TSTP Solution File: SEU325+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU325+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 : n007.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 10:58:25 EDT 2023

% Result   : Theorem 9.67s 3.21s
% Output   : CNFRefutation 9.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   48
% Syntax   : Number of formulae    :   86 (  23 unt;  36 typ;   0 def)
%            Number of atoms       :  100 (  19 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   89 (  39   ~;  26   |;  12   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  30   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   6 con; 0-3 aty)
%            Number of variables   :   53 (;  50   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > is_a_cover_of_carrier > 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 > union_of_subsets > #nlpp > union > the_carrier > powerset > cast_as_carrier_subset > empty_set > #skF_9 > #skF_8 > #skF_4 > #skF_7 > #skF_3 > #skF_10 > #skF_5 > #skF_13 > #skF_11 > #skF_2 > #skF_1 > #skF_6 > #skF_12

%Foreground sorts:

%Background operators:

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

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

tff(union,type,
    union: $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_8',type,
    '#skF_8': $i > $i ).

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

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

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

tff('#skF_10',type,
    '#skF_10': $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(is_a_cover_of_carrier,type,
    is_a_cover_of_carrier: ( $i * $i ) > $o ).

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

tff('#skF_13',type,
    '#skF_13': $i ).

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

tff(cast_as_carrier_subset,type,
    cast_as_carrier_subset: $i > $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_11',type,
    '#skF_11': $i > $i ).

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

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

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

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

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

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

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

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

tff('#skF_12',type,
    '#skF_12': $i ).

tff(f_206,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

tff(f_326,negated_conjecture,
    ~ ! [A] :
        ( ( ~ empty_carrier(A)
          & one_sorted_str(A) )
       => ! [B] :
            ( element(B,powerset(powerset(the_carrier(A))))
           => ~ ( is_a_cover_of_carrier(A,B)
                & ( B = empty_set ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).

tff(f_173,axiom,
    ! [A] :
      ( one_sorted_str(A)
     => ( cast_as_carrier_subset(A) = the_carrier(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).

tff(f_214,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_295,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(f_263,axiom,
    ! [A] :
    ? [B] :
      ( element(B,powerset(A))
      & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

tff(f_330,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_283,axiom,
    ! [A,B] :
      ( element(B,powerset(powerset(A)))
     => ( union_of_subsets(A,B) = union(B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).

tff(f_192,axiom,
    ! [A] :
      ( one_sorted_str(A)
     => ! [B] :
          ( element(B,powerset(powerset(the_carrier(A))))
         => ( is_a_cover_of_carrier(A,B)
          <=> ( cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).

tff(f_183,axiom,
    ! [A,B] :
      ( ( B = union(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ? [D] :
              ( in(C,D)
              & in(D,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).

tff(f_312,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

tff(f_236,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(c_124,plain,
    ! [A_64] : element('#skF_6'(A_64),A_64),
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_196,plain,
    ~ empty_carrier('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_326]) ).

tff(c_194,plain,
    one_sorted_str('#skF_12'),
    inference(cnfTransformation,[status(thm)],[f_326]) ).

tff(c_312,plain,
    ! [A_120] :
      ( ( the_carrier(A_120) = cast_as_carrier_subset(A_120) )
      | ~ one_sorted_str(A_120) ),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_324,plain,
    the_carrier('#skF_12') = cast_as_carrier_subset('#skF_12'),
    inference(resolution,[status(thm)],[c_194,c_312]) ).

tff(c_424,plain,
    ! [A_147] :
      ( ~ empty(the_carrier(A_147))
      | ~ one_sorted_str(A_147)
      | empty_carrier(A_147) ),
    inference(cnfTransformation,[status(thm)],[f_214]) ).

tff(c_427,plain,
    ( ~ empty(cast_as_carrier_subset('#skF_12'))
    | ~ one_sorted_str('#skF_12')
    | empty_carrier('#skF_12') ),
    inference(superposition,[status(thm),theory(equality)],[c_324,c_424]) ).

tff(c_435,plain,
    ( ~ empty(cast_as_carrier_subset('#skF_12'))
    | empty_carrier('#skF_12') ),
    inference(demodulation,[status(thm),theory(equality)],[c_194,c_427]) ).

