TSTP Solution File: SEU187+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU187+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 : n022.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 10:57:56 EDT 2023

% Result   : Theorem 3.95s 2.22s
% Output   : CNFRefutation 4.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   70 (  20 unt;  25 typ;   0 def)
%            Number of atoms       :   89 (  34 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   82 (  38   ~;  32   |;   3   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   36 (  20   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   5 con; 0-3 aty)
%            Number of variables   :   44 (;  40   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > element > relation > empty > unordered_pair > ordered_pair > #nlpp > singleton > relation_rng > relation_dom > empty_set > #skF_9 > #skF_6 > #skF_11 > #skF_4 > #skF_3 > #skF_10 > #skF_14 > #skF_13 > #skF_2 > #skF_8 > #skF_7 > #skF_1 > #skF_5 > #skF_15 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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_15',type,
    '#skF_15': ( $i * $i ) > $i ).

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

tff(f_98,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_133,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_100,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_129,negated_conjecture,
    ~ ( ( relation_dom(empty_set) = empty_set )
      & ( relation_rng(empty_set) = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).

tff(f_125,axiom,
    ! [A,B] :
      ( ! [C] :
          ( in(C,A)
        <=> in(C,B) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

tff(f_138,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

tff(f_48,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( ( B = relation_dom(A) )
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).

tff(f_59,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_68,plain,
    empty('#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_773,plain,
    ! [A_198] :
      ( ( empty_set = A_198 )
      | ~ empty(A_198) ),
    inference(cnfTransformation,[status(thm)],[f_133]) ).

tff(c_784,plain,
    empty_set = '#skF_10',
    inference(resolution,[status(thm)],[c_68,c_773]) ).

tff(c_70,plain,
    empty('#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_783,plain,
    empty_set = '#skF_11',
    inference(resolution,[status(thm)],[c_70,c_773]) ).

tff(c_797,plain,
    '#skF_11' = '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_784,c_783]) ).

tff(c_100,plain,
    ! [A_110] :
      ( ( empty_set = A_110 )
      | ~ empty(A_110) ),
    inference(cnfTransformation,[status(thm)],[f_133]) ).

tff(c_111,plain,
    empty_set = '#skF_10',
    inference(resolution,[status(thm)],[c_68,c_100]) ).

tff(c_110,plain,
    empty_set = '#skF_11',
    inference(resolution,[status(thm)],[c_70,c_100]) ).

tff(c_123,plain,
    '#skF_11' = '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_111,c_110]) ).

tff(c_90,plain,
    ( ( relation_rng(empty_set) != empty_set )
    | ( relation_dom(empty_set) != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_129]) ).

tff(c_99,plain,
    relation_dom(empty_set) != empty_set,
    inference(splitLeft,[status(thm)],[c_90]) ).

tff(c_115,plain,
    relation_dom('#skF_11') != '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_110,c_99]) ).

tff(c_137,plain,
    relation_dom('#skF_10') != '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_123,c_123,c_115]) ).

tff(c_66,plain,
    relation('#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_439,plain,
    ! [A_155,B_156] :
      ( in('#skF_14'(A_155,B_156),B_156)
      | in('#skF_15'(A_155,B_156),A_155)
      | ( B_156 = A_155 ) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_94,plain,
    ! [B_106,A_105] :
      ( ~ empty(B_106)
      | ~ in(A_105,B_106) ),
    inference(cnfTransformation,[status(thm)],[f_138]) ).

tff(c_474,plain,
    ! [A_155,B_156] :
      ( ~ empty(A_155)
      | in('#skF_14'(A_155,B_156),B_156)
      | ( B_156 = A_155 ) ),
    inference(resolution,[status(thm)],[c_439,c_94]) ).

tff(c_666,plain,
    ! [C_185,A_186] :
      ( in(ordered_pair(C_185,'#skF_4'(A_186,relation_dom(A_186),C_185)),A_186)
      | ~ in(C_185,relation_dom(A_186))
      | ~ relation(A_186) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_692,plain,
    ! [A_187,C_188] :
      ( ~ empty(A_187)
      | ~ in(C_188,relation_dom(A_187))
      | ~ relation(A_187) ),
    inference(resolution,[status(thm)],[c_666,c_94]) ).

tff(c_743,plain,
    ! [A_189,A_190] :
      ( ~ empty(A_189)
      | ~ relation(A_189)
      | ~ empty(A_190)
      | ( relation_dom(A_189) = A_190 ) ),
    inference(resolution,[status(thm)],[c_474,c_692]) ).

tff(c_749,plain,
    ! [A_190] :
      ( ~ empty('#skF_10')
      | ~ empty(A_190)
      | ( relation_dom('#skF_10') = A_190 ) ),
    inference(resolution,[status(thm)],[c_66,c_743]) ).

