TSTP Solution File: SEU061+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n027.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 10:57:33 EDT 2023

% Result   : Theorem 23.66s 12.21s
% Output   : CNFRefutation 23.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   47
% Syntax   : Number of formulae    :  100 (  33 unt;  39 typ;   0 def)
%            Number of atoms       :  114 (  38 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   93 (  40   ~;  39   |;   2   &)
%                                         (   8 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   50 (  28   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   31 (  31 usr;  11 con; 0-4 aty)
%            Number of variables   :   59 (;  55   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > unordered_pair > relation_inverse_image > ordered_pair > #nlpp > singleton > relation_rng > powerset > empty_set > #skF_7 > #skF_6 > #skF_1 > #skF_20 > #skF_18 > #skF_17 > #skF_19 > #skF_16 > #skF_15 > #skF_14 > #skF_13 > #skF_10 > #skF_2 > #skF_8 > #skF_21 > #skF_11 > #skF_4 > #skF_22 > #skF_3 > #skF_24 > #skF_23 > #skF_12 > #skF_9 > #skF_5

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_7',type,
    '#skF_7': $i > $i ).

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

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

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

tff('#skF_20',type,
    '#skF_20': $i ).

tff('#skF_18',type,
    '#skF_18': $i ).

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

tff('#skF_17',type,
    '#skF_17': $i ).

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

tff('#skF_19',type,
    '#skF_19': $i > $i ).

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

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

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

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

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

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

tff('#skF_16',type,
    '#skF_16': $i ).

tff('#skF_15',type,
    '#skF_15': $i > $i ).

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

tff('#skF_14',type,
    '#skF_14': $i ).

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

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

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

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

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

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

tff('#skF_21',type,
    '#skF_21': $i ).

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

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

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

tff('#skF_22',type,
    '#skF_22': $i ).

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

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

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

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

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

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

tff(f_188,negated_conjecture,
    ~ ! [A,B] :
        ( relation(B)
       => ( in(A,relation_rng(B))
        <=> ( relation_inverse_image(B,singleton(A)) != empty_set ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).

tff(f_138,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_219,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_149,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_79,axiom,
    ! [A] :
      ( ( A = empty_set )
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

tff(f_66,axiom,
    ! [A] :
      ( relation(A)
     => ! [B,C] :
          ( ( C = relation_inverse_image(A,B) )
        <=> ! [D] :
              ( in(D,C)
            <=> ? [E] :
                  ( in(ordered_pair(D,E),A)
                  & in(E,B) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).

tff(f_73,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_90,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( ( B = relation_rng(A) )
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).

tff(c_134,plain,
    relation('#skF_24'),
    inference(cnfTransformation,[status(thm)],[f_188]) ).

tff(c_98,plain,
    empty('#skF_14'),
    inference(cnfTransformation,[status(thm)],[f_138]) ).

tff(c_84370,plain,
    ! [A_1368] :
      ( ( empty_set = A_1368 )
      | ~ empty(A_1368) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_84388,plain,
    empty_set = '#skF_14',
    inference(resolution,[status(thm)],[c_98,c_84370]) ).

tff(c_136,plain,
    ( ( relation_inverse_image('#skF_24',singleton('#skF_23')) = empty_set )
    | ~ in('#skF_23',relation_rng('#skF_24')) ),
    inference(cnfTransformation,[status(thm)],[f_188]) ).

tff(c_164,plain,
    ~ in('#skF_23',relation_rng('#skF_24')),
    inference(splitLeft,[status(thm)],[c_136]) ).

tff(c_172,plain,
    ! [A_140] :
      ( ( empty_set = A_140 )
      | ~ empty(A_140) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_190,plain,
    empty_set = '#skF_14',
    inference(resolution,[status(thm)],[c_98,c_172]) ).

tff(c_142,plain,
    ( in('#skF_23',relation_rng('#skF_24'))
    | ( relation_inverse_image('#skF_24',singleton('#skF_23')) != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_188]) ).

tff(c_165,plain,
    relation_inverse_image('#skF_24',singleton('#skF_23')) != empty_set,
    inference(splitLeft,[status(thm)],[c_142]) ).

tff(c_231,plain,
    relation_inverse_image('#skF_24',singleton('#skF_23')) != '#skF_14',
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_165]) ).

tff(c_104,plain,
    empty('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_189,plain,
    empty_set = '#skF_16',
    inference(resolution,[status(thm)],[c_104,c_172]) ).

tff(c_213,plain,
    '#skF_16' = '#skF_14',
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_189]) ).

tff(c_46,plain,
    ! [B_58] : ~ in(B_58,empty_set),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_195,plain,
    ! [B_58] : ~ in(B_58,'#skF_16'),
    inference(demodulation,[status(thm),theory(equality)],[c_189,c_46]) ).

tff(c_236,plain,
    ! [B_58] : ~ in(B_58,'#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_213,c_195]) ).

