TSTP Solution File: SEU182+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 12:36:09 EDT 2023

% Result   : Theorem 219.28s 27.97s
% Output   : CNFRefutation 219.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   69 (  12 unt;   0 def)
%            Number of atoms       :  263 (  23 equ)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  317 ( 123   ~; 130   |;  39   &)
%                                         (  14 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   4 con; 0-5 aty)
%            Number of variables   :  165 (; 142   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_dom(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f13,axiom,
    ! [A,B] :
      ( ( relation(A)
        & relation(B) )
     => relation(relation_composition(A,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,conjecture,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( relation(B)
         => subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ! [B] :
            ( relation(B)
           => subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
    inference(negated_conjecture,[status(cth)],[f30]) ).

fof(f34,axiom,
    ! [A] :
      ( empty(A)
     => A = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f40,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f41,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)],[f40]) ).

fof(f42,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)],[f41]) ).

fof(f43,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)],[f42]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f47,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)],[f4]) ).

fof(f48,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)],[f47]) ).

fof(f49,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)],[f48]) ).

fof(f50,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(C,sk0_1(C,B,A)),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ( ( ~ in(sk0_2(B,A),B)
                | ! [D] : ~ in(ordered_pair(sk0_2(B,A),D),A) )
              & ( in(sk0_2(B,A),B)
                | in(ordered_pair(sk0_2(B,A),sk0_3(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f49]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | X1 != relation_dom(X0)
      | ~ in(X2,X1)
      | in(ordered_pair(X2,sk0_1(X2,X1,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,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)],[f50]) ).

fof(f56,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( C = relation_composition(A,B)
              <=> ! [D,E] :
                    ( in(ordered_pair(D,E),C)
                  <=> ? [F] :
                        ( in(ordered_pair(D,F),A)
                        & in(ordered_pair(F,E),B) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f57,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ! [D,E] :
                      ( ( ~ in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) )
                      & ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ? [D,E] :
                      ( ( ~ in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) )
                      & ( in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f56]) ).

fof(f58,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ( ! [D,E] :
                        ( ~ in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) )
                    & ! [D,E] :
                        ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ? [D,E] :
                      ( ( ~ in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) )
                      & ( in(ordered_pair(D,E),C)
                        | ? [F] :
                            ( in(ordered_pair(D,F),A)
                            & in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f57]) ).

fof(f59,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ~ relation(B)
          | ! [C] :
              ( ~ relation(C)
              | ( ( C != relation_composition(A,B)
                  | ( ! [D,E] :
                        ( ~ in(ordered_pair(D,E),C)
                        | ( in(ordered_pair(D,sk0_4(E,D,C,B,A)),A)
                          & in(ordered_pair(sk0_4(E,D,C,B,A),E),B) ) )
                    & ! [D,E] :
                        ( in(ordered_pair(D,E),C)
                        | ! [F] :
                            ( ~ in(ordered_pair(D,F),A)
                            | ~ in(ordered_pair(F,E),B) ) ) ) )
                & ( C = relation_composition(A,B)
                  | ( ( ~ in(ordered_pair(sk0_5(C,B,A),sk0_6(C,B,A)),C)
                      | ! [F] :
                          ( ~ in(ordered_pair(sk0_5(C,B,A),F),A)
                          | ~ in(ordered_pair(F,sk0_6(C,B,A)),B) ) )
                    & ( in(ordered_pair(sk0_5(C,B,A),sk0_6(C,B,A)),C)
                      | ( in(ordered_pair(sk0_5(C,B,A),sk0_7(C,B,A)),A)
                        & in(ordered_pair(sk0_7(C,B,A),sk0_6(C,B,A)),B) ) ) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f58]) ).

fof(f60,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(X2)
      | X2 != relation_composition(X0,X1)
      | ~ in(ordered_pair(X3,X4),X2)
      | in(ordered_pair(X3,sk0_4(X4,X3,X2,X1,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f66,plain,
    ! [A,B] :
      ( ~ relation(A)
      | ~ relation(B)
      | relation(relation_composition(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | relation(relation_composition(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f75,plain,
    ( empty(sk0_9)
    & relation(sk0_9) ),
    inference(skolemization,[status(esa)],[f21]) ).

fof(f76,plain,
    empty(sk0_9),
    inference(cnf_transformation,[status(esa)],[f75]) ).

fof(f77,plain,
    relation(sk0_9),
    inference(cnf_transformation,[status(esa)],[f75]) ).

fof(f99,plain,
    ? [A] :
      ( relation(A)
      & ? [B] :
          ( relation(B)
          & ~ subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f100,plain,
    ( relation(sk0_14)
    & relation(sk0_15)
    & ~ subset(relation_dom(relation_composition(sk0_14,sk0_15)),relation_dom(sk0_14)) ),
    inference(skolemization,[status(esa)],[f99]) ).

