TSTP Solution File: SET928+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET928+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 : n008.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 3.62s 1.94s
% Output   : CNFRefutation 3.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   86 (  38 unt;  13 typ;   0 def)
%            Number of atoms       :  116 (  40 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   92 (  49   ~;  36   |;   4   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   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    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   63 (;  63   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_difference > #nlpp > #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('#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(disjoint,type,
    disjoint: ( $i * $i ) > $o ).

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

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

tff(f_66,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) )
      <=> ( ~ in(A,C)
          & ~ in(B,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).

tff(f_57,axiom,
    ! [A,B,C] :
      ~ ( ~ in(A,B)
        & ~ in(C,B)
        & ~ disjoint(unordered_pair(A,C),B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).

tff(f_70,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> ( set_difference(A,B) = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).

tff(f_33,axiom,
    ! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

tff(f_42,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

tff(f_47,axiom,
    ! [A,B,C] :
      ~ ( disjoint(unordered_pair(A,B),C)
        & in(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).

tff(c_18,plain,
    ( ~ in('#skF_4','#skF_5')
    | in('#skF_7','#skF_8')
    | in('#skF_6','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_102,plain,
    ~ in('#skF_4','#skF_5'),
    inference(splitLeft,[status(thm)],[c_18]) ).

tff(c_20,plain,
    ( ~ in('#skF_3','#skF_5')
    | in('#skF_7','#skF_8')
    | in('#skF_6','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_121,plain,
    ~ in('#skF_3','#skF_5'),
    inference(splitLeft,[status(thm)],[c_20]) ).

tff(c_136,plain,
    ! [A_41,C_42,B_43] :
      ( disjoint(unordered_pair(A_41,C_42),B_43)
      | in(C_42,B_43)
      | in(A_41,B_43) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_28,plain,
    ! [A_13,B_14] :
      ( ( set_difference(A_13,B_14) = A_13 )
      | ~ disjoint(A_13,B_14) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_255,plain,
    ! [A_62,C_63,B_64] :
      ( ( set_difference(unordered_pair(A_62,C_63),B_64) = unordered_pair(A_62,C_63) )
      | in(C_63,B_64)
      | in(A_62,B_64) ),
    inference(resolution,[status(thm)],[c_136,c_28]) ).

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_16,plain,
    ( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != unordered_pair('#skF_3','#skF_4') )
    | in('#skF_7','#skF_8')
    | in('#skF_6','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_31,plain,
    ( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != unordered_pair('#skF_4','#skF_3') )
    | in('#skF_7','#skF_8')
    | in('#skF_6','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_16]) ).

tff(c_189,plain,
    set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != unordered_pair('#skF_4','#skF_3'),
    inference(splitLeft,[status(thm)],[c_31]) ).

tff(c_274,plain,
    ( in('#skF_3','#skF_5')
    | in('#skF_4','#skF_5') ),
    inference(superposition,[status(thm),theory(equality)],[c_255,c_189]) ).

tff(c_307,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_102,c_121,c_274]) ).

tff(c_308,plain,
    ( in('#skF_6','#skF_8')
    | in('#skF_7','#skF_8') ),
    inference(splitRight,[status(thm)],[c_31]) ).

tff(c_310,plain,
    in('#skF_7','#skF_8'),
    inference(splitLeft,[status(thm)],[c_308]) ).

tff(c_309,plain,
    set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') = unordered_pair('#skF_4','#skF_3'),
    inference(splitRight,[status(thm)],[c_31]) ).

tff(c_22,plain,
    ( ( set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != unordered_pair('#skF_3','#skF_4') )
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_32,plain,
    ( ( set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != unordered_pair('#skF_4','#skF_3') )
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_22]) ).

tff(c_326,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_309,c_32]) ).

tff(c_68,plain,
    ! [A_21,B_22] :
      ( disjoint(A_21,B_22)
      | ( set_difference(A_21,B_22) != A_21 ) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_10,plain,
    ! [B_6,A_5] :
      ( disjoint(B_6,A_5)
      | ~ disjoint(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_77,plain,
    ! [B_25,A_26] :
      ( disjoint(B_25,A_26)
      | ( set_difference(A_26,B_25) != A_26 ) ),
    inference(resolution,[status(thm)],[c_68,c_10]) ).

