TSTP Solution File: NUM385+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 12:29:00 EDT 2023

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   50 (  10 unt;   0 def)
%            Number of atoms       :  160 (  45 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  179 (  69   ~;  73   |;  26   &)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   77 (;  71   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] : succ(A) = set_union2(A,singleton(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( B = singleton(A)
    <=> ! [C] :
          ( in(C,B)
        <=> C = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C] :
      ( C = set_union2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [A] : in(A,succ(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,conjecture,
    ! [A,B] :
      ( succ(A) = succ(B)
     => A = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    ~ ! [A,B] :
        ( succ(A) = succ(B)
       => A = B ),
    inference(negated_conjecture,[status(cth)],[f29]) ).

fof(f37,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | ~ in(B,A) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f48,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f49,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)],[f7]) ).

fof(f50,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)],[f49]) ).

fof(f51,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)],[f50]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | ~ in(X2,X0)
      | X2 = X1 ),
    inference(cnf_transformation,[status(esa)],[f51]) ).

fof(f56,plain,
    ! [A,B,C] :
      ( ( C != set_union2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | in(D,A)
              | in(D,B) )
            & ( in(D,C)
              | ( ~ in(D,A)
                & ~ in(D,B) ) ) ) )
      & ( C = set_union2(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)],[f8]) ).

fof(f57,plain,
    ( ! [A,B,C] :
        ( C != set_union2(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_union2(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)],[f56]) ).

fof(f58,plain,
    ( ! [A,B,C] :
        ( C != set_union2(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_union2(A,B)
        | ( ( ~ in(sk0_1(C,B,A),C)
            | ( ~ in(sk0_1(C,B,A),A)
              & ~ in(sk0_1(C,B,A),B) ) )
          & ( in(sk0_1(C,B,A),C)
            | in(sk0_1(C,B,A),A)
            | in(sk0_1(C,B,A),B) ) ) ) ),
    inference(skolemization,[status(esa)],[f57]) ).

fof(f59,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_union2(X1,X2)
      | ~ in(X3,X0)
      | in(X3,X1)
      | in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f116,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f117,plain,
    ? [A,B] :
      ( succ(A) = succ(B)
      & A != B ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f118,plain,
    ( succ(sk0_13) = succ(sk0_14)
    & sk0_13 != sk0_14 ),
    inference(skolemization,[status(esa)],[f117]) ).

fof(f119,plain,
    succ(sk0_13) = succ(sk0_14),
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f120,plain,
    sk0_13 != sk0_14,
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | X0 = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f52]) ).

fof(f136,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_union2(X1,X2))
      | in(X0,X1)
      | in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f59]) ).

fof(f139,plain,
    in(sk0_14,succ(sk0_13)),
    inference(paramodulation,[status(thm)],[f119,f116]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ~ in(X0,succ(X1))
      | in(X0,X1)
      | in(X0,singleton(X1)) ),
    inference(paramodulation,[status(thm)],[f48,f136]) ).

fof(f261,plain,
    ( spl0_16
  <=> in(sk0_14,sk0_13) ),
    introduced(split_symbol_definition) ).

fof(f262,plain,
    ( in(sk0_14,sk0_13)
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f261]) ).

fof(f264,plain,
    ( spl0_17
  <=> in(sk0_14,singleton(sk0_13)) ),
    introduced(split_symbol_definition) ).

fof(f265,plain,
    ( in(sk0_14,singleton(sk0_13))
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f264]) ).

fof(f267,plain,
    ( in(sk0_14,sk0_13)
    | in(sk0_14,singleton(sk0_13)) ),
    inference(resolution,[status(thm)],[f257,f139]) ).

fof(f268,plain,
    ( spl0_16
    | spl0_17 ),
    inference(split_clause,[status(thm)],[f267,f261,f264]) ).

fof(f270,plain,
    ! [X0] :
      ( ~ in(X0,succ(sk0_13))
      | in(X0,sk0_14)
      | in(X0,singleton(sk0_14)) ),
    inference(paramodulation,[status(thm)],[f119,f257]) ).

fof(f272,plain,
    ( ~ in(sk0_13,sk0_14)
    | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f262,f38]) ).

fof(f282,plain,
    ( spl0_20
  <=> in(sk0_13,sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f283,plain,
    ( in(sk0_13,sk0_14)
    | ~ spl0_20 ),
    inference(component_clause,[status(thm)],[f282]) ).

fof(f285,plain,
    ( spl0_21
  <=> in(sk0_13,singleton(sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f286,plain,
    ( in(sk0_13,singleton(sk0_14))
    | ~ spl0_21 ),
    inference(component_clause,[status(thm)],[f285]) ).

fof(f288,plain,
    ( in(sk0_13,sk0_14)
    | in(sk0_13,singleton(sk0_14)) ),
    inference(resolution,[status(thm)],[f270,f116]) ).

fof(f289,plain,
    ( spl0_20
    | spl0_21 ),
    inference(split_clause,[status(thm)],[f288,f282,f285]) ).

fof(f290,plain,
    ( $false
    | ~ spl0_16
    | ~ spl0_20 ),
    inference(forward_subsumption_resolution,[status(thm)],[f283,f272]) ).

fof(f291,plain,
    ( ~ spl0_16
    | ~ spl0_20 ),
    inference(contradiction_clause,[status(thm)],[f290]) ).

fof(f296,plain,
    ( sk0_14 = sk0_13
    | ~ spl0_17 ),
    inference(resolution,[status(thm)],[f265,f134]) ).

fof(f297,plain,
    ( $false
    | ~ spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f296,f120]) ).

fof(f298,plain,
    ~ spl0_17,
    inference(contradiction_clause,[status(thm)],[f297]) ).

fof(f301,plain,
    ( sk0_13 = sk0_14
    | ~ spl0_21 ),
    inference(resolution,[status(thm)],[f286,f134]) ).

fof(f302,plain,
    ( $false
    | ~ spl0_21 ),
    inference(forward_subsumption_resolution,[status(thm)],[f301,f120]) ).

fof(f303,plain,
    ~ spl0_21,
    inference(contradiction_clause,[status(thm)],[f302]) ).

fof(f304,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f268,f289,f291,f298,f303]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 09:49:12 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.30/0.58  % Elapsed time: 0.020412 seconds
% 0.30/0.58  % CPU time: 0.081328 seconds
% 0.30/0.58  % Memory used: 15.303 MB
%------------------------------------------------------------------------------