TSTP Solution File: SET669+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 20:40:08 EDT 2024

% Result   : Theorem 2.80s 0.74s
% Output   : CNFRefutation 3.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  116 (  15 unt;   0 def)
%            Number of atoms       :  396 (  28 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  474 ( 194   ~; 198   |;  30   &)
%                                         (  14 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   7 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :  201 ( 196   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ( subset(B,C)
              & subset(C,B) )
           => B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ! [E] :
                  ( ilf_type(E,relation_type(B,C))
                 => ( subset(identity_relation_of(D),E)
                   => ( subset(D,domain(B,C,E))
                      & subset(D,range(B,C,E)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( subset(B,C)
          <=> ! [D] :
                ( ilf_type(D,set_type)
               => ( member(D,B)
                 => member(D,C) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ilf_type(C,subset_type(B))
          <=> ilf_type(C,member_type(power_set(B))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( member(B,power_set(C))
          <=> ! [D] :
                ( ilf_type(D,set_type)
               => ( member(D,B)
                 => member(D,C) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ~ empty(power_set(B))
        & ilf_type(power_set(B),set_type) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ( ~ empty(C)
            & ilf_type(C,set_type) )
         => ( ilf_type(B,member_type(C))
          <=> member(B,C) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => domain(B,C,D) = domain_of(D) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => range(B,C,D) = range_of(D) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ilf_type(range(B,C,D),subset_type(C)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,conjecture,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ( subset(identity_relation_of(C),D)
               => ( subset(C,domain(B,C,D))
                  & C = range(B,C,D) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,negated_conjecture,
    ~ ! [B] :
        ( ilf_type(B,set_type)
       => ! [C] :
            ( ilf_type(C,set_type)
           => ! [D] :
                ( ilf_type(D,relation_type(B,C))
               => ( subset(identity_relation_of(C),D)
                 => ( subset(C,domain(B,C,D))
                    & C = range(B,C,D) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f33]) ).

fof(f35,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ~ subset(B,C)
          | ~ subset(C,B)
          | B = C ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f37,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,set_type)
              | ! [E] :
                  ( ~ ilf_type(E,relation_type(B,C))
                  | ~ subset(identity_relation_of(D),E)
                  | ( subset(D,domain(B,C,E))
                    & subset(D,range(B,C,E)) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f38,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ subset(identity_relation_of(X2),X3)
      | subset(X2,domain(X0,X1,X3)) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f39,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ subset(identity_relation_of(X2),X3)
      | subset(X2,range(X0,X1,X3)) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f53,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( subset(B,C)
          <=> ! [D] :
                ( ~ ilf_type(D,set_type)
                | ~ member(D,B)
                | member(D,C) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f54,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ( ~ subset(B,C)
              | ! [D] :
                  ( ~ ilf_type(D,set_type)
                  | ~ member(D,B)
                  | member(D,C) ) )
            & ( subset(B,C)
              | ? [D] :
                  ( ilf_type(D,set_type)
                  & member(D,B)
                  & ~ member(D,C) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f53]) ).

fof(f55,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ( ~ subset(B,C)
              | ! [D] :
                  ( ~ ilf_type(D,set_type)
                  | ~ member(D,B)
                  | member(D,C) ) )
            & ( subset(B,C)
              | ( ilf_type(sk0_1(C,B),set_type)
                & member(sk0_1(C,B),B)
                & ~ member(sk0_1(C,B),C) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f54]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | subset(X0,X1)
      | member(sk0_1(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | subset(X0,X1)
      | ~ member(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f88,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ilf_type(C,subset_type(B))
          <=> ilf_type(C,member_type(power_set(B))) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f89,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ( ~ ilf_type(C,subset_type(B))
              | ilf_type(C,member_type(power_set(B))) )
            & ( ilf_type(C,subset_type(B))
              | ~ ilf_type(C,member_type(power_set(B))) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f88]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X1,subset_type(X0))
      | ilf_type(X1,member_type(power_set(X0))) ),
    inference(cnf_transformation,[status(esa)],[f89]) ).

fof(f99,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( member(B,power_set(C))
          <=> ! [D] :
                ( ~ ilf_type(D,set_type)
                | ~ member(D,B)
                | member(D,C) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f100,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ( ~ member(B,power_set(C))
              | ! [D] :
                  ( ~ ilf_type(D,set_type)
                  | ~ member(D,B)
                  | member(D,C) ) )
            & ( member(B,power_set(C))
              | ? [D] :
                  ( ilf_type(D,set_type)
                  & member(D,B)
                  & ~ member(D,C) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f99]) ).

