TSTP Solution File: SEU209+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU209+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 20:41:29 EDT 2024

% Result   : Theorem 0.18s 0.41s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   45 (   6 unt;   0 def)
%            Number of atoms       :  182 (  18 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  219 (  82   ~;  84   |;  35   &)
%                                         (  13 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   2 con; 0-4 aty)
%            Number of variables   :  120 (  98   !;  22   ?)

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

fof(f5,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

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

fof(f47,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B,C] :
          ( C = relation_inverse_image(A,B)
        <=> ! [D] :
              ( in(D,C)
            <=> ? [E] :
                  ( in(ordered_pair(D,E),A)
                  & in(E,B) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f48,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B,C] :
          ( ( C != relation_inverse_image(A,B)
            | ! [D] :
                ( ( ~ in(D,C)
                  | ? [E] :
                      ( in(ordered_pair(D,E),A)
                      & in(E,B) ) )
                & ( in(D,C)
                  | ! [E] :
                      ( ~ in(ordered_pair(D,E),A)
                      | ~ in(E,B) ) ) ) )
          & ( C = relation_inverse_image(A,B)
            | ? [D] :
                ( ( ~ in(D,C)
                  | ! [E] :
                      ( ~ in(ordered_pair(D,E),A)
                      | ~ in(E,B) ) )
                & ( in(D,C)
                  | ? [E] :
                      ( in(ordered_pair(D,E),A)
                      & in(E,B) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B,C] :
            ( C != relation_inverse_image(A,B)
            | ( ! [D] :
                  ( ~ in(D,C)
                  | ? [E] :
                      ( in(ordered_pair(D,E),A)
                      & in(E,B) ) )
              & ! [D] :
                  ( in(D,C)
                  | ! [E] :
                      ( ~ in(ordered_pair(D,E),A)
                      | ~ in(E,B) ) ) ) )
        & ! [B,C] :
            ( C = relation_inverse_image(A,B)
            | ? [D] :
                ( ( ~ in(D,C)
                  | ! [E] :
                      ( ~ in(ordered_pair(D,E),A)
                      | ~ in(E,B) ) )
                & ( in(D,C)
                  | ? [E] :
                      ( in(ordered_pair(D,E),A)
                      & in(E,B) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B,C] :
            ( C != relation_inverse_image(A,B)
            | ( ! [D] :
                  ( ~ in(D,C)
                  | ( in(ordered_pair(D,sk0_0(D,C,B,A)),A)
                    & in(sk0_0(D,C,B,A),B) ) )
              & ! [D] :
                  ( in(D,C)
                  | ! [E] :
                      ( ~ in(ordered_pair(D,E),A)
                      | ~ in(E,B) ) ) ) )
        & ! [B,C] :
            ( C = relation_inverse_image(A,B)
            | ( ( ~ in(sk0_1(C,B,A),C)
                | ! [E] :
                    ( ~ in(ordered_pair(sk0_1(C,B,A),E),A)
                    | ~ in(E,B) ) )
              & ( in(sk0_1(C,B,A),C)
                | ( in(ordered_pair(sk0_1(C,B,A),sk0_2(C,B,A)),A)
                  & in(sk0_2(C,B,A),B) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f49]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != relation_inverse_image(X0,X2)
      | ~ in(X3,X1)
      | in(ordered_pair(X3,sk0_0(X3,X1,X2,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f57,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f58,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)],[f57]) ).

fof(f59,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)],[f58]) ).

fof(f60,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_3(B,A),A)
          & ~ in(sk0_3(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f59]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_3(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_3(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f64,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B = relation_dom(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f65,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ( B != relation_dom(A)
            | ! [C] :
                ( ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
          & ( B = relation_dom(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f65]) ).

fof(f67,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(C,sk0_4(C,B,A)),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ( ( ~ in(sk0_5(B,A),B)
                | ! [D] : ~ in(ordered_pair(sk0_5(B,A),D),A) )
              & ( in(sk0_5(B,A),B)
                | in(ordered_pair(sk0_5(B,A),sk0_6(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f66]) ).

fof(f69,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != relation_dom(X0)
      | in(X2,X1)
      | ~ in(ordered_pair(X2,X3),X0) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

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

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

fof(f108,plain,
    ( relation(sk0_14)
    & ~ subset(relation_inverse_image(sk0_14,sk0_15),relation_dom(sk0_14)) ),
    inference(skolemization,[status(esa)],[f107]) ).

fof(f109,plain,
    relation(sk0_14),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f110,plain,
    ~ subset(relation_inverse_image(sk0_14,sk0_15),relation_dom(sk0_14)),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f133,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ in(X1,relation_inverse_image(X0,X2))
      | in(ordered_pair(X1,sk0_0(X1,relation_inverse_image(X0,X2),X2,X0)),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f51]) ).

fof(f137,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_dom(X0))
      | ~ in(ordered_pair(X1,X2),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f69]) ).

fof(f1128,plain,
    in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15)),
    inference(resolution,[status(thm)],[f62,f110]) ).

fof(f1169,plain,
    ( spl0_12
  <=> relation(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f1171,plain,
    ( ~ relation(sk0_14)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f1169]) ).

fof(f1177,plain,
    ( spl0_14
  <=> in(ordered_pair(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),sk0_0(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15),sk0_15,sk0_14)),sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f1178,plain,
    ( in(ordered_pair(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),sk0_0(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15),sk0_15,sk0_14)),sk0_14)
    | ~ spl0_14 ),
    inference(component_clause,[status(thm)],[f1177]) ).

fof(f1180,plain,
    ( ~ relation(sk0_14)
    | in(ordered_pair(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),sk0_0(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15),sk0_15,sk0_14)),sk0_14) ),
    inference(resolution,[status(thm)],[f1128,f133]) ).

fof(f1181,plain,
    ( ~ spl0_12
    | spl0_14 ),
    inference(split_clause,[status(thm)],[f1180,f1169,f1177]) ).

fof(f1186,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1171,f109]) ).

fof(f1187,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f1186]) ).

fof(f1200,plain,
    ( spl0_17
  <=> in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_dom(sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f1201,plain,
    ( in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_dom(sk0_14))
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f1200]) ).

fof(f1203,plain,
    ( ~ relation(sk0_14)
    | in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_dom(sk0_14))
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f1178,f137]) ).

fof(f1204,plain,
    ( ~ spl0_12
    | spl0_17
    | ~ spl0_14 ),
    inference(split_clause,[status(thm)],[f1203,f1169,f1200,f1177]) ).

fof(f1227,plain,
    ( subset(relation_inverse_image(sk0_14,sk0_15),relation_dom(sk0_14))
    | ~ spl0_17 ),
    inference(resolution,[status(thm)],[f1201,f63]) ).

fof(f1228,plain,
    ( $false
    | ~ spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1227,f110]) ).

fof(f1229,plain,
    ~ spl0_17,
    inference(contradiction_clause,[status(thm)],[f1228]) ).

fof(f1230,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1181,f1187,f1204,f1229]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU209+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35  % Computer : n029.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Mon Apr 29 20:07:34 EDT 2024
% 0.12/0.35  % CPUTime  : 
% 0.12/0.36  % Drodi V3.6.0
% 0.18/0.41  % Refutation found
% 0.18/0.41  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.42  % Elapsed time: 0.063559 seconds
% 0.18/0.42  % CPU time: 0.368566 seconds
% 0.18/0.42  % Total memory used: 66.866 MB
% 0.18/0.42  % Net memory used: 66.568 MB
%------------------------------------------------------------------------------