TSTP Solution File: SET916+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET916+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 : n014.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 10:57:20 EDT 2023

% Result   : Theorem 57.48s 43.43s
% Output   : CNFRefutation 57.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   39 (   9 unt;  15 typ;   0 def)
%            Number of atoms       :   49 (  16 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   41 (  16   ~;  15   |;   6   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  10   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :   40 (;  39   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_intersection2 > #nlpp > #skF_1 > #skF_4 > #skF_10 > #skF_5 > #skF_6 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_7

%Foreground sorts:

%Background operators:

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

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

tff('#skF_4',type,
    '#skF_4': ( $i * $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('#skF_6',type,
    '#skF_6': $i ).

tff(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

tff(f_89,negated_conjecture,
    ~ ! [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_78,axiom,
    ! [A,B] :
      ( ~ ( ~ disjoint(A,B)
          & ! [C] : ~ in(C,set_intersection2(A,B)) )
      & ~ ( ? [C] : in(C,set_intersection2(A,B))
          & disjoint(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

tff(f_53,axiom,
    ! [A,B,C] :
      ( ( C = set_intersection2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

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_44,axiom,
    ! [A,B,C] :
      ( ( C = unordered_pair(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( ( D = A )
            | ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

tff(c_56,plain,
    ~ disjoint(unordered_pair('#skF_8','#skF_10'),'#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_60,plain,
    ~ in('#skF_8','#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_58,plain,
    ~ in('#skF_10','#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_234,plain,
    ! [A_62,B_63] :
      ( in('#skF_7'(A_62,B_63),set_intersection2(A_62,B_63))
      | disjoint(A_62,B_63) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_30,plain,
    ! [D_18,A_13,B_14] :
      ( in(D_18,A_13)
      | ~ in(D_18,set_intersection2(A_13,B_14)) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_260,plain,
    ! [A_62,B_63] :
      ( in('#skF_7'(A_62,B_63),A_62)
      | disjoint(A_62,B_63) ),
    inference(resolution,[status(thm)],[c_234,c_30]) ).

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_206,plain,
    ! [D_54,B_55,A_56] :
      ( ( D_54 = B_55 )
      | ( D_54 = A_56 )
      | ~ in(D_54,unordered_pair(A_56,B_55)) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_552,plain,
    ! [D_106,A_107,B_108] :
      ( ( D_106 = A_107 )
      | ( D_106 = B_108 )
      | ~ in(D_106,unordered_pair(A_107,B_108)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_206]) ).

tff(c_246294,plain,
    ! [A_51955,B_51956,B_51957] :
      ( ( '#skF_7'(unordered_pair(A_51955,B_51956),B_51957) = A_51955 )
      | ( '#skF_7'(unordered_pair(A_51955,B_51956),B_51957) = B_51956 )
      | disjoint(unordered_pair(A_51955,B_51956),B_51957) ),
    inference(resolution,[status(thm)],[c_260,c_552]) ).

tff(c_247004,plain,
    ( ( '#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_8' )
    | ( '#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_10' ) ),
    inference(resolution,[status(thm)],[c_246294,c_56]) ).

tff(c_247005,plain,
    '#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_10',
    inference(splitLeft,[status(thm)],[c_247004]) ).

tff(c_28,plain,
    ! [D_18,B_14,A_13] :
      ( in(D_18,B_14)
      | ~ in(D_18,set_intersection2(A_13,B_14)) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_261,plain,
    ! [A_62,B_63] :
      ( in('#skF_7'(A_62,B_63),B_63)
      | disjoint(A_62,B_63) ),
    inference(resolution,[status(thm)],[c_234,c_28]) ).

tff(c_247024,plain,
    ( in('#skF_10','#skF_9')
    | disjoint(unordered_pair('#skF_8','#skF_10'),'#skF_9') ),
    inference(superposition,[status(thm),theory(equality)],[c_247005,c_261]) ).

tff(c_247218,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_56,c_58,c_247024]) ).

tff(c_247219,plain,
    '#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_8',
    inference(splitRight,[status(thm)],[c_247004]) ).

tff(c_247239,plain,
    ( in('#skF_8','#skF_9')
    | disjoint(unordered_pair('#skF_8','#skF_10'),'#skF_9') ),
    inference(superposition,[status(thm),theory(equality)],[c_247219,c_261]) ).

tff(c_247433,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_56,c_60,c_247239]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET916+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
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 16:57:48 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 57.48/43.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.48/43.43  
% 57.48/43.43  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 57.48/43.46  
% 57.48/43.46  Inference rules
% 57.48/43.46  ----------------------
% 57.48/43.46  #Ref     : 0
% 57.48/43.46  #Sup     : 57169
% 57.48/43.46  #Fact    : 412
% 57.48/43.46  #Define  : 0
% 57.48/43.46  #Split   : 7
% 57.48/43.46  #Chain   : 0
% 57.48/43.46  #Close   : 0
% 57.48/43.46  
% 57.48/43.46  Ordering : KBO
% 57.48/43.46  
% 57.48/43.46  Simplification rules
% 57.48/43.46  ----------------------
% 57.48/43.46  #Subsume      : 20256
% 57.48/43.46  #Demod        : 1906
% 57.48/43.46  #Tautology    : 13541
% 57.48/43.46  #SimpNegUnit  : 268
% 57.48/43.46  #BackRed      : 0
% 57.48/43.46  
% 57.48/43.46  #Partial instantiations: 33384
% 57.48/43.46  #Strategies tried      : 1
% 57.48/43.46  
% 57.48/43.46  Timing (in seconds)
% 57.48/43.46  ----------------------
% 57.48/43.47  Preprocessing        : 0.51
% 57.48/43.47  Parsing              : 0.25
% 57.48/43.47  CNF conversion       : 0.04
% 57.48/43.47  Main loop            : 41.90
% 57.48/43.47  Inferencing          : 6.01
% 57.48/43.47  Reduction            : 9.41
% 57.48/43.47  Demodulation         : 7.68
% 57.48/43.47  BG Simplification    : 0.55
% 57.48/43.47  Subsumption          : 24.70
% 57.48/43.47  Abstraction          : 0.74
% 57.48/43.47  MUC search           : 0.00
% 57.48/43.47  Cooper               : 0.00
% 57.48/43.47  Total                : 42.46
% 57.48/43.47  Index Insertion      : 0.00
% 57.48/43.47  Index Deletion       : 0.00
% 57.48/43.47  Index Matching       : 0.00
% 57.48/43.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------