TSTP Solution File: SET919+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET919+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:40:42 EDT 2024

% Result   : Theorem 35.95s 4.93s
% Output   : CNFRefutation 36.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   86 (  10 unt;   0 def)
%            Number of atoms       :  323 ( 170 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  370 ( 133   ~; 178   |;  48   &)
%                                         (   9 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  217 ( 205   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f6,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,conjecture,
    ! [A,B,C] :
      ( in(A,B)
     => ( ( in(C,B)
          & A != C )
        | set_intersection2(unordered_pair(A,C),B) = singleton(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,negated_conjecture,
    ~ ! [A,B,C] :
        ( in(A,B)
       => ( ( in(C,B)
            & A != C )
          | set_intersection2(unordered_pair(A,C),B) = singleton(A) ) ),
    inference(negated_conjecture,[status(cth)],[f10]) ).

fof(f15,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f16,plain,
    ! [A,B] :
      ( ( B != singleton(A)
        | ! [C] :
            ( ( ~ in(C,B)
              | C = A )
            & ( in(C,B)
              | C != A ) ) )
      & ( B = singleton(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | C != A )
            & ( in(C,B)
              | C = A ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

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

fof(f18,plain,
    ( ! [A,B] :
        ( B != singleton(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | C = A )
          & ! [C] :
              ( in(C,B)
              | C != A ) ) )
    & ! [A,B] :
        ( B = singleton(A)
        | ( ( ~ in(sk0_0(B,A),B)
            | sk0_0(B,A) != A )
          & ( in(sk0_0(B,A),B)
            | sk0_0(B,A) = A ) ) ) ),
    inference(skolemization,[status(esa)],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | ~ in(X2,X0)
      | X2 = X1 ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | in(X2,X0)
      | X2 != X1 ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( X0 = singleton(X1)
      | ~ in(sk0_0(X0,X1),X0)
      | sk0_0(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( X0 = singleton(X1)
      | in(sk0_0(X0,X1),X0)
      | sk0_0(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f23,plain,
    ! [A,B,C] :
      ( ( C != unordered_pair(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | D = A
              | D = B )
            & ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
      & ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f24,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ( D != A
                & D != B ) )
            & ( in(D,C)
              | D = A
              | D = B ) ) ) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f25,plain,
    ( ! [A,B,C] :
        ( C != unordered_pair(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | D = A
              | D = B )
          & ! [D] :
              ( in(D,C)
              | ( D != A
                & D != B ) ) ) )
    & ! [A,B,C] :
        ( C = unordered_pair(A,B)
        | ( ( ~ in(sk0_1(C,B,A),C)
            | ( sk0_1(C,B,A) != A
              & sk0_1(C,B,A) != B ) )
          & ( in(sk0_1(C,B,A),C)
            | sk0_1(C,B,A) = A
            | sk0_1(C,B,A) = B ) ) ) ),
    inference(skolemization,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | ~ in(X3,X0)
      | X3 = X1
      | X3 = X2 ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | in(X3,X0)
      | X3 != X1 ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != unordered_pair(X1,X2)
      | in(X3,X0)
      | X3 != X2 ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f32,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)],[f6]) ).

fof(f33,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)],[f32]) ).

fof(f34,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_2(C,B,A),C)
            | ~ in(sk0_2(C,B,A),A)
            | ~ in(sk0_2(C,B,A),B) )
          & ( in(sk0_2(C,B,A),C)
            | ( in(sk0_2(C,B,A),A)
              & in(sk0_2(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f33]) ).

fof(f35,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f47,plain,
    ? [A,B,C] :
      ( in(A,B)
      & ( ~ in(C,B)
        | A = C )
      & set_intersection2(unordered_pair(A,C),B) != singleton(A) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f48,plain,
    ? [A,B] :
      ( in(A,B)
      & ? [C] :
          ( ( ~ in(C,B)
            | A = C )
          & set_intersection2(unordered_pair(A,C),B) != singleton(A) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ( in(sk0_5,sk0_6)
    & ( ~ in(sk0_7,sk0_6)
      | sk0_5 = sk0_7 )
    & set_intersection2(unordered_pair(sk0_5,sk0_7),sk0_6) != singleton(sk0_5) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f50,plain,
    in(sk0_5,sk0_6),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ( ~ in(sk0_7,sk0_6)
    | sk0_5 = sk0_7 ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    set_intersection2(unordered_pair(sk0_5,sk0_7),sk0_6) != singleton(sk0_5),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f53,plain,
    ( spl0_0
  <=> in(sk0_7,sk0_6) ),
    introduced(split_symbol_definition) ).

fof(f56,plain,
    ( spl0_1
  <=> sk0_5 = sk0_7 ),
    introduced(split_symbol_definition) ).

