TSTP Solution File: SET929+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET929+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n032.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 10:57:22 EDT 2023

% Result   : Theorem 3.39s 1.99s
% Output   : CNFRefutation 3.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   67 (  26 unt;  14 typ;   0 def)
%            Number of atoms       :   92 (  26 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   84 (  45   ~;  34   |;   2   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   46 (;  46   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > set_difference > #nlpp > empty_set > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(set_difference,type,
    set_difference: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_58,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( set_difference(unordered_pair(A,B),C) = empty_set )
      <=> ( in(A,C)
          & in(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).

tff(f_45,axiom,
    ! [A,B] :
      ( ( set_difference(A,B) = empty_set )
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

tff(f_51,axiom,
    ! [A,B,C] :
      ( subset(unordered_pair(A,B),C)
    <=> ( in(A,C)
        & in(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

tff(f_33,axiom,
    ! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

tff(c_26,plain,
    ( in('#skF_4','#skF_5')
    | ~ in('#skF_7','#skF_8')
    | ~ in('#skF_6','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_89,plain,
    ~ in('#skF_6','#skF_8'),
    inference(splitLeft,[status(thm)],[c_26]) ).

tff(c_32,plain,
    ( in('#skF_4','#skF_5')
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_162,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set,
    inference(splitLeft,[status(thm)],[c_32]) ).

tff(c_14,plain,
    ! [A_7,B_8] :
      ( subset(A_7,B_8)
      | ( set_difference(A_7,B_8) != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_136,plain,
    ! [A_31,C_32,B_33] :
      ( in(A_31,C_32)
      | ~ subset(unordered_pair(A_31,B_33),C_32) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_168,plain,
    ! [A_36,B_37,B_38] :
      ( in(A_36,B_37)
      | ( set_difference(unordered_pair(A_36,B_38),B_37) != empty_set ) ),
    inference(resolution,[status(thm)],[c_14,c_136]) ).

tff(c_171,plain,
    in('#skF_6','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_162,c_168]) ).

tff(c_185,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_89,c_171]) ).

tff(c_186,plain,
    in('#skF_4','#skF_5'),
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_187,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') != empty_set,
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_34,plain,
    ( in('#skF_3','#skF_5')
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_191,plain,
    in('#skF_3','#skF_5'),
    inference(negUnitSimplification,[status(thm)],[c_187,c_34]) ).

tff(c_195,plain,
    ! [A_39,B_40,C_41] :
      ( subset(unordered_pair(A_39,B_40),C_41)
      | ~ in(B_40,C_41)
      | ~ in(A_39,C_41) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_16,plain,
    ! [A_7,B_8] :
      ( ( set_difference(A_7,B_8) = empty_set )
      | ~ subset(A_7,B_8) ),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_241,plain,
    ! [A_48,B_49,C_50] :
      ( ( set_difference(unordered_pair(A_48,B_49),C_50) = empty_set )
      | ~ in(B_49,C_50)
      | ~ in(A_48,C_50) ),
    inference(resolution,[status(thm)],[c_195,c_16]) ).

tff(c_4,plain,
    ! [B_4,A_3] : ( unordered_pair(B_4,A_3) = unordered_pair(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_30,plain,
    ( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != empty_set )
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_36,plain,
    ( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set )
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_30]) ).

tff(c_240,plain,
    set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set,
    inference(negUnitSimplification,[status(thm)],[c_187,c_36]) ).

tff(c_247,plain,
    ( ~ in('#skF_3','#skF_5')
    | ~ in('#skF_4','#skF_5') ),
    inference(superposition,[status(thm),theory(equality)],[c_241,c_240]) ).

tff(c_278,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_186,c_191,c_247]) ).

tff(c_279,plain,
    ( ~ in('#skF_7','#skF_8')
    | in('#skF_4','#skF_5') ),
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_284,plain,
    ~ in('#skF_7','#skF_8'),
    inference(splitLeft,[status(thm)],[c_279]) ).

tff(c_302,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = empty_set,
    inference(splitLeft,[status(thm)],[c_32]) ).

tff(c_285,plain,
    ! [B_51,C_52,A_53] :
      ( in(B_51,C_52)
      | ~ subset(unordered_pair(A_53,B_51),C_52) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_383,plain,
    ! [B_68,B_69,A_70] :
      ( in(B_68,B_69)
      | ( set_difference(unordered_pair(A_70,B_68),B_69) != empty_set ) ),
    inference(resolution,[status(thm)],[c_14,c_285]) ).

tff(c_386,plain,
    in('#skF_7','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_302,c_383]) ).

tff(c_400,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_284,c_386]) ).

tff(c_401,plain,
    in('#skF_4','#skF_5'),
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_402,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') != empty_set,
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_463,plain,
    in('#skF_3','#skF_5'),
    inference(negUnitSimplification,[status(thm)],[c_402,c_34]) ).