tff(c_1821,plain,
    ! [A_289,B_290,C_291] :
      ( in('#skF_2'(A_289,B_290,C_291),B_290)
      | in('#skF_3'(A_289,B_290,C_291),C_291)
      | ( relation_inverse_image(A_289,B_290) = C_291 )
      | ~ relation(A_289) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_34,plain,
    ! [C_54,A_50] :
      ( ( C_54 = A_50 )
      | ~ in(C_54,singleton(A_50)) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_38602,plain,
    ! [A_1035,A_1036,C_1037] :
      ( ( '#skF_2'(A_1035,singleton(A_1036),C_1037) = A_1036 )
      | in('#skF_3'(A_1035,singleton(A_1036),C_1037),C_1037)
      | ( relation_inverse_image(A_1035,singleton(A_1036)) = C_1037 )
      | ~ relation(A_1035) ),
    inference(resolution,[status(thm)],[c_1821,c_34]) ).

tff(c_83748,plain,
    ! [A_1352,A_1353] :
      ( ( '#skF_2'(A_1352,singleton(A_1353),'#skF_14') = A_1353 )
      | ( relation_inverse_image(A_1352,singleton(A_1353)) = '#skF_14' )
      | ~ relation(A_1352) ),
    inference(resolution,[status(thm)],[c_38602,c_236]) ).

tff(c_84077,plain,
    ( ( '#skF_2'('#skF_24',singleton('#skF_23'),'#skF_14') = '#skF_23' )
    | ~ relation('#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_83748,c_231]) ).

tff(c_84246,plain,
    '#skF_2'('#skF_24',singleton('#skF_23'),'#skF_14') = '#skF_23',
    inference(demodulation,[status(thm),theory(equality)],[c_134,c_84077]) ).

tff(c_2815,plain,
    ! [A_338,B_339,C_340] :
      ( in(ordered_pair('#skF_1'(A_338,B_339,C_340),'#skF_2'(A_338,B_339,C_340)),A_338)
      | in('#skF_3'(A_338,B_339,C_340),C_340)
      | ( relation_inverse_image(A_338,B_339) = C_340 )
      | ~ relation(A_338) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_52,plain,
    ! [C_95,A_59,D_98] :
      ( in(C_95,relation_rng(A_59))
      | ~ in(ordered_pair(D_98,C_95),A_59)
      | ~ relation(A_59) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_2884,plain,
    ! [A_338,B_339,C_340] :
      ( in('#skF_2'(A_338,B_339,C_340),relation_rng(A_338))
      | in('#skF_3'(A_338,B_339,C_340),C_340)
      | ( relation_inverse_image(A_338,B_339) = C_340 )
      | ~ relation(A_338) ),
    inference(resolution,[status(thm)],[c_2815,c_52]) ).

tff(c_84280,plain,
    ( in('#skF_23',relation_rng('#skF_24'))
    | in('#skF_3'('#skF_24',singleton('#skF_23'),'#skF_14'),'#skF_14')
    | ( relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14' )
    | ~ relation('#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_84246,c_2884]) ).

tff(c_84316,plain,
    ( in('#skF_23',relation_rng('#skF_24'))
    | in('#skF_3'('#skF_24',singleton('#skF_23'),'#skF_14'),'#skF_14')
    | ( relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_134,c_84280]) ).

tff(c_84318,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_231,c_236,c_164,c_84316]) ).

tff(c_84319,plain,
    in('#skF_23',relation_rng('#skF_24')),
    inference(splitRight,[status(thm)],[c_142]) ).

tff(c_84360,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_164,c_84319]) ).

tff(c_84361,plain,
    relation_inverse_image('#skF_24',singleton('#skF_23')) = empty_set,
    inference(splitRight,[status(thm)],[c_136]) ).

tff(c_84429,plain,
    relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14',
    inference(demodulation,[status(thm),theory(equality)],[c_84388,c_84361]) ).

tff(c_84363,plain,
    relation_inverse_image('#skF_24',singleton('#skF_23')) != empty_set,
    inference(splitLeft,[status(thm)],[c_142]) ).

tff(c_84455,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_84429,c_84388,c_84363]) ).

tff(c_84456,plain,
    in('#skF_23',relation_rng('#skF_24')),
    inference(splitRight,[status(thm)],[c_142]) ).

tff(c_50,plain,
    ! [A_59,C_95] :
      ( in(ordered_pair('#skF_11'(A_59,relation_rng(A_59),C_95),C_95),A_59)
      | ~ in(C_95,relation_rng(A_59))
      | ~ relation(A_59) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_84467,plain,
    ! [A_1386] :
      ( ( empty_set = A_1386 )
      | ~ empty(A_1386) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_84485,plain,
    empty_set = '#skF_14',
    inference(resolution,[status(thm)],[c_98,c_84467]) ).

