TSTP Solution File: SEU046+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU046+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 20:40:56 EDT 2024

% Result   : Theorem 0.16s 0.44s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   64 (   6 unt;   0 def)
%            Number of atoms       :  257 (  19 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  312 ( 119   ~; 124   |;  47   &)
%                                         (  13 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-3 aty)
%            Number of variables   :  135 ( 124   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
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,B] :
      ( relation(B)
     => relation(relation_rng_restriction(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ( relation(relation_rng_restriction(A,B))
        & function(relation_rng_restriction(A,B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [A,B] :
      ( relation(B)
     => subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( B = relation_rng_restriction(A,C)
          <=> ( ! [D] :
                  ( in(D,relation_dom(B))
                <=> ( in(D,relation_dom(C))
                    & in(apply(C,D),A) ) )
              & ! [D] :
                  ( in(D,relation_dom(B))
                 => apply(B,D) = apply(C,D) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f37,conjecture,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ( subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
        & subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f38,negated_conjecture,
    ~ ! [A,B] :
        ( ( relation(B)
          & function(B) )
       => ( subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
          & subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
    inference(negated_conjecture,[status(cth)],[f37]) ).

fof(f50,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

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

fof(f52,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)],[f51]) ).

fof(f53,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f52]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f57,plain,
    ! [A,B] :
      ( ~ relation(B)
      | relation(relation_rng_restriction(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f58,plain,
    ! [B] :
      ( ~ relation(B)
      | ! [A] : relation(relation_rng_restriction(A,B)) ),
    inference(miniscoping,[status(esa)],[f57]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | relation(relation_rng_restriction(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f69,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ( relation(relation_rng_restriction(A,B))
        & function(relation_rng_restriction(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f70,plain,
    ! [B] :
      ( ~ relation(B)
      | ~ function(B)
      | ( ! [A] : relation(relation_rng_restriction(A,B))
        & ! [A] : function(relation_rng_restriction(A,B)) ) ),
    inference(miniscoping,[status(esa)],[f69]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | function(relation_rng_restriction(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f116,plain,
    ! [A,B] :
      ( ~ relation(B)
      | subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f117,plain,
    ! [B] :
      ( ~ relation(B)
      | ! [A] : subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
    inference(miniscoping,[status(esa)],[f116]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0)) ),
    inference(cnf_transformation,[status(esa)],[f117]) ).

fof(f138,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( B = relation_rng_restriction(A,C)
          <=> ( ! [D] :
                  ( in(D,relation_dom(B))
                <=> ( in(D,relation_dom(C))
                    & in(apply(C,D),A) ) )
              & ! [D] :
                  ( ~ in(D,relation_dom(B))
                  | apply(B,D) = apply(C,D) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f36]) ).

fof(f139,plain,
    ! [A,C,D] :
      ( pd0_0(D,C,A)
    <=> ( in(D,relation_dom(C))
        & in(apply(C,D),A) ) ),
    introduced(predicate_definition,[f138]) ).

fof(f140,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( B = relation_rng_restriction(A,C)
          <=> ( ! [D] :
                  ( in(D,relation_dom(B))
                <=> pd0_0(D,C,A) )
              & ! [D] :
                  ( ~ in(D,relation_dom(B))
                  | apply(B,D) = apply(C,D) ) ) ) ) ),
    inference(formula_renaming,[status(thm)],[f138,f139]) ).

fof(f141,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ( B != relation_rng_restriction(A,C)
              | ( ! [D] :
                    ( ( ~ in(D,relation_dom(B))
                      | pd0_0(D,C,A) )
                    & ( in(D,relation_dom(B))
                      | ~ pd0_0(D,C,A) ) )
                & ! [D] :
                    ( ~ in(D,relation_dom(B))
                    | apply(B,D) = apply(C,D) ) ) )
            & ( B = relation_rng_restriction(A,C)
              | ? [D] :
                  ( ( ~ in(D,relation_dom(B))
                    | ~ pd0_0(D,C,A) )
                  & ( in(D,relation_dom(B))
                    | pd0_0(D,C,A) ) )
              | ? [D] :
                  ( in(D,relation_dom(B))
                  & apply(B,D) != apply(C,D) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f140]) ).

