status(thm)],[f245,f55]) ).

fof(f269,plain,
    ( $false
    | spl0_12 ),
    inference(backward_subsumption_resolution,[status(thm)],[f225,f267]) ).

fof(f270,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f269]) ).

fof(f271,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f152,f170,f228,f234,f247,f262,f270]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Apr 29 21:47:25 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.39  % Refutation found
% 0.12/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40  % Elapsed time: 0.055173 seconds
% 0.12/0.40  % CPU time: 0.323048 seconds
% 0.12/0.40  % Total memory used: 63.199 MB
% 0.12/0.40  % Net memory used: 63.061 MB
%------------------------------------------------------------------------------