TSTP Solution File: SET974+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET974+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 : n007.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 10:57:26 EDT 2023

% Result   : Theorem 7.05s 2.77s
% Output   : CNFRefutation 7.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   45 (  11 unt;  17 typ;   0 def)
%            Number of atoms       :   50 (   3 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   45 (  23   ~;  14   |;   6   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  11   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-5 aty)
%            Number of variables   :   63 (;  62   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_intersection2 > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_4 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_1 > #skF_3 > #skF_8 > #skF_9

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

tff(f_69,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( disjoint(A,B)
          | disjoint(C,D) )
       => disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).

tff(f_51,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

tff(f_83,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_62,axiom,
    ! [A,B,C,D,E] :
      ~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
        & ! [F,G] :
            ~ ( ( A = ordered_pair(F,G) )
              & in(F,set_intersection2(B,D))
              & in(G,set_intersection2(C,E)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).

tff(f_35,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(c_28,plain,
    ( disjoint('#skF_7','#skF_8')
    | disjoint('#skF_5','#skF_6') ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_110,plain,
    disjoint('#skF_5','#skF_6'),
    inference(splitLeft,[status(thm)],[c_28]) ).

tff(c_18,plain,
    ! [B_14,A_13] :
      ( disjoint(B_14,A_13)
      | ~ disjoint(A_13,B_14) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_113,plain,
    disjoint('#skF_6','#skF_5'),
    inference(resolution,[status(thm)],[c_110,c_18]) ).

tff(c_30,plain,
    ! [A_22,B_23] :
      ( in('#skF_9'(A_22,B_23),set_intersection2(A_22,B_23))
      | disjoint(A_22,B_23) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_296,plain,
    ! [C_56,A_60,E_59,B_58,D_57] :
      ( in('#skF_3'(C_56,D_57,B_58,E_59,A_60),set_intersection2(B_58,D_57))
      | ~ in(A_60,set_intersection2(cartesian_product2(B_58,C_56),cartesian_product2(D_57,E_59))) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_2411,plain,
    ! [C_237,D_238,B_239,E_240] :
      ( in('#skF_3'(C_237,D_238,B_239,E_240,'#skF_9'(cartesian_product2(B_239,C_237),cartesian_product2(D_238,E_240))),set_intersection2(B_239,D_238))
      | disjoint(cartesian_product2(B_239,C_237),cartesian_product2(D_238,E_240)) ),
    inference(resolution,[status(thm)],[c_30,c_296]) ).

tff(c_6,plain,
    ! [B_6,A_5] : ( set_intersection2(B_6,A_5) = set_intersection2(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_119,plain,
    ! [A_38,B_39,C_40] :
      ( ~ disjoint(A_38,B_39)
      | ~ in(C_40,set_intersection2(A_38,B_39)) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_122,plain,
    ! [A_5,B_6,C_40] :
      ( ~ disjoint(A_5,B_6)
      | ~ in(C_40,set_intersection2(B_6,A_5)) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_119]) ).

tff(c_2452,plain,
    ! [D_241,B_242,C_243,E_244] :
      ( ~ disjoint(D_241,B_242)
      | disjoint(cartesian_product2(B_242,C_243),cartesian_product2(D_241,E_244)) ),
    inference(resolution,[status(thm)],[c_2411,c_122]) ).

tff(c_26,plain,
    ~ disjoint(cartesian_product2('#skF_5','#skF_7'),cartesian_product2('#skF_6','#skF_8')),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_2476,plain,
    ~ disjoint('#skF_6','#skF_5'),
    inference(resolution,[status(thm)],[c_2452,c_26]) ).

tff(c_2489,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_113,c_2476]) ).

tff(c_2490,plain,
    disjoint('#skF_7','#skF_8'),
    inference(splitRight,[status(thm)],[c_28]) ).

tff(c_2494,plain,
    disjoint('#skF_8','#skF_7'),
    inference(resolution,[status(thm)],[c_2490,c_18]) ).

