TSTP Solution File: SEU321+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n010.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 10:58:24 EDT 2023

% Result   : Theorem 12.00s 3.78s
% Output   : CNFRefutation 12.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   65 (  20 unt;  28 typ;   0 def)
%            Number of atoms       :   76 (   5 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   73 (  34   ~;  19   |;  10   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  21   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :   24 (;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > one_sorted_str > natural > empty_carrier > empty > subset_complement > #nlpp > the_carrier > powerset > empty_set > #skF_4 > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_8

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(empty_carrier,type,
    empty_carrier: $i > $o ).

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

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

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

tff(v1_int_1,type,
    v1_int_1: $i > $o ).

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

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

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

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

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

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

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

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

tff(v3_membered,type,
    v3_membered: $i > $o ).

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

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

tff(v1_xreal_0,type,
    v1_xreal_0: $i > $o ).

tff(v5_membered,type,
    v5_membered: $i > $o ).

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

tff(v2_membered,type,
    v2_membered: $i > $o ).

tff(v1_membered,type,
    v1_membered: $i > $o ).

tff(v1_xcmplx_0,type,
    v1_xcmplx_0: $i > $o ).

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

tff(v1_rat_1,type,
    v1_rat_1: $i > $o ).

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

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

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

tff(v4_membered,type,
    v4_membered: $i > $o ).

tff(f_294,negated_conjecture,
    ~ ! [A] :
        ( ( ~ empty_carrier(A)
          & one_sorted_str(A) )
       => ! [B] :
            ( element(B,powerset(the_carrier(A)))
           => ! [C] :
                ( element(C,the_carrier(A))
               => ( in(C,subset_complement(the_carrier(A),B))
                <=> ~ in(C,B) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).

tff(f_254,axiom,
    ( empty(empty_set)
    & v1_membered(empty_set)
    & v2_membered(empty_set)
    & v3_membered(empty_set)
    & v4_membered(empty_set)
    & v5_membered(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).

tff(f_308,axiom,
    ! [A] :
      ( ( A != empty_set )
     => ! [B] :
          ( element(B,powerset(A))
         => ! [C] :
              ( element(C,A)
             => ( ~ in(C,B)
               => in(C,subset_complement(A,B)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).

tff(f_203,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

tff(f_243,axiom,
    ! [A] :
      ( ( ~ empty_carrier(A)
        & one_sorted_str(A) )
     => ~ empty(the_carrier(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).

tff(f_315,axiom,
    ! [A,B,C] :
      ( element(C,powerset(A))
     => ~ ( in(B,subset_complement(A,C))
          & in(B,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).

tff(c_156,plain,
    element('#skF_7',powerset(the_carrier('#skF_6'))),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_160,plain,
    ~ empty_carrier('#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_158,plain,
    one_sorted_str('#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_140,plain,
    empty(empty_set),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_168,plain,
    ( in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7'))
    | ~ in('#skF_8','#skF_7') ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_240,plain,
    ~ in('#skF_8','#skF_7'),
    inference(splitLeft,[status(thm)],[c_168]) ).

tff(c_154,plain,
    element('#skF_8',the_carrier('#skF_6')),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_10685,plain,
    ! [C_1316,A_1317,B_1318] :
      ( in(C_1316,subset_complement(A_1317,B_1318))
      | in(C_1316,B_1318)
      | ~ element(C_1316,A_1317)
      | ~ element(B_1318,powerset(A_1317))
      | ( empty_set = A_1317 ) ),
    inference(cnfTransformation,[status(thm)],[f_308]) ).

tff(c_162,plain,
    ( in('#skF_8','#skF_7')
    | ~ in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_253,plain,
    ~ in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
    inference(negUnitSimplification,[status(thm)],[c_240,c_162]) ).

tff(c_10698,plain,
    ( in('#skF_8','#skF_7')
    | ~ element('#skF_8',the_carrier('#skF_6'))
    | ~ element('#skF_7',powerset(the_carrier('#skF_6')))
    | ( the_carrier('#skF_6') = empty_set ) ),
    inference(resolution,[status(thm)],[c_10685,c_253]) ).

tff(c_10714,plain,
    ( in('#skF_8','#skF_7')
    | ( the_carrier('#skF_6') = empty_set ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_154,c_10698]) ).

tff(c_10715,plain,
    the_carrier('#skF_6') = empty_set,
    inference(negUnitSimplification,[status(thm)],[c_240,c_10714]) ).

tff(c_9996,plain,
    ! [C_1243,B_1244,A_1245] :
      ( ~ empty(C_1243)
      | ~ element(B_1244,powerset(C_1243))
      | ~ in(A_1245,B_1244) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_10006,plain,
    ! [A_1245] :
      ( ~ empty(the_carrier('#skF_6'))
      | ~ in(A_1245,'#skF_7') ),
    inference(resolution,[status(thm)],[c_156,c_9996]) ).