fof(f101,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ( ( ~ member(B,power_set(C))
              | ! [D] :
                  ( ~ ilf_type(D,set_type)
                  | ~ member(D,B)
                  | member(D,C) ) )
            & ( member(B,power_set(C))
              | ( ilf_type(sk0_6(C,B),set_type)
                & member(sk0_6(C,B),B)
                & ~ member(sk0_6(C,B),C) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f100]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f101]) ).

fof(f106,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ( ~ empty(power_set(B))
        & ilf_type(power_set(B),set_type) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f107,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ~ empty(power_set(X0)) ),
    inference(cnf_transformation,[status(esa)],[f106]) ).

fof(f109,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( empty(C)
          | ~ ilf_type(C,set_type)
          | ( ilf_type(B,member_type(C))
          <=> member(B,C) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f22]) ).

fof(f110,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( empty(C)
          | ~ ilf_type(C,set_type)
          | ( ( ~ ilf_type(B,member_type(C))
              | member(B,C) )
            & ( ilf_type(B,member_type(C))
              | ~ member(B,C) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f109]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | empty(X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,member_type(X1))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f110]) ).

fof(f135,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,relation_type(B,C))
              | domain(B,C,D) = domain_of(D) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f136,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | domain(X0,X1,X2) = domain_of(X2) ),
    inference(cnf_transformation,[status(esa)],[f135]) ).

fof(f139,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,relation_type(B,C))
              | range(B,C,D) = range_of(D) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f140,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | range(X0,X1,X2) = range_of(X2) ),
    inference(cnf_transformation,[status(esa)],[f139]) ).

fof(f141,plain,
    ! [B] :
      ( ~ ilf_type(B,set_type)
      | ! [C] :
          ( ~ ilf_type(C,set_type)
          | ! [D] :
              ( ~ ilf_type(D,relation_type(B,C))
              | ilf_type(range(B,C,D),subset_type(C)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f142,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(range(X0,X1,X2),subset_type(X1)) ),
    inference(cnf_transformation,[status(esa)],[f141]) ).

fof(f143,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f144,plain,
    ? [B] :
      ( ilf_type(B,set_type)
      & ? [C] :
          ( ilf_type(C,set_type)
          & ? [D] :
              ( ilf_type(D,relation_type(B,C))
              & subset(identity_relation_of(C),D)
              & ( ~ subset(C,domain(B,C,D))
                | C != range(B,C,D) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f34]) ).

fof(f145,plain,
    ( ilf_type(sk0_12,set_type)
    & ilf_type(sk0_13,set_type)
    & ilf_type(sk0_14,relation_type(sk0_12,sk0_13))
    & subset(identity_relation_of(sk0_13),sk0_14)
    & ( ~ subset(sk0_13,domain(sk0_12,sk0_13,sk0_14))
      | sk0_13 != range(sk0_12,sk0_13,sk0_14) ) ),
    inference(skolemization,[status(esa)],[f144]) ).

fof(f148,plain,
    ilf_type(sk0_14,relation_type(sk0_12,sk0_13)),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f149,plain,
    subset(identity_relation_of(sk0_13),sk0_14),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f150,plain,
    ( ~ subset(sk0_13,domain(sk0_12,sk0_13,sk0_14))
    | sk0_13 != range(sk0_12,sk0_13,sk0_14) ),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f151,plain,
    ( spl0_0
  <=> subset(sk0_13,domain(sk0_12,sk0_13,sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f153,plain,
    ( ~ subset(sk0_13,domain(sk0_12,sk0_13,sk0_14))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f151]) ).

fof(f154,plain,
    ( spl0_1
  <=> sk0_13 = range(sk0_12,sk0_13,sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f156,plain,
    ( sk0_13 != range(sk0_12,sk0_13,sk0_14)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f154]) ).

fof(f157,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f150,f151,f154]) ).

fof(f167,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,relation_type(X2,X0))
      | ilf_type(range(X2,X0,X1),subset_type(X0)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f142,f143]) ).

fof(f168,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,relation_type(X1,X2))
      | ilf_type(range(X1,X2,X0),subset_type(X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f167,f143]) ).

fof(f169,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,relation_type(X2,X0))
      | range(X2,X0,X1) = range_of(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[f140,f143]) ).

fof(f170,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,relation_type(X1,X2))
      | range(X1,X2,X0) = range_of(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f169,f143]) ).

fof(f173,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,relation_type(X2,X0))
      | domain(X2,X0,X1) = domain_of(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[f136,f143]) ).

