TSTP Solution File: SEU140+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU140+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n027.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 10:57:43 EDT 2023

% Result   : Theorem 7.68s 2.80s
% Output   : CNFRefutation 7.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   51 (  10 unt;  26 typ;   0 def)
%            Number of atoms       :   48 (   7 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   39 (  16   ~;  11   |;   7   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   44 (  20   >;  24   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   6 con; 0-3 aty)
%            Number of variables   :   37 (;  36   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > set_union2 > set_intersection2 > set_difference > #nlpp > empty_set > #skF_11 > #skF_17 > #skF_6 > #skF_15 > #skF_1 > #skF_13 > #skF_10 > #skF_16 > #skF_14 > #skF_12 > #skF_5 > #skF_2 > #skF_9 > #skF_7 > #skF_3 > #skF_8 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

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

tff('#skF_17',type,
    '#skF_17': $i ).

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

tff('#skF_15',type,
    '#skF_15': $i ).

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

tff('#skF_13',type,
    '#skF_13': ( $i * $i ) > $i ).

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

tff('#skF_16',type,
    '#skF_16': $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

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

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

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

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $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_7',type,
    '#skF_7': ( $i * $i * $i ) > $i ).

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

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

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

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

tff(f_245,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & disjoint(B,C) )
       => disjoint(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).

tff(f_205,lemma,
    ! [A,B] :
      ( ~ ( ~ disjoint(A,B)
          & ! [C] :
              ~ ( in(C,A)
                & in(C,B) ) )
      & ~ ( ? [C] :
              ( in(C,A)
              & in(C,B) )
          & disjoint(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).

tff(f_162,lemma,
    ! [A,B] :
      ( subset(A,B)
     => ( set_intersection2(A,B) = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

tff(f_40,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(f_77,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_134,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

tff(c_182,plain,
    ~ disjoint('#skF_15','#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_2339,plain,
    ! [A_234,B_235] :
      ( in('#skF_13'(A_234,B_235),B_235)
      | disjoint(A_234,B_235) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_186,plain,
    subset('#skF_15','#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_996,plain,
    ! [A_188,B_189] :
      ( ( set_intersection2(A_188,B_189) = A_188 )
      | ~ subset(A_188,B_189) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_1036,plain,
    set_intersection2('#skF_15','#skF_16') = '#skF_15',
    inference(resolution,[status(thm)],[c_186,c_996]) ).

tff(c_8,plain,
    ! [B_8,A_7] : ( set_intersection2(B_8,A_7) = set_intersection2(A_7,B_8) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_1048,plain,
    set_intersection2('#skF_16','#skF_15') = '#skF_15',
    inference(superposition,[status(thm),theory(equality)],[c_1036,c_8]) ).

tff(c_1577,plain,
    ! [D_209,A_210,B_211] :
      ( in(D_209,A_210)
      | ~ in(D_209,set_intersection2(A_210,B_211)) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_1586,plain,
    ! [D_209] :
      ( in(D_209,'#skF_16')
      | ~ in(D_209,'#skF_15') ),
    inference(superposition,[status(thm),theory(equality)],[c_1048,c_1577]) ).

tff(c_2361,plain,
    ! [A_234] :
      ( in('#skF_13'(A_234,'#skF_15'),'#skF_16')
      | disjoint(A_234,'#skF_15') ),
    inference(resolution,[status(thm)],[c_2339,c_1586]) ).

tff(c_164,plain,
    ! [A_89,B_90] :
      ( in('#skF_13'(A_89,B_90),A_89)
      | disjoint(A_89,B_90) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_184,plain,
    disjoint('#skF_16','#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_5404,plain,
    ! [A_353,B_354,C_355] :
      ( ~ disjoint(A_353,B_354)
      | ~ in(C_355,B_354)
      | ~ in(C_355,A_353) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_5460,plain,
    ! [C_357] :
      ( ~ in(C_357,'#skF_17')
      | ~ in(C_357,'#skF_16') ),
    inference(resolution,[status(thm)],[c_184,c_5404]) ).

tff(c_7065,plain,
    ! [B_382] :
      ( ~ in('#skF_13'('#skF_17',B_382),'#skF_16')
      | disjoint('#skF_17',B_382) ),
    inference(resolution,[status(thm)],[c_164,c_5460]) ).

tff(c_7074,plain,
    disjoint('#skF_17','#skF_15'),
    inference(resolution,[status(thm)],[c_2361,c_7065]) ).

tff(c_120,plain,
    ! [B_57,A_56] :
      ( disjoint(B_57,A_56)
      | ~ disjoint(A_56,B_57) ),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_7083,plain,
    disjoint('#skF_15','#skF_17'),
    inference(resolution,[status(thm)],[c_7074,c_120]) ).

tff(c_7089,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_182,c_7083]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU140+2 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 12:30:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 7.68/2.80  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.68/2.81  
% 7.68/2.81  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.68/2.84  
% 7.68/2.84  Inference rules
% 7.68/2.84  ----------------------
% 7.68/2.84  #Ref     : 0
% 7.68/2.84  #Sup     : 1782
% 7.68/2.84  #Fact    : 0
% 7.68/2.84  #Define  : 0
% 7.68/2.84  #Split   : 8
% 7.68/2.84  #Chain   : 0
% 7.68/2.84  #Close   : 0
% 7.68/2.84  
% 7.68/2.84  Ordering : KBO
% 7.68/2.84  
% 7.68/2.84  Simplification rules
% 7.68/2.84  ----------------------
% 7.68/2.84  #Subsume      : 488
% 7.68/2.84  #Demod        : 731
% 7.68/2.84  #Tautology    : 864
% 7.68/2.84  #SimpNegUnit  : 48
% 7.68/2.84  #BackRed      : 40
% 7.68/2.84  
% 7.68/2.84  #Partial instantiations: 0
% 7.68/2.84  #Strategies tried      : 1
% 7.68/2.84  
% 7.68/2.84  Timing (in seconds)
% 7.68/2.84  ----------------------
% 7.68/2.84  Preprocessing        : 0.62
% 7.68/2.84  Parsing              : 0.32
% 7.68/2.84  CNF conversion       : 0.06
% 7.68/2.84  Main loop            : 1.15
% 7.68/2.84  Inferencing          : 0.35
% 7.68/2.84  Reduction            : 0.43
% 7.68/2.84  Demodulation         : 0.31
% 7.68/2.84  BG Simplification    : 0.05
% 7.68/2.84  Subsumption          : 0.23
% 7.68/2.84  Abstraction          : 0.04
% 7.68/2.84  MUC search           : 0.00
% 7.68/2.84  Cooper               : 0.00
% 7.68/2.84  Total                : 1.81
% 7.68/2.84  Index Insertion      : 0.00
% 7.68/2.84  Index Deletion       : 0.00
% 7.68/2.84  Index Matching       : 0.00
% 7.68/2.84  BG Taut test         : 0.00
%------------------------------------------------------------------------------