tff(c_436,plain,
    ~ empty(cast_as_carrier_subset('#skF_12')),
    inference(negUnitSimplification,[status(thm)],[c_196,c_435]) ).

tff(c_178,plain,
    ! [A_81,B_82] :
      ( in(A_81,B_82)
      | empty(B_82)
      | ~ element(A_81,B_82) ),
    inference(cnfTransformation,[status(thm)],[f_295]) ).

tff(c_190,plain,
    is_a_cover_of_carrier('#skF_12','#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_326]) ).

tff(c_160,plain,
    ! [A_71] : empty('#skF_9'(A_71)),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_188,plain,
    empty_set = '#skF_13',
    inference(cnfTransformation,[status(thm)],[f_326]) ).

tff(c_198,plain,
    ! [A_92] :
      ( ( empty_set = A_92 )
      | ~ empty(A_92) ),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_228,plain,
    ! [A_101] :
      ( ( A_101 = '#skF_13' )
      | ~ empty(A_101) ),
    inference(demodulation,[status(thm),theory(equality)],[c_188,c_198]) ).

tff(c_235,plain,
    ! [A_71] : ( '#skF_9'(A_71) = '#skF_13' ),
    inference(resolution,[status(thm)],[c_160,c_228]) ).

tff(c_162,plain,
    ! [A_71] : element('#skF_9'(A_71),powerset(A_71)),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_302,plain,
    ! [A_71] : element('#skF_13',powerset(A_71)),
    inference(demodulation,[status(thm),theory(equality)],[c_235,c_162]) ).

tff(c_2210,plain,
    ! [A_297,B_298] :
      ( ( union_of_subsets(A_297,B_298) = union(B_298) )
      | ~ element(B_298,powerset(powerset(A_297))) ),
    inference(cnfTransformation,[status(thm)],[f_283]) ).

tff(c_2231,plain,
    ! [A_297] : ( union_of_subsets(A_297,'#skF_13') = union('#skF_13') ),
    inference(resolution,[status(thm)],[c_302,c_2210]) ).

tff(c_7181,plain,
    ! [A_445,B_446] :
      ( ( union_of_subsets(the_carrier(A_445),B_446) = cast_as_carrier_subset(A_445) )
      | ~ is_a_cover_of_carrier(A_445,B_446)
      | ~ element(B_446,powerset(powerset(the_carrier(A_445))))
      | ~ one_sorted_str(A_445) ),
    inference(cnfTransformation,[status(thm)],[f_192]) ).

tff(c_7200,plain,
    ! [B_446] :
      ( ( union_of_subsets(the_carrier('#skF_12'),B_446) = cast_as_carrier_subset('#skF_12') )
      | ~ is_a_cover_of_carrier('#skF_12',B_446)
      | ~ element(B_446,powerset(powerset(cast_as_carrier_subset('#skF_12'))))
      | ~ one_sorted_str('#skF_12') ),
    inference(superposition,[status(thm),theory(equality)],[c_324,c_7181]) ).

tff(c_7788,plain,
    ! [B_463] :
      ( ( union_of_subsets(cast_as_carrier_subset('#skF_12'),B_463) = cast_as_carrier_subset('#skF_12') )
      | ~ is_a_cover_of_carrier('#skF_12',B_463)
      | ~ element(B_463,powerset(powerset(cast_as_carrier_subset('#skF_12')))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_194,c_324,c_7200]) ).

tff(c_7812,plain,
    ( ( union_of_subsets(cast_as_carrier_subset('#skF_12'),'#skF_13') = cast_as_carrier_subset('#skF_12') )
    | ~ is_a_cover_of_carrier('#skF_12','#skF_13') ),
    inference(resolution,[status(thm)],[c_302,c_7788]) ).

tff(c_7827,plain,
    union('#skF_13') = cast_as_carrier_subset('#skF_12'),
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_2231,c_7812]) ).