tff(c_2749,plain,
    ! [B_274,D_273,E_275,A_276,C_272] :
      ( in('#skF_4'(C_272,D_273,B_274,E_275,A_276),set_intersection2(C_272,E_275))
      | ~ in(A_276,set_intersection2(cartesian_product2(B_274,C_272),cartesian_product2(D_273,E_275))) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_5146,plain,
    ! [C_468,D_469,B_470,E_471] :
      ( in('#skF_4'(C_468,D_469,B_470,E_471,'#skF_9'(cartesian_product2(B_470,C_468),cartesian_product2(D_469,E_471))),set_intersection2(C_468,E_471))
      | disjoint(cartesian_product2(B_470,C_468),cartesian_product2(D_469,E_471)) ),
    inference(resolution,[status(thm)],[c_30,c_2749]) ).

tff(c_2500,plain,
    ! [A_247,B_248,C_249] :
      ( ~ disjoint(A_247,B_248)
      | ~ in(C_249,set_intersection2(A_247,B_248)) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_2503,plain,
    ! [A_5,B_6,C_249] :
      ( ~ disjoint(A_5,B_6)
      | ~ in(C_249,set_intersection2(B_6,A_5)) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_2500]) ).

tff(c_5187,plain,
    ! [E_472,C_473,B_474,D_475] :
      ( ~ disjoint(E_472,C_473)
      | disjoint(cartesian_product2(B_474,C_473),cartesian_product2(D_475,E_472)) ),
    inference(resolution,[status(thm)],[c_5146,c_2503]) ).

tff(c_5211,plain,
    ~ disjoint('#skF_8','#skF_7'),
    inference(resolution,[status(thm)],[c_5187,c_26]) ).

tff(c_5224,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2494,c_5211]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % 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
% 0.15/0.37  % Computer : n007.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 16:25:24 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 7.05/2.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.05/2.78  
% 7.05/2.78  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.37/2.81  
% 7.37/2.81  Inference rules
% 7.37/2.81  ----------------------
% 7.37/2.81  #Ref     : 0
% 7.37/2.81  #Sup     : 1339
% 7.37/2.81  #Fact    : 0
% 7.37/2.81  #Define  : 0
% 7.37/2.81  #Split   : 1
% 7.37/2.81  #Chain   : 0
% 7.37/2.81  #Close   : 0
% 7.37/2.81  
% 7.37/2.81  Ordering : KBO
% 7.37/2.81  
% 7.37/2.81  Simplification rules
% 7.37/2.81  ----------------------
% 7.37/2.81  #Subsume      : 302
% 7.37/2.81  #Demod        : 810
% 7.37/2.81  #Tautology    : 288
% 7.37/2.81  #SimpNegUnit  : 0
% 7.37/2.81  #BackRed      : 0
% 7.37/2.81  
% 7.37/2.81  #Partial instantiations: 0
% 7.37/2.81  #Strategies tried      : 1
% 7.37/2.81  
% 7.37/2.81  Timing (in seconds)
% 7.37/2.81  ----------------------
% 7.37/2.81  Preprocessing        : 0.47
% 7.37/2.81  Parsing              : 0.25
% 7.37/2.81  CNF conversion       : 0.03
% 7.37/2.81  Main loop            : 1.25
% 7.37/2.81  Inferencing          : 0.41
% 7.37/2.81  Reduction            : 0.48
% 7.37/2.81  Demodulation         : 0.40
% 7.37/2.81  BG Simplification    : 0.04
% 7.37/2.81  Subsumption          : 0.23
% 7.37/2.81  Abstraction          : 0.07
% 7.37/2.81  MUC search           : 0.00
% 7.37/2.81  Cooper               : 0.00
% 7.37/2.81  Total                : 1.76
% 7.37/2.81  Index Insertion      : 0.00
% 7.37/2.81  Index Deletion       : 0.00
% 7.37/2.81  Index Matching       : 0.00
% 7.37/2.81  BG Taut test         : 0.00
%------------------------------------------------------------------------------