tff(c_84484,plain,
    empty_set = '#skF_16',
    inference(resolution,[status(thm)],[c_104,c_84467]) ).

tff(c_84499,plain,
    '#skF_16' = '#skF_14',
    inference(demodulation,[status(thm),theory(equality)],[c_84485,c_84484]) ).

tff(c_84490,plain,
    ! [B_58] : ~ in(B_58,'#skF_16'),
    inference(demodulation,[status(thm),theory(equality)],[c_84484,c_46]) ).

tff(c_84538,plain,
    ! [B_58] : ~ in(B_58,'#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_84499,c_84490]) ).

tff(c_84457,plain,
    relation_inverse_image('#skF_24',singleton('#skF_23')) = empty_set,
    inference(splitRight,[status(thm)],[c_142]) ).

tff(c_84522,plain,
    relation_inverse_image('#skF_24',singleton('#skF_23')) = '#skF_14',
    inference(demodulation,[status(thm),theory(equality)],[c_84485,c_84457]) ).

tff(c_36,plain,
    ! [C_54] : in(C_54,singleton(C_54)),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_85526,plain,
    ! [D_1497,A_1498,B_1499,E_1500] :
      ( in(D_1497,relation_inverse_image(A_1498,B_1499))
      | ~ in(E_1500,B_1499)
      | ~ in(ordered_pair(D_1497,E_1500),A_1498)
      | ~ relation(A_1498) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_94128,plain,
    ! [D_1817,A_1818,C_1819] :
      ( in(D_1817,relation_inverse_image(A_1818,singleton(C_1819)))
      | ~ in(ordered_pair(D_1817,C_1819),A_1818)
      | ~ relation(A_1818) ),
    inference(resolution,[status(thm)],[c_36,c_85526]) ).

tff(c_94260,plain,
    ! [D_1817] :
      ( in(D_1817,'#skF_14')
      | ~ in(ordered_pair(D_1817,'#skF_23'),'#skF_24')
      | ~ relation('#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_84522,c_94128]) ).

tff(c_94302,plain,
    ! [D_1817] :
      ( in(D_1817,'#skF_14')
      | ~ in(ordered_pair(D_1817,'#skF_23'),'#skF_24') ),
    inference(demodulation,[status(thm),theory(equality)],[c_134,c_94260]) ).

tff(c_94304,plain,
    ! [D_1820] : ~ in(ordered_pair(D_1820,'#skF_23'),'#skF_24'),
    inference(negUnitSimplification,[status(thm)],[c_84538,c_94302]) ).

tff(c_94308,plain,
    ( ~ in('#skF_23',relation_rng('#skF_24'))
    | ~ relation('#skF_24') ),
    inference(resolution,[status(thm)],[c_50,c_94304]) ).

tff(c_94315,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_134,c_84456,c_94308]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 12:16:08 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 23.66/12.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.66/12.21  
% 23.66/12.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.81/12.25  
% 23.81/12.25  Inference rules
% 23.81/12.25  ----------------------
% 23.81/12.25  #Ref     : 0
% 23.81/12.25  #Sup     : 25527
% 23.81/12.25  #Fact    : 0
% 23.81/12.25  #Define  : 0
% 23.81/12.25  #Split   : 58
% 23.81/12.25  #Chain   : 0
% 23.81/12.25  #Close   : 0
% 23.81/12.25  
% 23.81/12.25  Ordering : KBO
% 23.81/12.25  
% 23.81/12.25  Simplification rules
% 23.81/12.25  ----------------------
% 23.81/12.25  #Subsume      : 10005
% 23.81/12.25  #Demod        : 9325
% 23.81/12.25  #Tautology    : 4320
% 23.81/12.25  #SimpNegUnit  : 317
% 23.81/12.25  #BackRed      : 48
% 23.81/12.25  
% 23.81/12.25  #Partial instantiations: 0
% 23.81/12.25  #Strategies tried      : 1
% 23.81/12.25  
% 23.81/12.25  Timing (in seconds)
% 23.81/12.25  ----------------------
% 23.81/12.25  Preprocessing        : 0.61
% 23.81/12.25  Parsing              : 0.31
% 23.81/12.25  CNF conversion       : 0.06
% 23.81/12.25  Main loop            : 10.49
% 23.81/12.25  Inferencing          : 1.79
% 23.81/12.25  Reduction            : 2.95
% 23.81/12.25  Demodulation         : 2.13
% 23.81/12.25  BG Simplification    : 0.15
% 23.81/12.25  Subsumption          : 5.07
% 23.81/12.25  Abstraction          : 0.20
% 23.81/12.25  MUC search           : 0.00
% 23.81/12.25  Cooper               : 0.00
% 23.81/12.25  Total                : 11.16
% 23.81/12.25  Index Insertion      : 0.00
% 23.81/12.25  Index Deletion       : 0.00
% 23.81/12.25  Index Matching       : 0.00
% 23.81/12.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------