TSTP Solution File: SET607+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET607+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 20:39:57 EDT 2024

% Result   : Theorem 72.85s 9.55s
% Output   : CNFRefutation 72.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   67 (  10 unt;   0 def)
%            Number of atoms       :  194 (  25 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  205 (  78   ~;  92   |;  23   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   8 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   90 (  86   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B,C,D] :
      ( member(D,union(B,C))
    <=> ( member(D,B)
        | member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B,C,D] :
      ( member(D,difference(B,C))
    <=> ( member(D,B)
        & ~ member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f8,conjecture,
    ! [B,C] : union(B,difference(C,B)) = union(B,C),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [B,C] : union(B,difference(C,B)) = union(B,C),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f10,plain,
    ! [B,C,D] :
      ( ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
      & ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f11,plain,
    ( ! [B,C,D] :
        ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
    & ! [B,C,D] :
        ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f15,plain,
    ! [B,C,D] :
      ( ( ~ member(D,difference(B,C))
        | ( member(D,B)
          & ~ member(D,C) ) )
      & ( member(D,difference(B,C))
        | ~ member(D,B)
        | member(D,C) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f16,plain,
    ( ! [B,C,D] :
        ( ~ member(D,difference(B,C))
        | ( member(D,B)
          & ~ member(D,C) ) )
    & ! [B,C,D] :
        ( member(D,difference(B,C))
        | ~ member(D,B)
        | member(D,C) ) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,difference(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X1,X2))
      | ~ member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f20,plain,
    ! [B,C] :
      ( ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
      & ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f21,plain,
    ( ! [B,C] :
        ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
    & ! [B,C] :
        ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f34,plain,
    ! [B,C] :
      ( ( B != C
        | ! [D] :
            ( ( ~ member(D,B)
              | member(D,C) )
            & ( member(D,B)
              | ~ member(D,C) ) ) )
      & ( B = C
        | ? [D] :
            ( ( ~ member(D,B)
              | ~ member(D,C) )
            & ( member(D,B)
              | member(D,C) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f35,plain,
    ( ! [B,C] :
        ( B != C
        | ( ! [D] :
              ( ~ member(D,B)
              | member(D,C) )
          & ! [D] :
              ( member(D,B)
              | ~ member(D,C) ) ) )
    & ! [B,C] :
        ( B = C
        | ? [D] :
            ( ( ~ member(D,B)
              | ~ member(D,C) )
            & ( member(D,B)
              | member(D,C) ) ) ) ),
    inference(miniscoping,[status(esa)],[f34]) ).

fof(f36,plain,
    ( ! [B,C] :
        ( B != C
        | ( ! [D] :
              ( ~ member(D,B)
              | member(D,C) )
          & ! [D] :
              ( member(D,B)
              | ~ member(D,C) ) ) )
    & ! [B,C] :
        ( B = C
        | ( ( ~ member(sk0_1(C,B),B)
            | ~ member(sk0_1(C,B),C) )
          & ( member(sk0_1(C,B),B)
            | member(sk0_1(C,B),C) ) ) ) ),
    inference(skolemization,[status(esa)],[f35]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sk0_1(X1,X0),X0)
      | ~ member(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sk0_1(X1,X0),X0)
      | member(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f41,plain,
    ? [B,C] : union(B,difference(C,B)) != union(B,C),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f42,plain,
    union(sk0_2,difference(sk0_3,sk0_2)) != union(sk0_2,sk0_3),
    inference(skolemization,[status(esa)],[f41]) ).

fof(f43,plain,
    union(sk0_2,difference(sk0_3,sk0_2)) != union(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f44,plain,
    ! [X0] : subset(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f22]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,union(X1,difference(X2,X3)))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(resolution,[status(thm)],[f12,f17]) ).

fof(f195,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,X1)
      | member(X0,X2)
      | member(X0,union(X3,difference(X1,X2))) ),
    inference(resolution,[status(thm)],[f19,f14]) ).

fof(f477,plain,
    ( spl0_8
  <=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f478,plain,
    ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f477]) ).

fof(f480,plain,
    ( spl0_9
  <=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2))) ),
    introduced(split_symbol_definition) ).

fof(f481,plain,
    ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f480]) ).

fof(f482,plain,
    ( ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f480]) ).

fof(f523,plain,
    ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3))
    | member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2))) ),
    inference(resolution,[status(thm)],[f40,f43]) ).

fof(f524,plain,
    ( spl0_8
    | spl0_9 ),
    inference(split_clause,[status(thm)],[f523,f477,f480]) ).

fof(f801,plain,
    ( spl0_10
  <=> union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2)) ),
    introduced(split_symbol_definition) ).