tff(c_755,plain,
    ! [A_191] :
      ( ~ empty(A_191)
      | ( relation_dom('#skF_10') = A_191 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_749]) ).

tff(c_758,plain,
    relation_dom('#skF_10') = '#skF_10',
    inference(resolution,[status(thm)],[c_68,c_755]) ).

tff(c_762,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_137,c_758]) ).

tff(c_763,plain,
    relation_rng(empty_set) != empty_set,
    inference(splitRight,[status(thm)],[c_90]) ).

tff(c_789,plain,
    relation_rng('#skF_11') != '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_783,c_783,c_763]) ).

tff(c_815,plain,
    relation_rng('#skF_10') != '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_797,c_797,c_789]) ).

tff(c_1135,plain,
    ! [A_239,B_240] :
      ( in('#skF_14'(A_239,B_240),B_240)
      | in('#skF_15'(A_239,B_240),A_239)
      | ( B_240 = A_239 ) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_1250,plain,
    ! [A_247,B_248] :
      ( ~ empty(A_247)
      | in('#skF_14'(A_247,B_248),B_248)
      | ( B_248 = A_247 ) ),
    inference(resolution,[status(thm)],[c_1135,c_94]) ).

tff(c_1193,plain,
    ! [A_243,C_244] :
      ( in(ordered_pair('#skF_8'(A_243,relation_rng(A_243),C_244),C_244),A_243)
      | ~ in(C_244,relation_rng(A_243))
      | ~ relation(A_243) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_1218,plain,
    ! [A_243,C_244] :
      ( ~ empty(A_243)
      | ~ in(C_244,relation_rng(A_243))
      | ~ relation(A_243) ),
    inference(resolution,[status(thm)],[c_1193,c_94]) ).

tff(c_1321,plain,
    ! [A_259,A_260] :
      ( ~ empty(A_259)
      | ~ relation(A_259)
      | ~ empty(A_260)
      | ( relation_rng(A_259) = A_260 ) ),
    inference(resolution,[status(thm)],[c_1250,c_1218]) ).

tff(c_1327,plain,
    ! [A_260] :
      ( ~ empty('#skF_10')
      | ~ empty(A_260)
      | ( relation_rng('#skF_10') = A_260 ) ),
    inference(resolution,[status(thm)],[c_66,c_1321]) ).

tff(c_1333,plain,
    ! [A_261] :
      ( ~ empty(A_261)
      | ( relation_rng('#skF_10') = A_261 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_1327]) ).

tff(c_1336,plain,
    relation_rng('#skF_10') = '#skF_10',
    inference(resolution,[status(thm)],[c_68,c_1333]) ).

tff(c_1340,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_815,c_1336]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU187+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
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 11:53:18 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 3.95/2.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.28/2.23  
% 4.28/2.23  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.75/2.26  
% 4.75/2.26  Inference rules
% 4.75/2.26  ----------------------
% 4.75/2.26  #Ref     : 0
% 4.75/2.26  #Sup     : 297
% 4.75/2.26  #Fact    : 0
% 4.75/2.26  #Define  : 0
% 4.75/2.26  #Split   : 1
% 4.75/2.26  #Chain   : 0
% 4.75/2.26  #Close   : 0
% 4.75/2.26  
% 4.75/2.26  Ordering : KBO
% 4.75/2.26  
% 4.75/2.26  Simplification rules
% 4.75/2.26  ----------------------
% 4.75/2.26  #Subsume      : 37
% 4.75/2.26  #Demod        : 64
% 4.75/2.26  #Tautology    : 120
% 4.75/2.26  #SimpNegUnit  : 4
% 4.75/2.26  #BackRed      : 16
% 4.75/2.26  
% 4.75/2.26  #Partial instantiations: 0
% 4.75/2.26  #Strategies tried      : 1
% 4.75/2.26  
% 4.75/2.26  Timing (in seconds)
% 4.75/2.26  ----------------------
% 4.75/2.26  Preprocessing        : 0.55
% 4.75/2.26  Parsing              : 0.28
% 4.75/2.26  CNF conversion       : 0.05
% 4.75/2.26  Main loop            : 0.55
% 4.75/2.26  Inferencing          : 0.20
% 4.75/2.26  Reduction            : 0.16
% 4.75/2.26  Demodulation         : 0.12
% 4.75/2.26  BG Simplification    : 0.03
% 4.75/2.26  Subsumption          : 0.11
% 4.75/2.26  Abstraction          : 0.02
% 4.75/2.26  MUC search           : 0.00
% 4.75/2.26  Cooper               : 0.00
% 4.75/2.26  Total                : 1.15
% 4.75/2.26  Index Insertion      : 0.00
% 4.75/2.26  Index Deletion       : 0.00
% 4.75/2.26  Index Matching       : 0.00
% 4.75/2.26  BG Taut test         : 0.00
%------------------------------------------------------------------------------