TSTP Solution File: SEU102+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU102+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 : n022.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 10:57:36 EDT 2023

% Result   : Theorem 5.43s 2.27s
% Output   : CNFRefutation 5.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   66 (  14 unt;  34 typ;   0 def)
%            Number of atoms       :   82 (  14 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   84 (  34   ~;  38   |;   8   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  26   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-3 aty)
%            Number of variables   :   35 (;  35   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > prebool_difference > set_intersection2 > set_difference > #nlpp > powerset > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_1 > #skF_5 > #skF_10 > #skF_13 > #skF_2 > #skF_3 > #skF_8 > #skF_6 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(powerset,type,
    powerset: $i > $i ).

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

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

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

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

tff(f_56,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(f_191,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( ~ empty(C)
          & preboolean(C) )
       => ( ( element(A,C)
            & element(B,C) )
         => element(set_intersection2(A,B),C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finsub_1) ).

tff(f_211,axiom,
    ! [A,B] : ( set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).

tff(f_177,axiom,
    ! [A,B,C] :
      ( ( ~ empty(A)
        & preboolean(A)
        & element(B,A)
        & element(C,A) )
     => ( prebool_difference(A,B,C) = set_difference(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).

tff(f_67,axiom,
    ! [A,B,C] :
      ( ( ~ empty(A)
        & preboolean(A)
        & element(B,A)
        & element(C,A) )
     => element(prebool_difference(A,B,C),A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).

tff(c_14,plain,
    ! [B_10,A_9] : ( set_intersection2(B_10,A_9) = set_intersection2(A_9,B_10) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_94,plain,
    ~ element(set_intersection2('#skF_11','#skF_12'),'#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_129,plain,
    ~ element(set_intersection2('#skF_12','#skF_11'),'#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_94]) ).

tff(c_98,plain,
    element('#skF_11','#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_116,plain,
    ! [A_48,B_49] : ( set_difference(A_48,set_difference(A_48,B_49)) = set_intersection2(A_48,B_49) ),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_102,plain,
    ~ empty('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_100,plain,
    preboolean('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_96,plain,
    element('#skF_12','#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_773,plain,
    ! [A_163,B_164,C_165] :
      ( ( prebool_difference(A_163,B_164,C_165) = set_difference(B_164,C_165) )
      | ~ element(C_165,A_163)
      | ~ element(B_164,A_163)
      | ~ preboolean(A_163)
      | empty(A_163) ),
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_791,plain,
    ! [B_164] :
      ( ( prebool_difference('#skF_13',B_164,'#skF_12') = set_difference(B_164,'#skF_12') )
      | ~ element(B_164,'#skF_13')
      | ~ preboolean('#skF_13')
      | empty('#skF_13') ),
    inference(resolution,[status(thm)],[c_96,c_773]) ).

tff(c_815,plain,
    ! [B_164] :
      ( ( prebool_difference('#skF_13',B_164,'#skF_12') = set_difference(B_164,'#skF_12') )
      | ~ element(B_164,'#skF_13')
      | empty('#skF_13') ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_791]) ).

tff(c_941,plain,
    ! [B_168] :
      ( ( prebool_difference('#skF_13',B_168,'#skF_12') = set_difference(B_168,'#skF_12') )
      | ~ element(B_168,'#skF_13') ),
    inference(negUnitSimplification,[status(thm)],[c_102,c_815]) ).

tff(c_970,plain,
    prebool_difference('#skF_13','#skF_11','#skF_12') = set_difference('#skF_11','#skF_12'),
    inference(resolution,[status(thm)],[c_98,c_941]) ).

tff(c_16,plain,
    ! [A_11,B_12,C_13] :
      ( element(prebool_difference(A_11,B_12,C_13),A_11)
      | ~ element(C_13,A_11)
      | ~ element(B_12,A_11)
      | ~ preboolean(A_11)
      | empty(A_11) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_1006,plain,
    ( element(set_difference('#skF_11','#skF_12'),'#skF_13')
    | ~ element('#skF_12','#skF_13')
    | ~ element('#skF_11','#skF_13')
    | ~ preboolean('#skF_13')
    | empty('#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_970,c_16]) ).