fof(f142,plain,
    ! [B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ! [A] :
                ( B != relation_rng_restriction(A,C)
                | ( ! [D] :
                      ( ~ in(D,relation_dom(B))
                      | pd0_0(D,C,A) )
                  & ! [D] :
                      ( in(D,relation_dom(B))
                      | ~ pd0_0(D,C,A) )
                  & ! [D] :
                      ( ~ in(D,relation_dom(B))
                      | apply(B,D) = apply(C,D) ) ) )
            & ! [A] :
                ( B = relation_rng_restriction(A,C)
                | ? [D] :
                    ( ( ~ in(D,relation_dom(B))
                      | ~ pd0_0(D,C,A) )
                    & ( in(D,relation_dom(B))
                      | pd0_0(D,C,A) ) )
                | ? [D] :
                    ( in(D,relation_dom(B))
                    & apply(B,D) != apply(C,D) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f141]) ).

fof(f143,plain,
    ! [B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ! [A] :
                ( B != relation_rng_restriction(A,C)
                | ( ! [D] :
                      ( ~ in(D,relation_dom(B))
                      | pd0_0(D,C,A) )
                  & ! [D] :
                      ( in(D,relation_dom(B))
                      | ~ pd0_0(D,C,A) )
                  & ! [D] :
                      ( ~ in(D,relation_dom(B))
                      | apply(B,D) = apply(C,D) ) ) )
            & ! [A] :
                ( B = relation_rng_restriction(A,C)
                | ( ( ~ in(sk0_12(A,C,B),relation_dom(B))
                    | ~ pd0_0(sk0_12(A,C,B),C,A) )
                  & ( in(sk0_12(A,C,B),relation_dom(B))
                    | pd0_0(sk0_12(A,C,B),C,A) ) )
                | ( in(sk0_13(A,C,B),relation_dom(B))
                  & apply(B,sk0_13(A,C,B)) != apply(C,sk0_13(A,C,B)) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f142]) ).

fof(f144,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | X0 != relation_rng_restriction(X2,X1)
      | ~ in(X3,relation_dom(X0))
      | pd0_0(X3,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f143]) ).

fof(f151,plain,
    ? [A,B] :
      ( relation(B)
      & function(B)
      & ( ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
        | ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f38]) ).

fof(f152,plain,
    ? [B] :
      ( relation(B)
      & function(B)
      & ( ? [A] : ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
        | ? [A] : ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ),
    inference(miniscoping,[status(esa)],[f151]) ).

fof(f153,plain,
    ( relation(sk0_14)
    & function(sk0_14)
    & ( ~ subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14))
      | ~ subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14)) ) ),
    inference(skolemization,[status(esa)],[f152]) ).

fof(f154,plain,
    relation(sk0_14),
    inference(cnf_transformation,[status(esa)],[f153]) ).

fof(f155,plain,
    function(sk0_14),
    inference(cnf_transformation,[status(esa)],[f153]) ).

fof(f156,plain,
    ( ~ subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14))
    | ~ subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14)) ),
    inference(cnf_transformation,[status(esa)],[f153]) ).

fof(f160,plain,
    ! [A,C,D] :
      ( ( ~ pd0_0(D,C,A)
        | ( in(D,relation_dom(C))
          & in(apply(C,D),A) ) )
      & ( pd0_0(D,C,A)
        | ~ in(D,relation_dom(C))
        | ~ in(apply(C,D),A) ) ),
    inference(NNF_transformation,[status(esa)],[f139]) ).

fof(f161,plain,
    ( ! [A,C,D] :
        ( ~ pd0_0(D,C,A)
        | ( in(D,relation_dom(C))
          & in(apply(C,D),A) ) )
    & ! [A,C,D] :
        ( pd0_0(D,C,A)
        | ~ in(D,relation_dom(C))
        | ~ in(apply(C,D),A) ) ),
    inference(miniscoping,[status(esa)],[f160]) ).

