TSTP Solution File: SET662+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n031.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 Aug 22 10:56:49 EDT 2023

% Result   : Theorem 3.77s 1.91s
% Output   : CNFRefutation 4.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   53 (   9 unt;  25 typ;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   72 (  27   ~;  23   |;   3   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  21   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   4 con; 0-2 aty)
%            Number of variables   :   47 (;  47   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ type > subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > set_type > empty_set > #skF_9 > #skF_2 > #skF_4 > #skF_11 > #skF_3 > #skF_10 > #skF_8 > #skF_7 > #skF_1 > #skF_5 > #skF_6

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

tff(relation_type,type,
    relation_type: ( $i * $i ) > $i ).

tff(power_set,type,
    power_set: $i > $i ).

tff('#skF_2',type,
    '#skF_2': $i > $i ).

tff('#skF_4',type,
    '#skF_4': $i > $i ).

tff('#skF_11',type,
    '#skF_11': $i ).

tff(ordered_pair,type,
    ordered_pair: ( $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i ) > $i ).

tff('#skF_10',type,
    '#skF_10': $i ).

tff(cross_product,type,
    cross_product: ( $i * $i ) > $i ).

tff(set_type,type,
    set_type: $i ).

tff(subset,type,
    subset: ( $i * $i ) > $o ).

tff(member,type,
    member: ( $i * $i ) > $o ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff(empty,type,
    empty: $i > $o ).

tff(ilf_type,type,
    ilf_type: ( $i * $i ) > $o ).

tff(member_type,type,
    member_type: $i > $i ).

tff(empty_set,type,
    empty_set: $i ).

tff(type,type,
    type: ( $i * $i ) > $o ).

tff(subset_type,type,
    subset_type: $i > $i ).

tff(relation_like,type,
    relation_like: $i > $o ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff('#skF_6',type,
    '#skF_6': $i > $i ).

tff(f_215,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).

tff(f_138,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/sandbox2/benchmark/theBenchmark.p',p12) ).

tff(f_64,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ~ member(B,empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).

tff(f_146,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ~ empty(power_set(B))
        & ilf_type(power_set(B),set_type) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).

tff(f_159,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/sandbox2/benchmark/theBenchmark.p',p14) ).

tff(f_86,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/sandbox2/benchmark/theBenchmark.p',p7) ).

tff(f_49,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ! [D] :
                ( ilf_type(D,subset_type(cross_product(B,C)))
               => ilf_type(D,relation_type(B,C)) )
            & ! [E] :
                ( ilf_type(E,relation_type(B,C))
               => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

tff(f_224,negated_conjecture,
    ~ ! [B] :
        ( ilf_type(B,set_type)
       => ! [C] :
            ( ilf_type(C,set_type)
           => ilf_type(empty_set,relation_type(B,C)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_25) ).

tff(c_76,plain,
    ! [B_98] : ilf_type(B_98,set_type),
    inference(cnfTransformation,[status(thm)],[f_215]) ).

tff(c_44,plain,
    ! [B_45,C_51] :
      ( member('#skF_5'(B_45,C_51),B_45)
      | member(B_45,power_set(C_51))
      | ~ ilf_type(C_51,set_type)
      | ~ ilf_type(B_45,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_138]) ).

tff(c_227,plain,
    ! [B_139,C_140] :
      ( member('#skF_5'(B_139,C_140),B_139)
      | member(B_139,power_set(C_140)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_44]) ).

tff(c_10,plain,
    ! [B_21] :
      ( ~ member(B_21,empty_set)
      | ~ ilf_type(B_21,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_146,plain,
    ! [B_21] : ~ member(B_21,empty_set),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_10]) ).

tff(c_244,plain,
    ! [C_140] : member(empty_set,power_set(C_140)),
    inference(resolution,[status(thm)],[c_227,c_146]) ).

tff(c_50,plain,
    ! [B_55] :
      ( ~ empty(power_set(B_55))
      | ~ ilf_type(B_55,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_110,plain,
    ! [B_55] : ~ empty(power_set(B_55)),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_50]) ).

tff(c_52,plain,
    ! [B_56,C_58] :
      ( ilf_type(B_56,member_type(C_58))
      | ~ member(B_56,C_58)
      | ~ ilf_type(C_58,set_type)
      | empty(C_58)
      | ~ ilf_type(B_56,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_108,plain,
    ! [B_56,C_58] :
      ( ilf_type(B_56,member_type(C_58))
      | ~ member(B_56,C_58)
      | empty(C_58) ),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_52]) ).