fof(f174,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,relation_type(X1,X2))
      | domain(X1,X2,X0) = domain_of(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f173,f143]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( empty(X0)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,member_type(X0))
      | member(X1,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f111,f143]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( empty(X0)
      | ~ ilf_type(X1,member_type(X0))
      | member(X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f187,f143]) ).

fof(f189,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(backward_subsumption_resolution,[status(thm)],[f107,f143]) ).

fof(f194,plain,
    ! [X0,X1,X2] :
      ( ~ ilf_type(X0,set_type)
      | ~ member(X1,power_set(X0))
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X1)
      | member(X2,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f102,f143]) ).

fof(f195,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,power_set(X1))
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f194,f143]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X0,subset_type(X1))
      | ilf_type(X0,member_type(power_set(X1))) ),
    inference(backward_subsumption_resolution,[status(thm)],[f90,f143]) ).

fof(f200,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,subset_type(X1))
      | ilf_type(X0,member_type(power_set(X1))) ),
    inference(forward_subsumption_resolution,[status(thm)],[f199,f143]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | subset(X1,X0)
      | ~ member(sk0_1(X0,X1),X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f59,f143]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_1(X1,X0),X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f206,f143]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | subset(X1,X0)
      | member(sk0_1(X0,X1),X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[f58,f143]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_1(X1,X0),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f208,f143]) ).

fof(f225,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X3,X0))
      | ~ subset(identity_relation_of(X1),X2)
      | subset(X1,range(X3,X0,X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f39,f143]) ).

fof(f226,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,relation_type(X2,X3))
      | ~ subset(identity_relation_of(X0),X1)
      | subset(X0,range(X2,X3,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f225,f143]) ).

fof(f227,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X3,X0))
      | ~ subset(identity_relation_of(X1),X2)
      | subset(X1,domain(X3,X0,X2)) ),
    inference(backward_subsumption_resolution,[status(thm)],[f38,f143]) ).

fof(f228,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,relation_type(X2,X3))
      | ~ subset(identity_relation_of(X0),X1)
      | subset(X0,domain(X2,X3,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f227,f143]) ).

fof(f229,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | X1 = X0 ),
    inference(backward_subsumption_resolution,[status(thm)],[f36,f143]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | X0 = X1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f229,f143]) ).

fof(f234,plain,
    range(sk0_12,sk0_13,sk0_14) = range_of(sk0_14),
    inference(resolution,[status(thm)],[f170,f148]) ).

fof(f251,plain,
    ( spl0_4
  <=> ilf_type(sk0_14,relation_type(sk0_12,sk0_13)) ),
    introduced(split_symbol_definition) ).

fof(f253,plain,
    ( ~ ilf_type(sk0_14,relation_type(sk0_12,sk0_13))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f251]) ).

fof(f254,plain,
    ( spl0_5
  <=> ilf_type(range_of(sk0_14),subset_type(sk0_13)) ),
    introduced(split_symbol_definition) ).

fof(f255,plain,
    ( ilf_type(range_of(sk0_14),subset_type(sk0_13))
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f254]) ).

fof(f257,plain,
    ( ~ ilf_type(sk0_14,relation_type(sk0_12,sk0_13))
    | ilf_type(range_of(sk0_14),subset_type(sk0_13)) ),
    inference(paramodulation,[status(thm)],[f234,f168]) ).

fof(f258,plain,
    ( ~ spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f257,f251,f254]) ).

fof(f259,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f253,f148]) ).

fof(f260,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f259]) ).

fof(f273,plain,
    domain(sk0_12,sk0_13,sk0_14) = domain_of(sk0_14),
    inference(resolution,[status(thm)],[f174,f148]) ).

fof(f274,plain,
    ( ~ subset(sk0_13,domain_of(sk0_14))
    | spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f273,f153]) ).

fof(f310,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,subset_type(X1))
      | empty(power_set(X1))
      | member(X0,power_set(X1)) ),
    inference(resolution,[status(thm)],[f200,f188]) ).

fof(f311,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,subset_type(X1))
      | member(X0,power_set(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f310,f189]) ).

fof(f327,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,power_set(X1))
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(resolution,[status(thm)],[f195,f143]) ).

fof(f388,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,power_set(X1))
      | ~ member(sk0_1(X1,X2),X0)
      | subset(X2,X1) ),
    inference(resolution,[status(thm)],[f327,f207]) ).

fof(f444,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,relation_type(X1,X2))
      | ~ subset(identity_relation_of(X3),X0)
      | subset(X3,range(X1,X2,X0)) ),
    inference(resolution,[status(thm)],[f226,f143]) ).

fof(f445,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ilf_type(X0,relation_type(X1,X2))
      | ~ subset(identity_relation_of(X3),X0)
      | subset(X3,domain(X1,X2,X0)) ),
    inference(resolution,[status(thm)],[f228,f143]) ).