tff(c_10007,plain,
    ~ empty(the_carrier('#skF_6')),
    inference(splitLeft,[status(thm)],[c_10006]) ).

tff(c_10720,plain,
    ~ empty(empty_set),
    inference(demodulation,[status(thm),theory(equality)],[c_10715,c_10007]) ).

tff(c_10739,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_140,c_10720]) ).

tff(c_10741,plain,
    empty(the_carrier('#skF_6')),
    inference(splitRight,[status(thm)],[c_10006]) ).

tff(c_128,plain,
    ! [A_55] :
      ( ~ empty(the_carrier(A_55))
      | ~ one_sorted_str(A_55)
      | empty_carrier(A_55) ),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_10750,plain,
    ( ~ one_sorted_str('#skF_6')
    | empty_carrier('#skF_6') ),
    inference(resolution,[status(thm)],[c_10741,c_128]) ).

tff(c_10758,plain,
    empty_carrier('#skF_6'),
    inference(demodulation,[status(thm),theory(equality)],[c_158,c_10750]) ).

tff(c_10760,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_160,c_10758]) ).

tff(c_10762,plain,
    in('#skF_8','#skF_7'),
    inference(splitRight,[status(thm)],[c_168]) ).

tff(c_10761,plain,
    in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
    inference(splitRight,[status(thm)],[c_168]) ).

tff(c_10763,plain,
    ~ in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_10800,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_10761,c_10763]) ).

tff(c_10802,plain,
    in('#skF_8',subset_complement(the_carrier('#skF_6'),'#skF_7')),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_12522,plain,
    ! [B_1540,C_1541,A_1542] :
      ( ~ in(B_1540,C_1541)
      | ~ in(B_1540,subset_complement(A_1542,C_1541))
      | ~ element(C_1541,powerset(A_1542)) ),
    inference(cnfTransformation,[status(thm)],[f_315]) ).

tff(c_12532,plain,
    ( ~ in('#skF_8','#skF_7')
    | ~ element('#skF_7',powerset(the_carrier('#skF_6'))) ),
    inference(resolution,[status(thm)],[c_10802,c_12522]) ).

tff(c_12537,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_10762,c_12532]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % 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
% 0.15/0.33  % Computer : n010.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit : 300
% 0.15/0.33  % WCLimit  : 300
% 0.15/0.33  % DateTime : Thu Aug  3 11:53:59 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 12.00/3.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.00/3.79  
% 12.00/3.79  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.14/3.81  
% 12.14/3.81  Inference rules
% 12.14/3.81  ----------------------
% 12.14/3.81  #Ref     : 0
% 12.14/3.81  #Sup     : 2634
% 12.14/3.81  #Fact    : 0
% 12.14/3.81  #Define  : 0
% 12.14/3.81  #Split   : 79
% 12.14/3.82  #Chain   : 0
% 12.14/3.82  #Close   : 0
% 12.14/3.82  
% 12.14/3.82  Ordering : KBO
% 12.14/3.82  
% 12.14/3.82  Simplification rules
% 12.14/3.82  ----------------------
% 12.14/3.82  #Subsume      : 790
% 12.14/3.82  #Demod        : 820
% 12.14/3.82  #Tautology    : 418
% 12.14/3.82  #SimpNegUnit  : 54
% 12.14/3.82  #BackRed      : 274
% 12.14/3.82  
% 12.14/3.82  #Partial instantiations: 0
% 12.14/3.82  #Strategies tried      : 1
% 12.14/3.82  
% 12.14/3.82  Timing (in seconds)
% 12.14/3.82  ----------------------
% 12.14/3.82  Preprocessing        : 0.59
% 12.14/3.82  Parsing              : 0.32
% 12.14/3.82  CNF conversion       : 0.05
% 12.14/3.82  Main loop            : 2.19
% 12.14/3.82  Inferencing          : 0.80
% 12.14/3.82  Reduction            : 0.69
% 12.14/3.82  Demodulation         : 0.44
% 12.14/3.82  BG Simplification    : 0.06
% 12.14/3.82  Subsumption          : 0.45
% 12.14/3.82  Abstraction          : 0.05
% 12.14/3.82  MUC search           : 0.00
% 12.14/3.82  Cooper               : 0.00
% 12.14/3.82  Total                : 2.82
% 12.14/3.82  Index Insertion      : 0.00
% 12.14/3.82  Index Deletion       : 0.00
% 12.14/3.82  Index Matching       : 0.00
% 12.14/3.82  BG Taut test         : 0.00
%------------------------------------------------------------------------------