fof(f57,plain,
    ( sk0_5 = sk0_7
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f56]) ).

fof(f59,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f51,f53,f56]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | X0 = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f19]) ).

fof(f61,plain,
    ! [X0] : in(X0,singleton(X0)),
    inference(destructive_equality_resolution,[status(esa)],[f20]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(destructive_equality_resolution,[status(esa)],[f26]) ).

fof(f63,plain,
    ! [X0,X1] : in(X0,unordered_pair(X0,X1)),
    inference(destructive_equality_resolution,[status(esa)],[f27]) ).

fof(f64,plain,
    ! [X0,X1] : in(X0,unordered_pair(X1,X0)),
    inference(destructive_equality_resolution,[status(esa)],[f28]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | in(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f35]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f36]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_intersection2(X1,X2))
      | ~ in(X0,X1)
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f37]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = singleton(X2)
      | sk0_0(set_intersection2(X0,X1),X2) = X2
      | in(sk0_0(set_intersection2(X0,X1),X2),X1) ),
    inference(resolution,[status(thm)],[f22,f66]) ).

fof(f106,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = singleton(X2)
      | sk0_0(set_intersection2(X0,X1),X2) = X2
      | in(sk0_0(set_intersection2(X0,X1),X2),X0) ),
    inference(resolution,[status(thm)],[f22,f65]) ).

fof(f107,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = singleton(X2)
      | sk0_0(unordered_pair(X0,X1),X2) = X2
      | sk0_0(unordered_pair(X0,X1),X2) = X0
      | sk0_0(unordered_pair(X0,X1),X2) = X1 ),
    inference(resolution,[status(thm)],[f22,f62]) ).

fof(f210,plain,
    ! [X0,X1,X2,X3] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X3)
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X3
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X1
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X2 ),
    inference(resolution,[status(thm)],[f105,f62]) ).

fof(f211,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X2)
      | sk0_0(set_intersection2(X0,singleton(X1)),X2) = X2
      | sk0_0(set_intersection2(X0,singleton(X1)),X2) = X1 ),
    inference(resolution,[status(thm)],[f105,f60]) ).

fof(f289,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = singleton(X2)
      | sk0_0(unordered_pair(X0,X1),X2) = X1
      | X2 != X0
      | sk0_0(unordered_pair(X0,X1),X2) = X0 ),
    inference(equality_factoring,[status(esa)],[f107]) ).

fof(f290,plain,
    ! [X0,X1] :
      ( unordered_pair(X0,X1) = singleton(X0)
      | sk0_0(unordered_pair(X0,X1),X0) = X1
      | sk0_0(unordered_pair(X0,X1),X0) = X0 ),
    inference(destructive_equality_resolution,[status(esa)],[f289]) ).

fof(f319,plain,
    ! [X0,X1] :
      ( unordered_pair(X0,X1) = singleton(X0)
      | X1 != X0
      | sk0_0(unordered_pair(X0,X1),X0) = X0 ),
    inference(equality_factoring,[status(esa)],[f290]) ).

fof(f320,plain,
    ! [X0] :
      ( unordered_pair(X0,X0) = singleton(X0)
      | sk0_0(unordered_pair(X0,X0),X0) = X0 ),
    inference(destructive_equality_resolution,[status(esa)],[f319]) ).

fof(f325,plain,
    ! [X0] :
      ( unordered_pair(X0,X0) = singleton(X0)
      | ~ in(X0,unordered_pair(X0,X0))
      | sk0_0(unordered_pair(X0,X0),X0) != X0
      | unordered_pair(X0,X0) = singleton(X0) ),
    inference(paramodulation,[status(thm)],[f320,f21]) ).

fof(f326,plain,
    ! [X0] :
      ( unordered_pair(X0,X0) = singleton(X0)
      | ~ in(X0,unordered_pair(X0,X0))
      | sk0_0(unordered_pair(X0,X0),X0) != X0 ),
    inference(duplicate_literals_removal,[status(esa)],[f325]) ).

fof(f327,plain,
    ! [X0] :
      ( unordered_pair(X0,X0) = singleton(X0)
      | sk0_0(unordered_pair(X0,X0),X0) != X0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f326,f64]) ).

fof(f328,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(forward_subsumption_resolution,[status(thm)],[f327,f320]) ).

fof(f1226,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X2)
      | X2 != X1
      | sk0_0(set_intersection2(X0,singleton(X1)),X2) = X1 ),
    inference(equality_factoring,[status(esa)],[f211]) ).

fof(f1227,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X1)
      | sk0_0(set_intersection2(X0,singleton(X1)),X1) = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f1226]) ).