fof(f482,plain,
    ( sk0_13 != range_of(sk0_14)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f234,f156]) ).

fof(f668,plain,
    ! [X0,X1] :
      ( ~ member(X0,power_set(X1))
      | subset(X0,X1)
      | subset(X0,X1) ),
    inference(resolution,[status(thm)],[f388,f209]) ).

fof(f669,plain,
    ! [X0,X1] :
      ( ~ member(X0,power_set(X1))
      | subset(X0,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f668]) ).

fof(f683,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ ilf_type(X0,subset_type(X1)) ),
    inference(resolution,[status(thm)],[f669,f311]) ).

fof(f698,plain,
    ( subset(range_of(sk0_14),sk0_13)
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f683,f255]) ).

fof(f908,plain,
    ( spl0_54
  <=> subset(sk0_13,range_of(sk0_14)) ),
    introduced(split_symbol_definition) ).

fof(f910,plain,
    ( ~ subset(sk0_13,range_of(sk0_14))
    | spl0_54 ),
    inference(component_clause,[status(thm)],[f908]) ).

fof(f911,plain,
    ( spl0_55
  <=> sk0_13 = range_of(sk0_14) ),
    introduced(split_symbol_definition) ).

fof(f912,plain,
    ( sk0_13 = range_of(sk0_14)
    | ~ spl0_55 ),
    inference(component_clause,[status(thm)],[f911]) ).

fof(f914,plain,
    ( ~ subset(sk0_13,range_of(sk0_14))
    | sk0_13 = range_of(sk0_14)
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f698,f230]) ).

fof(f915,plain,
    ( ~ spl0_54
    | spl0_55
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f914,f908,f911,f254]) ).

fof(f916,plain,
    ( $false
    | spl0_1
    | ~ spl0_55 ),
    inference(forward_subsumption_resolution,[status(thm)],[f912,f482]) ).

fof(f917,plain,
    ( spl0_1
    | ~ spl0_55 ),
    inference(contradiction_clause,[status(thm)],[f916]) ).

fof(f1255,plain,
    ! [X0,X1] :
      ( ~ ilf_type(sk0_14,relation_type(X0,X1))
      | subset(sk0_13,range(X0,X1,sk0_14)) ),
    inference(resolution,[status(thm)],[f444,f149]) ).

fof(f1258,plain,
    ! [X0,X1] :
      ( ~ ilf_type(sk0_14,relation_type(X0,X1))
      | subset(sk0_13,domain(X0,X1,sk0_14)) ),
    inference(resolution,[status(thm)],[f445,f149]) ).

fof(f1613,plain,
    subset(sk0_13,range(sk0_12,sk0_13,sk0_14)),
    inference(resolution,[status(thm)],[f1255,f148]) ).

fof(f1614,plain,
    subset(sk0_13,range_of(sk0_14)),
    inference(forward_demodulation,[status(thm)],[f234,f1613]) ).

fof(f1615,plain,
    ( $false
    | spl0_54 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1614,f910]) ).

fof(f1616,plain,
    spl0_54,
    inference(contradiction_clause,[status(thm)],[f1615]) ).

fof(f1622,plain,
    subset(sk0_13,domain(sk0_12,sk0_13,sk0_14)),
    inference(resolution,[status(thm)],[f1258,f148]) ).

fof(f1623,plain,
    subset(sk0_13,domain_of(sk0_14)),
    inference(forward_demodulation,[status(thm)],[f273,f1622]) ).

fof(f1624,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1623,f274]) ).

fof(f1625,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f1624]) ).

fof(f1626,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f157,f258,f260,f915,f917,f1616,f1625]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13  % Problem  : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.35  % Computer : n002.cluster.edu
% 0.10/0.35  % Model    : x86_64 x86_64
% 0.10/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35  % Memory   : 8042.1875MB
% 0.10/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.35  % CPULimit : 300
% 0.10/0.35  % WCLimit  : 300
% 0.10/0.35  % DateTime : Mon Apr 29 21:56:24 EDT 2024
% 0.10/0.35  % CPUTime  : 
% 0.10/0.36  % Drodi V3.6.0
% 2.80/0.74  % Refutation found
% 2.80/0.74  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.80/0.74  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.02/0.85  % Elapsed time: 0.501781 seconds
% 3.02/0.86  % CPU time: 3.115292 seconds
% 3.02/0.86  % Total memory used: 89.407 MB
% 3.02/0.86  % Net memory used: 88.348 MB
%------------------------------------------------------------------------------