fof(f162,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | in(X0,relation_dom(X1)) ),
    inference(cnf_transformation,[status(esa)],[f161]) ).

fof(f165,plain,
    ( spl0_0
  <=> subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f167,plain,
    ( ~ subset(relation_dom(relation_rng_restriction(sk0_15,sk0_14)),relation_dom(sk0_14))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f165]) ).

fof(f168,plain,
    ( spl0_1
  <=> subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f170,plain,
    ( ~ subset(relation_rng(relation_rng_restriction(sk0_16,sk0_14)),relation_rng(sk0_14))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f168]) ).

fof(f171,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f156,f165,f168]) ).

fof(f172,plain,
    ! [X0,X1,X2] :
      ( ~ relation(relation_rng_restriction(X0,X1))
      | ~ function(relation_rng_restriction(X0,X1))
      | ~ relation(X1)
      | ~ function(X1)
      | ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
      | pd0_0(X2,X1,X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f144]) ).

fof(f226,plain,
    ! [X0,X1,X2] :
      ( ~ function(relation_rng_restriction(X0,X1))
      | ~ relation(X1)
      | ~ function(X1)
      | ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
      | pd0_0(X2,X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f172,f59]) ).

fof(f237,plain,
    ! [X0,X1,X2] :
      ( subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
      | ~ function(relation_rng_restriction(X0,X1))
      | ~ relation(X1)
      | ~ function(X1)
      | pd0_0(sk0_0(X2,relation_dom(relation_rng_restriction(X0,X1))),X1,X0) ),
    inference(resolution,[status(thm)],[f55,f226]) ).

fof(f238,plain,
    ! [X0,X1,X2] :
      ( subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
      | ~ relation(X1)
      | ~ function(X1)
      | pd0_0(sk0_0(X2,relation_dom(relation_rng_restriction(X0,X1))),X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f237,f72]) ).

fof(f246,plain,
    ! [X0,X1,X2] :
      ( subset(relation_dom(relation_rng_restriction(X0,X1)),X2)
      | ~ relation(X1)
      | ~ function(X1)
      | in(sk0_0(X2,relation_dom(relation_rng_restriction(X0,X1))),relation_dom(X1)) ),
    inference(resolution,[status(thm)],[f238,f162]) ).

fof(f259,plain,
    ( spl0_10
  <=> relation(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f261,plain,
    ( ~ relation(sk0_14)
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f259]) ).

fof(f262,plain,
    ( spl0_11
  <=> function(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f264,plain,
    ( ~ function(sk0_14)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f262]) ).

fof(f379,plain,
    ( ~ relation(sk0_14)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f170,f118]) ).

fof(f380,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f379,f154]) ).

fof(f381,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f380]) ).

fof(f492,plain,
    ! [X0,X1] :
      ( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
      | subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(resolution,[status(thm)],[f56,f246]) ).

fof(f493,plain,
    ! [X0,X1] :
      ( subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1))
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f492]) ).

fof(f676,plain,
    ( ~ relation(sk0_14)
    | ~ function(sk0_14)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f493,f167]) ).

fof(f677,plain,
    ( ~ spl0_10
    | ~ spl0_11
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f676,f259,f262,f165]) ).

fof(f679,plain,
    ( $false
    | spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f261,f154]) ).

fof(f680,plain,
    spl0_10,
    inference(contradiction_clause,[status(thm)],[f679]) ).

fof(f681,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f264,f155]) ).

fof(f682,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f681]) ).

fof(f683,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f171,f381,f677,f680,f682]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : SEU046+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n004.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
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon Apr 29 19:39:18 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.32  % Drodi V3.6.0
% 0.16/0.44  % Refutation found
% 0.16/0.44  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.45  % Elapsed time: 0.135784 seconds
% 0.16/0.45  % CPU time: 0.953837 seconds
% 0.16/0.45  % Total memory used: 65.812 MB
% 0.16/0.45  % Net memory used: 65.408 MB
%------------------------------------------------------------------------------