fof(f802,plain,
    ( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f801]) ).

fof(f806,plain,
    ( spl0_11
  <=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f807,plain,
    ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f806]) ).

fof(f809,plain,
    ( spl0_12
  <=> member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f810,plain,
    ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f809]) ).

fof(f812,plain,
    ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
    | member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f478,f12]) ).

fof(f813,plain,
    ( spl0_11
    | spl0_12
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f812,f806,f809,f477]) ).

fof(f855,plain,
    ! [X0] :
      ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,X0))
      | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f807,f13]) ).

fof(f1029,plain,
    ( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
    | ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,sk0_3))
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f855,f39]) ).

fof(f1030,plain,
    ( spl0_10
    | ~ spl0_8
    | ~ spl0_11 ),
    inference(split_clause,[status(thm)],[f1029,f801,f477,f806]) ).

fof(f1031,plain,
    ( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
    | ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f855,f39]) ).

fof(f1032,plain,
    ( spl0_10
    | ~ spl0_9
    | ~ spl0_11 ),
    inference(split_clause,[status(thm)],[f1031,f801,f480,f806]) ).

fof(f1070,plain,
    ( $false
    | ~ spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f802,f43]) ).

fof(f1071,plain,
    ~ spl0_10,
    inference(contradiction_clause,[status(thm)],[f1070]) ).

fof(f1079,plain,
    ! [X0] :
      ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(X0,sk0_3))
      | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f810,f14]) ).

fof(f1332,plain,
    ( union(sk0_2,sk0_3) = union(sk0_2,difference(sk0_3,sk0_2))
    | ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),union(sk0_2,difference(sk0_3,sk0_2)))
    | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f1079,f39]) ).

fof(f1333,plain,
    ( spl0_10
    | ~ spl0_9
    | ~ spl0_12 ),
    inference(split_clause,[status(thm)],[f1332,f801,f480,f809]) ).

fof(f9176,plain,
    ( spl0_69
  <=> subset(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,difference(sk0_3,sk0_2))) ),
    introduced(split_symbol_definition) ).

fof(f9178,plain,
    ( ~ subset(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,difference(sk0_3,sk0_2)))
    | spl0_69 ),
    inference(component_clause,[status(thm)],[f9176]) ).

fof(f9312,plain,
    ( $false
    | spl0_69 ),
    inference(forward_subsumption_resolution,[status(thm)],[f9178,f44]) ).

fof(f9313,plain,
    spl0_69,
    inference(contradiction_clause,[status(thm)],[f9312]) ).

fof(f15197,plain,
    ( spl0_159
  <=> subset(union(sk0_2,sk0_3),union(sk0_2,sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f15199,plain,
    ( ~ subset(union(sk0_2,sk0_3),union(sk0_2,sk0_3))
    | spl0_159 ),
    inference(component_clause,[status(thm)],[f15197]) ).

fof(f15614,plain,
    ( $false
    | spl0_159 ),
    inference(forward_subsumption_resolution,[status(thm)],[f15199,f44]) ).

fof(f15615,plain,
    spl0_159,
    inference(contradiction_clause,[status(thm)],[f15614]) ).

fof(f24440,plain,
    ( ~ member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
    | member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
    | spl0_9 ),
    inference(resolution,[status(thm)],[f195,f482]) ).

fof(f24441,plain,
    ( ~ spl0_12
    | spl0_11
    | spl0_9 ),
    inference(split_clause,[status(thm)],[f24440,f809,f806,f480]) ).

fof(f25264,plain,
    ( member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_2)
    | member(sk0_1(union(sk0_2,difference(sk0_3,sk0_2)),union(sk0_2,sk0_3)),sk0_3)
    | ~ spl0_9 ),
    inference(resolution,[status(thm)],[f481,f74]) ).

fof(f25265,plain,
    ( spl0_11
    | spl0_12
    | ~ spl0_9 ),
    inference(split_clause,[status(thm)],[f25264,f806,f809,f480]) ).

fof(f25378,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f524,f813,f1030,f1032,f1071,f1333,f9313,f15615,f24441,f25265]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET607+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 21:52:43 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 72.85/9.55  % Refutation found
% 72.85/9.55  % SZS status Theorem for theBenchmark: Theorem is valid
% 72.85/9.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 73.51/9.67  % Elapsed time: 9.298321 seconds
% 73.51/9.67  % CPU time: 73.504299 seconds
% 73.51/9.67  % Total memory used: 515.743 MB
% 73.51/9.67  % Net memory used: 503.984 MB
%------------------------------------------------------------------------------