tff(c_83,plain,
    ! [B_25,A_26] :
      ( ( set_difference(B_25,A_26) = B_25 )
      | ( set_difference(A_26,B_25) != A_26 ) ),
    inference(resolution,[status(thm)],[c_77,c_28]) ).

tff(c_336,plain,
    set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
    inference(superposition,[status(thm),theory(equality)],[c_326,c_83]) ).

tff(c_71,plain,
    ! [B_22,A_21] :
      ( disjoint(B_22,A_21)
      | ( set_difference(A_21,B_22) != A_21 ) ),
    inference(resolution,[status(thm)],[c_68,c_10]) ).

tff(c_85,plain,
    ! [A_27,C_28,B_29] :
      ( ~ in(A_27,C_28)
      | ~ disjoint(unordered_pair(A_27,B_29),C_28) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_103,plain,
    ! [B_30,C_31,A_32] :
      ( ~ in(B_30,C_31)
      | ~ disjoint(unordered_pair(A_32,B_30),C_31) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_85]) ).

tff(c_118,plain,
    ! [B_30,A_21,A_32] :
      ( ~ in(B_30,A_21)
      | ( set_difference(A_21,unordered_pair(A_32,B_30)) != A_21 ) ),
    inference(resolution,[status(thm)],[c_71,c_103]) ).

tff(c_357,plain,
    ~ in('#skF_7','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_336,c_118]) ).

tff(c_368,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_310,c_357]) ).

tff(c_369,plain,
    in('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_308]) ).

tff(c_414,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_309,c_32]) ).

tff(c_30,plain,
    ! [A_13,B_14] :
      ( disjoint(A_13,B_14)
      | ( set_difference(A_13,B_14) != A_13 ) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_101,plain,
    ! [A_27,B_14,B_29] :
      ( ~ in(A_27,B_14)
      | ( set_difference(unordered_pair(A_27,B_29),B_14) != unordered_pair(A_27,B_29) ) ),
    inference(resolution,[status(thm)],[c_30,c_85]) ).

tff(c_421,plain,
    ~ in('#skF_6','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_414,c_101]) ).

tff(c_431,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_369,c_421]) ).

tff(c_432,plain,
    ( in('#skF_6','#skF_8')
    | in('#skF_7','#skF_8') ),
    inference(splitRight,[status(thm)],[c_20]) ).

tff(c_437,plain,
    in('#skF_7','#skF_8'),
    inference(splitLeft,[status(thm)],[c_432]) ).

tff(c_433,plain,
    in('#skF_3','#skF_5'),
    inference(splitRight,[status(thm)],[c_20]) ).

tff(c_26,plain,
    ( ~ in('#skF_3','#skF_5')
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_456,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_26]) ).

tff(c_462,plain,
    set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
    inference(superposition,[status(thm),theory(equality)],[c_456,c_83]) ).

tff(c_467,plain,
    ~ in('#skF_7','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_462,c_118]) ).

tff(c_478,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_437,c_467]) ).

tff(c_479,plain,
    in('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_432]) ).

tff(c_492,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_26]) ).

tff(c_498,plain,
    set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
    inference(superposition,[status(thm),theory(equality)],[c_492,c_83]) ).

tff(c_512,plain,
    ! [A_77,A_78,B_79] :
      ( ~ in(A_77,A_78)
      | ( set_difference(A_78,unordered_pair(A_77,B_79)) != A_78 ) ),
    inference(resolution,[status(thm)],[c_71,c_85]) ).

tff(c_515,plain,
    ~ in('#skF_6','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_498,c_512]) ).

tff(c_525,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_479,c_515]) ).

tff(c_526,plain,
    ( in('#skF_6','#skF_8')
    | in('#skF_7','#skF_8') ),
    inference(splitRight,[status(thm)],[c_18]) ).

tff(c_532,plain,
    in('#skF_7','#skF_8'),
    inference(splitLeft,[status(thm)],[c_526]) ).

tff(c_527,plain,
    in('#skF_4','#skF_5'),
    inference(splitRight,[status(thm)],[c_18]) ).