tff(c_5725,plain,
    ! [A_394,C_395] :
      ( in('#skF_4'(A_394,union(A_394),C_395),A_394)
      | ~ in(C_395,union(A_394)) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_2080,plain,
    ! [C_280,B_281,A_282] :
      ( ~ empty(C_280)
      | ~ element(B_281,powerset(C_280))
      | ~ in(A_282,B_281) ),
    inference(cnfTransformation,[status(thm)],[f_312]) ).

tff(c_2104,plain,
    ! [A_71,A_282] :
      ( ~ empty(A_71)
      | ~ in(A_282,'#skF_13') ),
    inference(resolution,[status(thm)],[c_302,c_2080]) ).

tff(c_2106,plain,
    ! [A_282] : ~ in(A_282,'#skF_13'),
    inference(splitLeft,[status(thm)],[c_2104]) ).

tff(c_5758,plain,
    ! [C_395] : ~ in(C_395,union('#skF_13')),
    inference(resolution,[status(thm)],[c_5725,c_2106]) ).

tff(c_7874,plain,
    ! [C_464] : ~ in(C_464,cast_as_carrier_subset('#skF_12')),
    inference(demodulation,[status(thm),theory(equality)],[c_7827,c_5758]) ).

tff(c_7894,plain,
    ! [A_81] :
      ( empty(cast_as_carrier_subset('#skF_12'))
      | ~ element(A_81,cast_as_carrier_subset('#skF_12')) ),
    inference(resolution,[status(thm)],[c_178,c_7874]) ).

tff(c_8000,plain,
    ! [A_467] : ~ element(A_467,cast_as_carrier_subset('#skF_12')),
    inference(negUnitSimplification,[status(thm)],[c_436,c_7894]) ).

tff(c_8005,plain,
    $false,
    inference(resolution,[status(thm)],[c_124,c_8000]) ).

tff(c_8006,plain,
    ! [A_71] : ~ empty(A_71),
    inference(splitRight,[status(thm)],[c_2104]) ).

tff(c_142,plain,
    empty(empty_set),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_204,plain,
    empty('#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_188,c_142]) ).

tff(c_8026,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8006,c_204]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU325+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % 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
% 0.16/0.35  % Computer : n007.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Thu Aug  3 11:31:38 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 9.67/3.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.67/3.21  
% 9.67/3.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.67/3.24  
% 9.67/3.24  Inference rules
% 9.67/3.24  ----------------------
% 9.67/3.24  #Ref     : 0
% 9.67/3.24  #Sup     : 1632
% 9.67/3.24  #Fact    : 0
% 9.67/3.24  #Define  : 0
% 9.67/3.24  #Split   : 53
% 9.67/3.24  #Chain   : 0
% 9.67/3.24  #Close   : 0
% 9.67/3.24  
% 9.67/3.24  Ordering : KBO
% 9.67/3.24  
% 9.67/3.24  Simplification rules
% 9.67/3.24  ----------------------
% 9.67/3.24  #Subsume      : 1163
% 9.67/3.24  #Demod        : 598
% 9.67/3.24  #Tautology    : 343
% 9.67/3.24  #SimpNegUnit  : 244
% 9.67/3.24  #BackRed      : 198
% 9.67/3.24  
% 9.67/3.24  #Partial instantiations: 0
% 9.67/3.24  #Strategies tried      : 1
% 9.67/3.24  
% 9.67/3.24  Timing (in seconds)
% 9.67/3.24  ----------------------
% 9.67/3.25  Preprocessing        : 0.65
% 9.67/3.25  Parsing              : 0.33
% 9.67/3.25  CNF conversion       : 0.06
% 9.67/3.25  Main loop            : 1.52
% 9.67/3.25  Inferencing          : 0.48
% 9.67/3.25  Reduction            : 0.50
% 9.67/3.25  Demodulation         : 0.32
% 9.67/3.25  BG Simplification    : 0.05
% 9.67/3.25  Subsumption          : 0.36
% 9.67/3.25  Abstraction          : 0.04
% 9.67/3.25  MUC search           : 0.00
% 9.67/3.25  Cooper               : 0.00
% 9.67/3.25  Total                : 2.23
% 9.67/3.25  Index Insertion      : 0.00
% 9.67/3.25  Index Deletion       : 0.00
% 9.67/3.25  Index Matching       : 0.00
% 9.67/3.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------