tff(c_493,plain,
    ! [A_88,B_89,C_90] :
      ( subset(unordered_pair(A_88,B_89),C_90)
      | ~ in(B_89,C_90)
      | ~ in(A_88,C_90) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_515,plain,
    ! [A_91,B_92,C_93] :
      ( ( set_difference(unordered_pair(A_91,B_92),C_93) = empty_set )
      | ~ in(B_92,C_93)
      | ~ in(A_91,C_93) ),
    inference(resolution,[status(thm)],[c_493,c_16]) ).

tff(c_512,plain,
    set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set,
    inference(negUnitSimplification,[status(thm)],[c_402,c_36]) ).

tff(c_521,plain,
    ( ~ in('#skF_3','#skF_5')
    | ~ in('#skF_4','#skF_5') ),
    inference(superposition,[status(thm),theory(equality)],[c_515,c_512]) ).

tff(c_552,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_401,c_463,c_521]) ).

tff(c_553,plain,
    in('#skF_4','#skF_5'),
    inference(splitRight,[status(thm)],[c_279]) ).

tff(c_280,plain,
    in('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_554,plain,
    in('#skF_7','#skF_8'),
    inference(splitRight,[status(thm)],[c_279]) ).

tff(c_28,plain,
    ( in('#skF_3','#skF_5')
    | ~ in('#skF_7','#skF_8')
    | ~ in('#skF_6','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_640,plain,
    in('#skF_3','#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_280,c_554,c_28]) ).

tff(c_681,plain,
    ! [A_114,B_115,C_116] :
      ( subset(unordered_pair(A_114,B_115),C_116)
      | ~ in(B_115,C_116)
      | ~ in(A_114,C_116) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_702,plain,
    ! [A_117,B_118,C_119] :
      ( ( set_difference(unordered_pair(A_117,B_118),C_119) = empty_set )
      | ~ in(B_118,C_119)
      | ~ in(A_117,C_119) ),
    inference(resolution,[status(thm)],[c_681,c_16]) ).

tff(c_24,plain,
    ( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != empty_set )
    | ~ in('#skF_7','#skF_8')
    | ~ in('#skF_6','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_35,plain,
    ( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set )
    | ~ in('#skF_7','#skF_8')
    | ~ in('#skF_6','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_24]) ).

tff(c_701,plain,
    set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set,
    inference(demodulation,[status(thm),theory(equality)],[c_280,c_554,c_35]) ).

tff(c_708,plain,
    ( ~ in('#skF_3','#skF_5')
    | ~ in('#skF_4','#skF_5') ),
    inference(superposition,[status(thm),theory(equality)],[c_702,c_701]) ).

tff(c_742,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_553,c_640,c_708]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.33  % Computer : n032.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Thu Aug  3 16:15:21 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 3.39/1.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.99  
% 3.39/1.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.65/2.03  
% 3.65/2.03  Inference rules
% 3.65/2.03  ----------------------
% 3.65/2.03  #Ref     : 0
% 3.65/2.03  #Sup     : 172
% 3.65/2.03  #Fact    : 0
% 3.65/2.03  #Define  : 0
% 3.65/2.03  #Split   : 5
% 3.65/2.03  #Chain   : 0
% 3.65/2.03  #Close   : 0
% 3.65/2.03  
% 3.65/2.03  Ordering : KBO
% 3.65/2.03  
% 3.65/2.03  Simplification rules
% 3.65/2.03  ----------------------
% 3.65/2.03  #Subsume      : 59
% 3.65/2.03  #Demod        : 45
% 3.65/2.03  #Tautology    : 56
% 3.65/2.03  #SimpNegUnit  : 6
% 3.65/2.03  #BackRed      : 0
% 3.65/2.03  
% 3.65/2.03  #Partial instantiations: 0
% 3.65/2.03  #Strategies tried      : 1
% 3.65/2.03  
% 3.65/2.03  Timing (in seconds)
% 3.65/2.03  ----------------------
% 3.65/2.03  Preprocessing        : 0.47
% 3.65/2.03  Parsing              : 0.25
% 3.65/2.03  CNF conversion       : 0.03
% 3.65/2.03  Main loop            : 0.48
% 3.65/2.03  Inferencing          : 0.18
% 3.65/2.03  Reduction            : 0.15
% 3.65/2.03  Demodulation         : 0.11
% 3.65/2.03  BG Simplification    : 0.02
% 3.65/2.03  Subsumption          : 0.10
% 3.65/2.03  Abstraction          : 0.02
% 3.65/2.03  MUC search           : 0.00
% 3.65/2.03  Cooper               : 0.00
% 3.65/2.03  Total                : 1.00
% 3.65/2.03  Index Insertion      : 0.00
% 3.65/2.03  Index Deletion       : 0.00
% 3.65/2.03  Index Matching       : 0.00
% 3.65/2.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------