fof(f101,plain,
    relation(sk0_14),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f102,plain,
    relation(sk0_15),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f103,plain,
    ~ subset(relation_dom(relation_composition(sk0_14,sk0_15)),relation_dom(sk0_14)),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f110,plain,
    ! [A] :
      ( ~ empty(A)
      | A = empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f34]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ empty(X0)
      | X0 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f110]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ in(X1,relation_dom(X0))
      | in(ordered_pair(X1,sk0_1(X1,relation_dom(X0),X0)),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f51]) ).

fof(f119,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_dom(X0))
      | ~ in(ordered_pair(X1,X2),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f52]) ).

fof(f120,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ relation(relation_composition(X0,X1))
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(X2,sk0_4(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f60]) ).

fof(f2800,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(ordered_pair(X2,sk0_4(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f120,f67]) ).

fof(f2857,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | ~ relation(X0)
      | in(X2,relation_dom(X0)) ),
    inference(resolution,[status(thm)],[f2800,f119]) ).

fof(f2858,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
      | in(X2,relation_dom(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f2857]) ).

fof(f2972,plain,
    sk0_9 = empty_set,
    inference(resolution,[status(thm)],[f76,f111]) ).

fof(f2998,plain,
    ( spl0_7
  <=> relation(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f3000,plain,
    ( ~ relation(sk0_14)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f2998]) ).

fof(f3001,plain,
    ( spl0_8
  <=> relation(sk0_15) ),
    introduced(split_symbol_definition) ).

fof(f3003,plain,
    ( ~ relation(sk0_15)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f3001]) ).

fof(f3579,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | in(X2,relation_dom(X0))
      | ~ relation(relation_composition(X0,X1))
      | ~ in(X2,relation_dom(relation_composition(X0,X1))) ),
    inference(resolution,[status(thm)],[f2858,f118]) ).

fof(f3580,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | in(X2,relation_dom(X0))
      | ~ in(X2,relation_dom(relation_composition(X0,X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[f3579,f67]) ).

fof(f4197,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3003,f102]) ).

fof(f4198,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f4197]) ).

fof(f4199,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3000,f101]) ).

fof(f4200,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f4199]) ).

fof(f5435,plain,
    ( spl0_60
  <=> relation(sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f5437,plain,
    ( ~ relation(sk0_9)
    | spl0_60 ),
    inference(component_clause,[status(thm)],[f5435]) ).

fof(f5495,plain,
    ( $false
    | spl0_60 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5437,f77]) ).

fof(f5496,plain,
    spl0_60,
    inference(contradiction_clause,[status(thm)],[f5495]) ).

fof(f8056,plain,
    relation(empty_set),
    inference(backward_demodulation,[status(thm)],[f2972,f77]) ).

fof(f8105,plain,
    ( spl0_136
  <=> relation(empty_set) ),
    introduced(split_symbol_definition) ).

fof(f8107,plain,
    ( ~ relation(empty_set)
    | spl0_136 ),
    inference(component_clause,[status(thm)],[f8105]) ).

fof(f8185,plain,
    ( $false
    | spl0_136 ),
    inference(forward_subsumption_resolution,[status(thm)],[f8107,f8056]) ).

fof(f8186,plain,
    spl0_136,
    inference(contradiction_clause,[status(thm)],[f8185]) ).

fof(f9423,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | in(sk0_0(X2,relation_dom(relation_composition(X0,X1))),relation_dom(X0))
      | subset(relation_dom(relation_composition(X0,X1)),X2) ),
    inference(resolution,[status(thm)],[f3580,f45]) ).

fof(f9860,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
      | subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
    inference(resolution,[status(thm)],[f9423,f46]) ).

fof(f9861,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ relation(X1)
      | subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f9860]) ).

fof(f9883,plain,
    ( ~ relation(sk0_14)
    | ~ relation(sk0_15) ),
    inference(resolution,[status(thm)],[f9861,f103]) ).

fof(f9884,plain,
    ( ~ spl0_7
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f9883,f2998,f3001]) ).

fof(f9890,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f4198,f4200,f5496,f8186,f9884]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem  : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n015.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Tue May 30 09:26:34 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.15/0.31  % Drodi V3.5.1
% 219.28/27.97  % Refutation found
% 219.28/27.97  % SZS status Theorem for theBenchmark: Theorem is valid
% 219.28/27.97  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 220.88/28.65  % Elapsed time: 28.325805 seconds
% 220.88/28.65  % CPU time: 220.894889 seconds
% 220.88/28.65  % Memory used: 786.657 MB
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