fof(f1289,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X1)
      | ~ in(X1,set_intersection2(X0,singleton(X1)))
      | sk0_0(set_intersection2(X0,singleton(X1)),X1) != X1
      | set_intersection2(X0,singleton(X1)) = singleton(X1) ),
    inference(paramodulation,[status(thm)],[f1227,f21]) ).

fof(f1290,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X1)
      | ~ in(X1,set_intersection2(X0,singleton(X1)))
      | sk0_0(set_intersection2(X0,singleton(X1)),X1) != X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f1289]) ).

fof(f1291,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X1)
      | ~ in(X1,set_intersection2(X0,singleton(X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1290,f1227]) ).

fof(f1292,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X1)
      | ~ in(X1,X0)
      | ~ in(X1,singleton(X1)) ),
    inference(resolution,[status(thm)],[f1291,f67]) ).

fof(f1293,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X1)
      | ~ in(X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1292,f61]) ).

fof(f1297,plain,
    ! [X0,X1] :
      ( set_intersection2(singleton(X0),X1) = singleton(X0)
      | ~ in(X0,X1) ),
    inference(paramodulation,[status(thm)],[f15,f1293]) ).

fof(f1893,plain,
    ! [X0,X1,X2,X3] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X3)
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X2
      | X3 != X1
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X1 ),
    inference(equality_factoring,[status(esa)],[f210]) ).

fof(f1894,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X1) = X2
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X1) = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f1893]) ).

fof(f30815,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X1) = X1
      | in(X2,X0)
      | set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X1) = X1 ),
    inference(paramodulation,[status(thm)],[f1894,f106]) ).

fof(f30816,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X1) = X1
      | in(X2,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f30815]) ).

fof(f30959,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | ~ in(X1,set_intersection2(X0,unordered_pair(X1,X2)))
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X1) != X1
      | set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | in(X2,X0) ),
    inference(paramodulation,[status(thm)],[f30816,f21]) ).

fof(f30960,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | ~ in(X1,set_intersection2(X0,unordered_pair(X1,X2)))
      | sk0_0(set_intersection2(X0,unordered_pair(X1,X2)),X1) != X1
      | in(X2,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f30959]) ).

fof(f30961,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | ~ in(X1,set_intersection2(X0,unordered_pair(X1,X2)))
      | in(X2,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f30960,f30816]) ).

fof(f30962,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | in(X2,X0)
      | ~ in(X1,X0)
      | ~ in(X1,unordered_pair(X1,X2)) ),
    inference(resolution,[status(thm)],[f30961,f67]) ).

fof(f30963,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X1)
      | in(X2,X0)
      | ~ in(X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f30962,f63]) ).

fof(f30972,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(unordered_pair(X0,X1),X2) = singleton(X0)
      | in(X1,X2)
      | ~ in(X0,X2) ),
    inference(paramodulation,[status(thm)],[f15,f30963]) ).

fof(f30977,plain,
    ( spl0_2
  <=> in(sk0_5,sk0_6) ),
    introduced(split_symbol_definition) ).

fof(f30979,plain,
    ( ~ in(sk0_5,sk0_6)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f30977]) ).

fof(f30980,plain,
    ( in(sk0_7,sk0_6)
    | ~ in(sk0_5,sk0_6) ),
    inference(resolution,[status(thm)],[f30972,f52]) ).

fof(f30981,plain,
    ( spl0_0
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f30980,f53,f30977]) ).

fof(f30987,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f30979,f50]) ).

fof(f30988,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f30987]) ).

fof(f31688,plain,
    ( set_intersection2(unordered_pair(sk0_5,sk0_5),sk0_6) != singleton(sk0_5)
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f57,f52]) ).

fof(f31689,plain,
    ( set_intersection2(singleton(sk0_5),sk0_6) != singleton(sk0_5)
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f328,f31688]) ).

fof(f31696,plain,
    ( ~ in(sk0_5,sk0_6)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f31689,f1297]) ).

fof(f31697,plain,
    ( ~ spl0_2
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f31696,f30977,f56]) ).

fof(f31702,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f59,f30981,f30988,f31697]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET919+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n005.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon Apr 29 21:23:41 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.6.0
% 35.95/4.93  % Refutation found
% 35.95/4.93  % SZS status Theorem for theBenchmark: Theorem is valid
% 35.95/4.93  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 36.79/4.98  % Elapsed time: 4.651137 seconds
% 36.79/4.98  % CPU time: 36.748302 seconds
% 36.79/4.98  % Total memory used: 379.685 MB
% 36.79/4.98  % Net memory used: 372.411 MB
%------------------------------------------------------------------------------