TSTP Solution File: SET945+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET945+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 : n003.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 10:57:23 EDT 2023

% Result   : Theorem 7.89s 3.02s
% Output   : CNFRefutation 8.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   41 (   4 unt;  16 typ;   0 def)
%            Number of atoms       :   56 (   2 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   57 (  26   ~;  19   |;   5   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  12   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   50 (;  48   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > disjoint > empty > set_intersection2 > #nlpp > union > #skF_1 > #skF_11 > #skF_6 > #skF_7 > #skF_3 > #skF_10 > #skF_2 > #skF_8 > #skF_9 > #skF_5 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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_8',type,
    '#skF_8': $i ).

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

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

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

tff(f_85,negated_conjecture,
    ~ ! [A,B] :
        ( ! [C] :
            ( in(C,A)
           => disjoint(C,B) )
       => disjoint(union(A),B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).

tff(f_77,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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

tff(f_42,axiom,
    ! [A,B,C] :
      ( ( C = set_intersection2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

tff(f_52,axiom,
    ! [A,B] :
      ( ( B = union(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ? [D] :
              ( in(C,D)
              & in(D,A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

tff(f_63,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

tff(c_54,plain,
    ~ disjoint(union('#skF_10'),'#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_143,plain,
    ! [A_63,B_64] :
      ( in('#skF_9'(A_63,B_64),set_intersection2(A_63,B_64))
      | disjoint(A_63,B_64) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_10,plain,
    ! [D_10,A_5,B_6] :
      ( in(D_10,A_5)
      | ~ in(D_10,set_intersection2(A_5,B_6)) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_168,plain,
    ! [A_63,B_64] :
      ( in('#skF_9'(A_63,B_64),A_63)
      | disjoint(A_63,B_64) ),
    inference(resolution,[status(thm)],[c_143,c_10]) ).

tff(c_8,plain,
    ! [D_10,B_6,A_5] :
      ( in(D_10,B_6)
      | ~ in(D_10,set_intersection2(A_5,B_6)) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_169,plain,
    ! [A_63,B_64] :
      ( in('#skF_9'(A_63,B_64),B_64)
      | disjoint(A_63,B_64) ),
    inference(resolution,[status(thm)],[c_143,c_8]) ).

tff(c_28,plain,
    ! [C_26,A_11] :
      ( in(C_26,'#skF_6'(A_11,union(A_11),C_26))
      | ~ in(C_26,union(A_11)) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_392,plain,
    ! [A_99,C_100] :
      ( in('#skF_6'(A_99,union(A_99),C_100),A_99)
      | ~ in(C_100,union(A_99)) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_56,plain,
    ! [C_40] :
      ( disjoint(C_40,'#skF_11')
      | ~ in(C_40,'#skF_10') ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_523,plain,
    ! [C_114] :
      ( disjoint('#skF_6'('#skF_10',union('#skF_10'),C_114),'#skF_11')
      | ~ in(C_114,union('#skF_10')) ),
    inference(resolution,[status(thm)],[c_392,c_56]) ).

tff(c_360,plain,
    ! [D_96,A_97,B_98] :
      ( in(D_96,set_intersection2(A_97,B_98))
      | ~ in(D_96,B_98)
      | ~ in(D_96,A_97) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_52,plain,
    ! [A_34,B_35,C_38] :
      ( ~ disjoint(A_34,B_35)
      | ~ in(C_38,set_intersection2(A_34,B_35)) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_390,plain,
    ! [A_97,B_98,D_96] :
      ( ~ disjoint(A_97,B_98)
      | ~ in(D_96,B_98)
      | ~ in(D_96,A_97) ),
    inference(resolution,[status(thm)],[c_360,c_52]) ).

tff(c_6818,plain,
    ! [D_410,C_411] :
      ( ~ in(D_410,'#skF_11')
      | ~ in(D_410,'#skF_6'('#skF_10',union('#skF_10'),C_411))
      | ~ in(C_411,union('#skF_10')) ),
    inference(resolution,[status(thm)],[c_523,c_390]) ).

tff(c_6899,plain,
    ! [C_412] :
      ( ~ in(C_412,'#skF_11')
      | ~ in(C_412,union('#skF_10')) ),
    inference(resolution,[status(thm)],[c_28,c_6818]) ).

tff(c_6975,plain,
    ! [A_413] :
      ( ~ in('#skF_9'(A_413,union('#skF_10')),'#skF_11')
      | disjoint(A_413,union('#skF_10')) ),
    inference(resolution,[status(thm)],[c_169,c_6899]) ).

tff(c_6980,plain,
    disjoint('#skF_11',union('#skF_10')),
    inference(resolution,[status(thm)],[c_168,c_6975]) ).

tff(c_48,plain,
    ! [B_33,A_32] :
      ( disjoint(B_33,A_32)
      | ~ disjoint(A_32,B_33) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_6984,plain,
    disjoint(union('#skF_10'),'#skF_11'),
    inference(resolution,[status(thm)],[c_6980,c_48]) ).

tff(c_6989,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_54,c_6984]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.15  % 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
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 16:21:38 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 7.89/3.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.89/3.03  
% 7.89/3.03  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.34/3.08  
% 8.34/3.08  Inference rules
% 8.34/3.08  ----------------------
% 8.34/3.08  #Ref     : 0
% 8.34/3.08  #Sup     : 1781
% 8.34/3.08  #Fact    : 0
% 8.34/3.08  #Define  : 0
% 8.34/3.08  #Split   : 3
% 8.34/3.08  #Chain   : 0
% 8.34/3.08  #Close   : 0
% 8.34/3.08  
% 8.34/3.08  Ordering : KBO
% 8.34/3.08  
% 8.34/3.08  Simplification rules
% 8.34/3.08  ----------------------
% 8.34/3.08  #Subsume      : 770
% 8.34/3.08  #Demod        : 32
% 8.34/3.08  #Tautology    : 81
% 8.34/3.08  #SimpNegUnit  : 3
% 8.34/3.08  #BackRed      : 2
% 8.34/3.08  
% 8.34/3.08  #Partial instantiations: 0
% 8.34/3.08  #Strategies tried      : 1
% 8.34/3.08  
% 8.34/3.08  Timing (in seconds)
% 8.34/3.08  ----------------------
% 8.34/3.08  Preprocessing        : 0.50
% 8.34/3.08  Parsing              : 0.26
% 8.34/3.08  CNF conversion       : 0.04
% 8.34/3.08  Main loop            : 1.49
% 8.34/3.08  Inferencing          : 0.55
% 8.34/3.08  Reduction            : 0.38
% 8.34/3.08  Demodulation         : 0.28
% 8.34/3.08  BG Simplification    : 0.05
% 8.34/3.08  Subsumption          : 0.39
% 8.34/3.08  Abstraction          : 0.06
% 8.34/3.08  MUC search           : 0.00
% 8.34/3.08  Cooper               : 0.00
% 8.34/3.08  Total                : 2.06
% 8.34/3.08  Index Insertion      : 0.00
% 8.34/3.08  Index Deletion       : 0.00
% 8.34/3.08  Index Matching       : 0.00
% 8.34/3.08  BG Taut test         : 0.00
%------------------------------------------------------------------------------