TSTP Solution File: SEU204+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU204+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 : Wed May 31 12:36:14 EDT 2023

% Result   : Theorem 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% 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_image(A,B)
        <=> ! [D] :
              ( in(D,C)
            <=> ? [E] :
                  ( in(ordered_pair(E,D),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_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

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

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

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

fof(f50,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B,C] :
            ( C != relation_image(A,B)
            | ( ! [D] :
                  ( ~ in(D,C)
                  | ( in(ordered_pair(sk0_0(D,C,B,A),D),A)
                    & in(sk0_0(D,C,B,A),B) ) )
              & ! [D] :
                  ( in(D,C)
                  | ! [E] :
                      ( ~ in(ordered_pair(E,D),A)
                      | ~ in(E,B) ) ) ) )
        & ! [B,C] :
            ( C = relation_image(A,B)
            | ( ( ~ in(sk0_1(C,B,A),C)
                | ! [E] :
                    ( ~ in(ordered_pair(E,sk0_1(C,B,A)),A)
                    | ~ in(E,B) ) )
              & ( in(sk0_1(C,B,A),C)
                | ( in(ordered_pair(sk0_2(C,B,A),sk0_1(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_image(X0,X2)
      | ~ in(X3,X1)
      | in(ordered_pair(sk0_0(X3,X1,X2,X0),X3),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_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

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

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

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

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

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

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

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

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

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

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

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

fof(f139,plain,
    in(sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15)),relation_image(sk0_14,sk0_15)),
    inference(resolution,[status(thm)],[f62,f110]) ).

fof(f140,plain,
    ( spl0_0
  <=> relation(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f142,plain,
    ( ~ relation(sk0_14)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f140]) ).

fof(f143,plain,
    ( spl0_1
  <=> in(ordered_pair(sk0_0(sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15)),relation_image(sk0_14,sk0_15),sk0_15,sk0_14),sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15))),sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f144,plain,
    ( in(ordered_pair(sk0_0(sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15)),relation_image(sk0_14,sk0_15),sk0_15,sk0_14),sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15))),sk0_14)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f143]) ).

fof(f146,plain,
    ( ~ relation(sk0_14)
    | in(ordered_pair(sk0_0(sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15)),relation_image(sk0_14,sk0_15),sk0_15,sk0_14),sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15))),sk0_14) ),
    inference(resolution,[status(thm)],[f139,f133]) ).

fof(f147,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f146,f140,f143]) ).

fof(f152,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f142,f109]) ).

fof(f153,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f152]) ).

fof(f183,plain,
    ( spl0_7
  <=> in(sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15)),relation_rng(sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f184,plain,
    ( in(sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15)),relation_rng(sk0_14))
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f183]) ).

fof(f186,plain,
    ( ~ relation(sk0_14)
    | in(sk0_3(relation_rng(sk0_14),relation_image(sk0_14,sk0_15)),relation_rng(sk0_14))
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f144,f137]) ).

fof(f187,plain,
    ( ~ spl0_0
    | spl0_7
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f186,f140,f183,f143]) ).

fof(f491,plain,
    ( subset(relation_image(sk0_14,sk0_15),relation_rng(sk0_14))
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f63,f184]) ).

fof(f492,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f491,f110]) ).

fof(f493,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f492]) ).

fof(f494,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f147,f153,f187,f493]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n029.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 09:24:36 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  % Drodi V3.5.1
% 0.14/0.37  % Refutation found
% 0.14/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.39  % Elapsed time: 0.090374 seconds
% 0.14/0.39  % CPU time: 0.326733 seconds
% 0.14/0.39  % Memory used: 44.940 MB
%------------------------------------------------------------------------------