tff(c_24,plain,
    ( ~ in('#skF_4','#skF_5')
    | ( set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7') ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_591,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_527,c_24]) ).

tff(c_597,plain,
    set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
    inference(superposition,[status(thm),theory(equality)],[c_591,c_83]) ).

tff(c_554,plain,
    ! [B_83,C_84,A_85] :
      ( ~ in(B_83,C_84)
      | ~ disjoint(unordered_pair(A_85,B_83),C_84) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_85]) ).

tff(c_573,plain,
    ! [B_83,A_21,A_85] :
      ( ~ in(B_83,A_21)
      | ( set_difference(A_21,unordered_pair(A_85,B_83)) != A_21 ) ),
    inference(resolution,[status(thm)],[c_71,c_554]) ).

tff(c_603,plain,
    ~ in('#skF_7','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_597,c_573]) ).

tff(c_614,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_532,c_603]) ).

tff(c_615,plain,
    in('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_526]) ).

tff(c_621,plain,
    set_difference(unordered_pair('#skF_6','#skF_7'),'#skF_8') = unordered_pair('#skF_6','#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_527,c_24]) ).

tff(c_643,plain,
    ! [B_97,A_98] :
      ( ( set_difference(B_97,A_98) = B_97 )
      | ( set_difference(A_98,B_97) != A_98 ) ),
    inference(resolution,[status(thm)],[c_77,c_28]) ).

tff(c_646,plain,
    set_difference('#skF_8',unordered_pair('#skF_6','#skF_7')) = '#skF_8',
    inference(superposition,[status(thm),theory(equality)],[c_621,c_643]) ).

tff(c_667,plain,
    ! [A_102,A_103,B_104] :
      ( ~ in(A_102,A_103)
      | ( set_difference(A_103,unordered_pair(A_102,B_104)) != A_103 ) ),
    inference(resolution,[status(thm)],[c_71,c_85]) ).

tff(c_670,plain,
    ~ in('#skF_6','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_646,c_667]) ).

tff(c_680,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_615,c_670]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET928+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 16:44:34 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 3.62/1.94  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.62/1.94  
% 3.62/1.94  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/1.98  
% 3.81/1.98  Inference rules
% 3.81/1.98  ----------------------
% 3.81/1.98  #Ref     : 0
% 3.81/1.98  #Sup     : 174
% 3.81/1.98  #Fact    : 0
% 3.81/1.98  #Define  : 0
% 3.81/1.98  #Split   : 7
% 3.81/1.98  #Chain   : 0
% 3.81/1.98  #Close   : 0
% 3.81/1.98  
% 3.81/1.98  Ordering : KBO
% 3.81/1.98  
% 3.81/1.98  Simplification rules
% 3.81/1.98  ----------------------
% 3.81/1.98  #Subsume      : 54
% 3.81/1.98  #Demod        : 24
% 3.81/1.98  #Tautology    : 53
% 3.81/1.98  #SimpNegUnit  : 1
% 3.81/1.98  #BackRed      : 0
% 3.81/1.98  
% 3.81/1.98  #Partial instantiations: 0
% 3.81/1.98  #Strategies tried      : 1
% 3.81/1.98  
% 3.81/1.98  Timing (in seconds)
% 3.81/1.98  ----------------------
% 3.81/1.98  Preprocessing        : 0.44
% 3.81/1.98  Parsing              : 0.24
% 3.81/1.98  CNF conversion       : 0.03
% 3.81/1.98  Main loop            : 0.47
% 3.81/1.98  Inferencing          : 0.18
% 3.81/1.98  Reduction            : 0.13
% 3.81/1.98  Demodulation         : 0.10
% 3.81/1.98  BG Simplification    : 0.02
% 3.81/1.98  Subsumption          : 0.10
% 3.81/1.99  Abstraction          : 0.02
% 3.81/1.99  MUC search           : 0.00
% 3.81/1.99  Cooper               : 0.00
% 3.81/1.99  Total                : 0.97
% 3.81/1.99  Index Insertion      : 0.00
% 3.81/1.99  Index Deletion       : 0.00
% 3.81/1.99  Index Matching       : 0.00
% 3.81/1.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------