TSTP Solution File: SEU251+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 12:36:28 EDT 2023

% Result   : Theorem 0.14s 0.39s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   66 (   7 unt;   0 def)
%            Number of atoms       :  216 (  31 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  252 ( 102   ~;  98   |;  32   &)
%                                         (  14 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  118 (; 108   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [A] :
      ( relation(A)
     => ! [B,C] :
          ( C = fiber(A,B)
        <=> ! [D] :
              ( in(D,C)
            <=> ( D != B
                & in(ordered_pair(D,B),A) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [A,B] :
      ( relation(A)
     => relation(relation_restriction(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ! [A,B,C] :
      ( relation(C)
     => ( in(A,relation_restriction(C,B))
      <=> ( in(A,C)
          & in(A,cartesian_product2(B,B)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,conjecture,
    ! [A,B,C] :
      ( relation(C)
     => subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,negated_conjecture,
    ~ ! [A,B,C] :
        ( relation(C)
       => subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
    inference(negated_conjecture,[status(cth)],[f32]) ).

fof(f52,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B,C] :
          ( C = fiber(A,B)
        <=> ! [D] :
              ( in(D,C)
            <=> ( D != B
                & in(ordered_pair(D,B),A) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f53,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B,C] :
          ( ( C != fiber(A,B)
            | ! [D] :
                ( ( ~ in(D,C)
                  | ( D != B
                    & in(ordered_pair(D,B),A) ) )
                & ( in(D,C)
                  | D = B
                  | ~ in(ordered_pair(D,B),A) ) ) )
          & ( C = fiber(A,B)
            | ? [D] :
                ( ( ~ in(D,C)
                  | D = B
                  | ~ in(ordered_pair(D,B),A) )
                & ( in(D,C)
                  | ( D != B
                    & in(ordered_pair(D,B),A) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f52]) ).

fof(f54,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B,C] :
            ( C != fiber(A,B)
            | ( ! [D] :
                  ( ~ in(D,C)
                  | ( D != B
                    & in(ordered_pair(D,B),A) ) )
              & ! [D] :
                  ( in(D,C)
                  | D = B
                  | ~ in(ordered_pair(D,B),A) ) ) )
        & ! [B,C] :
            ( C = fiber(A,B)
            | ? [D] :
                ( ( ~ in(D,C)
                  | D = B
                  | ~ in(ordered_pair(D,B),A) )
                & ( in(D,C)
                  | ( D != B
                    & in(ordered_pair(D,B),A) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f53]) ).

fof(f55,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B,C] :
            ( C != fiber(A,B)
            | ( ! [D] :
                  ( ~ in(D,C)
                  | ( D != B
                    & in(ordered_pair(D,B),A) ) )
              & ! [D] :
                  ( in(D,C)
                  | D = B
                  | ~ in(ordered_pair(D,B),A) ) ) )
        & ! [B,C] :
            ( C = fiber(A,B)
            | ( ( ~ in(sk0_0(C,B,A),C)
                | sk0_0(C,B,A) = B
                | ~ in(ordered_pair(sk0_0(C,B,A),B),A) )
              & ( in(sk0_0(C,B,A),C)
                | ( sk0_0(C,B,A) != B
                  & in(ordered_pair(sk0_0(C,B,A),B),A) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f54]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != fiber(X0,X2)
      | ~ in(X3,X1)
      | X3 != X2 ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f57,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != fiber(X0,X2)
      | ~ in(X3,X1)
      | in(ordered_pair(X3,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f58,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != fiber(X0,X2)
      | in(X3,X1)
      | X3 = X2
      | ~ in(ordered_pair(X3,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f62,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f63,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f62]) ).

fof(f64,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f63]) ).

fof(f65,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_1(B,A),A)
          & ~ in(sk0_1(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f64]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_1(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f72,plain,
    ! [A,B] :
      ( ~ relation(A)
      | relation(relation_restriction(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f73,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] : relation(relation_restriction(A,B)) ),
    inference(miniscoping,[status(esa)],[f72]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | relation(relation_restriction(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f73]) ).

fof(f98,plain,
    ! [A,B,C] :
      ( ~ relation(C)
      | ( in(A,relation_restriction(C,B))
      <=> ( in(A,C)
          & in(A,cartesian_product2(B,B)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f99,plain,
    ! [A,B,C] :
      ( ~ relation(C)
      | ( ( ~ in(A,relation_restriction(C,B))
          | ( in(A,C)
            & in(A,cartesian_product2(B,B)) ) )
        & ( in(A,relation_restriction(C,B))
          | ~ in(A,C)
          | ~ in(A,cartesian_product2(B,B)) ) ) ),
    inference(NNF_transformation,[status(esa)],[f98]) ).

fof(f100,plain,
    ! [C] :
      ( ~ relation(C)
      | ( ! [A,B] :
            ( ~ in(A,relation_restriction(C,B))
            | ( in(A,C)
              & in(A,cartesian_product2(B,B)) ) )
        & ! [A,B] :
            ( in(A,relation_restriction(C,B))
            | ~ in(A,C)
            | ~ in(A,cartesian_product2(B,B)) ) ) ),
    inference(miniscoping,[status(esa)],[f99]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ in(X1,relation_restriction(X0,X2))
      | in(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f106,plain,
    ? [A,B,C] :
      ( relation(C)
      & ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f33]) ).