tff(c_18,plain,
    ! [C_27,B_25] :
      ( ilf_type(C_27,subset_type(B_25))
      | ~ ilf_type(C_27,member_type(power_set(B_25)))
      | ~ ilf_type(C_27,set_type)
      | ~ ilf_type(B_25,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_332,plain,
    ! [C_152,B_153] :
      ( ilf_type(C_152,subset_type(B_153))
      | ~ ilf_type(C_152,member_type(power_set(B_153))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_18]) ).

tff(c_336,plain,
    ! [B_56,B_153] :
      ( ilf_type(B_56,subset_type(B_153))
      | ~ member(B_56,power_set(B_153))
      | empty(power_set(B_153)) ),
    inference(resolution,[status(thm)],[c_108,c_332]) ).

tff(c_404,plain,
    ! [B_162,B_163] :
      ( ilf_type(B_162,subset_type(B_163))
      | ~ member(B_162,power_set(B_163)) ),
    inference(negUnitSimplification,[status(thm)],[c_110,c_336]) ).

tff(c_442,plain,
    ! [C_140] : ilf_type(empty_set,subset_type(C_140)),
    inference(resolution,[status(thm)],[c_244,c_404]) ).

tff(c_6,plain,
    ! [D_13,B_4,C_10] :
      ( ilf_type(D_13,relation_type(B_4,C_10))
      | ~ ilf_type(D_13,subset_type(cross_product(B_4,C_10)))
      | ~ ilf_type(C_10,set_type)
      | ~ ilf_type(B_4,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_487,plain,
    ! [D_179,B_180,C_181] :
      ( ilf_type(D_179,relation_type(B_180,C_181))
      | ~ ilf_type(D_179,subset_type(cross_product(B_180,C_181))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_76,c_6]) ).

tff(c_519,plain,
    ! [B_180,C_181] : ilf_type(empty_set,relation_type(B_180,C_181)),
    inference(resolution,[status(thm)],[c_442,c_487]) ).

tff(c_78,plain,
    ~ ilf_type(empty_set,relation_type('#skF_10','#skF_11')),
    inference(cnfTransformation,[status(thm)],[f_224]) ).

tff(c_525,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_519,c_78]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.37  % Computer : n031.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 16:46:44 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 3.77/1.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.77/1.92  
% 3.77/1.92  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.06/1.95  
% 4.06/1.95  Inference rules
% 4.06/1.95  ----------------------
% 4.06/1.95  #Ref     : 0
% 4.06/1.95  #Sup     : 72
% 4.06/1.95  #Fact    : 0
% 4.06/1.95  #Define  : 0
% 4.06/1.95  #Split   : 0
% 4.06/1.95  #Chain   : 0
% 4.06/1.95  #Close   : 0
% 4.06/1.95  
% 4.06/1.95  Ordering : KBO
% 4.06/1.95  
% 4.06/1.95  Simplification rules
% 4.06/1.95  ----------------------
% 4.06/1.95  #Subsume      : 8
% 4.06/1.95  #Demod        : 82
% 4.06/1.95  #Tautology    : 25
% 4.06/1.95  #SimpNegUnit  : 5
% 4.06/1.95  #BackRed      : 1
% 4.06/1.95  
% 4.06/1.95  #Partial instantiations: 0
% 4.06/1.95  #Strategies tried      : 1
% 4.06/1.95  
% 4.06/1.95  Timing (in seconds)
% 4.06/1.95  ----------------------
% 4.06/1.95  Preprocessing        : 0.54
% 4.06/1.95  Parsing              : 0.29
% 4.06/1.95  CNF conversion       : 0.05
% 4.06/1.95  Main loop            : 0.37
% 4.06/1.95  Inferencing          : 0.15
% 4.06/1.95  Reduction            : 0.11
% 4.06/1.95  Demodulation         : 0.07
% 4.06/1.95  BG Simplification    : 0.03
% 4.06/1.95  Subsumption          : 0.07
% 4.06/1.95  Abstraction          : 0.01
% 4.06/1.95  MUC search           : 0.00
% 4.06/1.95  Cooper               : 0.00
% 4.06/1.95  Total                : 0.96
% 4.06/1.95  Index Insertion      : 0.00
% 4.06/1.95  Index Deletion       : 0.00
% 4.06/1.95  Index Matching       : 0.00
% 4.06/1.95  BG Taut test         : 0.00
%------------------------------------------------------------------------------