fof(f107,plain,
    ? [C] :
      ( relation(C)
      & ? [A,B] : ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
    inference(miniscoping,[status(esa)],[f106]) ).

fof(f108,plain,
    ( relation(sk0_8)
    & ~ subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10)) ),
    inference(skolemization,[status(esa)],[f107]) ).

fof(f109,plain,
    relation(sk0_8),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f110,plain,
    ~ subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10)),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ in(X1,fiber(X0,X1)) ),
    inference(destructive_equality_resolution,[status(esa)],[f56]) ).

fof(f133,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ in(X1,fiber(X0,X2))
      | in(ordered_pair(X1,X2),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f57]) ).

fof(f134,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,fiber(X0,X2))
      | X1 = X2
      | ~ in(ordered_pair(X1,X2),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f58]) ).

fof(f135,plain,
    in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),
    inference(resolution,[status(thm)],[f67,f110]) ).

fof(f158,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(relation_restriction(X0,X1))
      | ~ in(X2,fiber(relation_restriction(X0,X1),X3))
      | ~ relation(X0)
      | in(ordered_pair(X2,X3),X0) ),
    inference(resolution,[status(thm)],[f133,f101]) ).

fof(f159,plain,
    ! [X0,X1,X2,X3] :
      ( ~ in(X0,fiber(relation_restriction(X1,X2),X3))
      | ~ relation(X1)
      | in(ordered_pair(X0,X3),X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f158,f74]) ).

fof(f165,plain,
    ( spl0_3
  <=> relation(sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f167,plain,
    ( ~ relation(sk0_8)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f165]) ).

fof(f168,plain,
    ( spl0_4
  <=> in(ordered_pair(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),sk0_10),sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f169,plain,
    ( in(ordered_pair(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),sk0_10),sk0_8)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f168]) ).

fof(f171,plain,
    ( ~ relation(sk0_8)
    | in(ordered_pair(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),sk0_10),sk0_8) ),
    inference(resolution,[status(thm)],[f159,f135]) ).

fof(f172,plain,
    ( ~ spl0_3
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f171,f165,f168]) ).

fof(f183,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f167,f109]) ).

fof(f184,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f183]) ).

fof(f190,plain,
    ( spl0_7
  <=> relation(relation_restriction(sk0_8,sk0_9)) ),
    introduced(split_symbol_definition) ).

fof(f192,plain,
    ( ~ relation(relation_restriction(sk0_8,sk0_9))
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f190]) ).

fof(f216,plain,
    ( ~ relation(sk0_8)
    | spl0_7 ),
    inference(resolution,[status(thm)],[f192,f74]) ).

fof(f217,plain,
    ( ~ spl0_3
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f216,f165,f190]) ).

fof(f218,plain,
    ( spl0_11
  <=> in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(sk0_8,sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f219,plain,
    ( in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(sk0_8,sk0_10))
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f218]) ).

fof(f221,plain,
    ( spl0_12
  <=> sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)) = sk0_10 ),
    introduced(split_symbol_definition) ).

fof(f222,plain,
    ( sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)) = sk0_10
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f221]) ).

fof(f224,plain,
    ( ~ relation(sk0_8)
    | in(sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)),fiber(sk0_8,sk0_10))
    | sk0_1(fiber(sk0_8,sk0_10),fiber(relation_restriction(sk0_8,sk0_9),sk0_10)) = sk0_10
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f169,f134]) ).

fof(f225,plain,
    ( ~ spl0_3
    | spl0_11
    | spl0_12
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f224,f165,f218,f221,f168]) ).

fof(f228,plain,
    ( subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10))
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f219,f68]) ).

fof(f229,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f228,f110]) ).

fof(f230,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f229]) ).

fof(f260,plain,
    ( in(sk0_10,fiber(relation_restriction(sk0_8,sk0_9),sk0_10))
    | ~ spl0_12 ),
    inference(backward_demodulation,[status(thm)],[f222,f135]) ).

fof(f261,plain,
    ( spl0_17
  <=> subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f262,plain,
    ( subset(fiber(relation_restriction(sk0_8,sk0_9),sk0_10),fiber(sk0_8,sk0_10))
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f261]) ).

fof(f276,plain,
    ( $false
    | ~ spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f262,f110]) ).

fof(f277,plain,
    ~ spl0_17,
    inference(contradiction_clause,[status(thm)],[f276]) ).

fof(f288,plain,
    ( ~ relation(relation_restriction(sk0_8,sk0_9))
    | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f260,f132]) ).

fof(f289,plain,
    ( ~ spl0_7
    | ~ spl0_12 ),
    inference(split_clause,[status(thm)],[f288,f190,f221]) ).

fof(f292,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f172,f184,f217,f225,f230,f277,f289]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SEU251+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n026.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue May 30 09:32:58 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  % Drodi V3.5.1
% 0.14/0.39  % Refutation found
% 0.14/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41  % Elapsed time: 0.107349 seconds
% 0.14/0.41  % CPU time: 0.320174 seconds
% 0.14/0.41  % Memory used: 53.346 MB
%------------------------------------------------------------------------------