tff(c_1010,plain,
    ( element(set_difference('#skF_11','#skF_12'),'#skF_13')
    | empty('#skF_13') ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_98,c_96,c_1006]) ).

tff(c_1011,plain,
    element(set_difference('#skF_11','#skF_12'),'#skF_13'),
    inference(negUnitSimplification,[status(thm)],[c_102,c_1010]) ).

tff(c_90,plain,
    ! [A_35,B_36,C_37] :
      ( ( prebool_difference(A_35,B_36,C_37) = set_difference(B_36,C_37) )
      | ~ element(C_37,A_35)
      | ~ element(B_36,A_35)
      | ~ preboolean(A_35)
      | empty(A_35) ),
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_1023,plain,
    ! [B_36] :
      ( ( prebool_difference('#skF_13',B_36,set_difference('#skF_11','#skF_12')) = set_difference(B_36,set_difference('#skF_11','#skF_12')) )
      | ~ element(B_36,'#skF_13')
      | ~ preboolean('#skF_13')
      | empty('#skF_13') ),
    inference(resolution,[status(thm)],[c_1011,c_90]) ).

tff(c_1029,plain,
    ! [B_36] :
      ( ( prebool_difference('#skF_13',B_36,set_difference('#skF_11','#skF_12')) = set_difference(B_36,set_difference('#skF_11','#skF_12')) )
      | ~ element(B_36,'#skF_13')
      | empty('#skF_13') ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_1023]) ).

tff(c_1131,plain,
    ! [B_171] :
      ( ( prebool_difference('#skF_13',B_171,set_difference('#skF_11','#skF_12')) = set_difference(B_171,set_difference('#skF_11','#skF_12')) )
      | ~ element(B_171,'#skF_13') ),
    inference(negUnitSimplification,[status(thm)],[c_102,c_1029]) ).

tff(c_1137,plain,
    ! [B_171] :
      ( element(set_difference(B_171,set_difference('#skF_11','#skF_12')),'#skF_13')
      | ~ element(set_difference('#skF_11','#skF_12'),'#skF_13')
      | ~ element(B_171,'#skF_13')
      | ~ preboolean('#skF_13')
      | empty('#skF_13')
      | ~ element(B_171,'#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_1131,c_16]) ).

tff(c_1143,plain,
    ! [B_171] :
      ( element(set_difference(B_171,set_difference('#skF_11','#skF_12')),'#skF_13')
      | empty('#skF_13')
      | ~ element(B_171,'#skF_13') ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_1011,c_1137]) ).

tff(c_1356,plain,
    ! [B_194] :
      ( element(set_difference(B_194,set_difference('#skF_11','#skF_12')),'#skF_13')
      | ~ element(B_194,'#skF_13') ),
    inference(negUnitSimplification,[status(thm)],[c_102,c_1143]) ).

tff(c_1377,plain,
    ( element(set_intersection2('#skF_11','#skF_12'),'#skF_13')
    | ~ element('#skF_11','#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_116,c_1356]) ).

tff(c_1395,plain,
    element(set_intersection2('#skF_12','#skF_11'),'#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_98,c_14,c_1377]) ).

tff(c_1397,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_129,c_1395]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU102+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/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
% 0.13/0.34  % Computer : n022.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 11:32:03 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 5.43/2.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.43/2.27  
% 5.43/2.27  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.43/2.30  
% 5.43/2.30  Inference rules
% 5.43/2.30  ----------------------
% 5.43/2.30  #Ref     : 0
% 5.43/2.30  #Sup     : 280
% 5.43/2.30  #Fact    : 0
% 5.43/2.30  #Define  : 0
% 5.43/2.30  #Split   : 5
% 5.43/2.30  #Chain   : 0
% 5.43/2.30  #Close   : 0
% 5.43/2.30  
% 5.43/2.30  Ordering : KBO
% 5.43/2.30  
% 5.43/2.30  Simplification rules
% 5.43/2.30  ----------------------
% 5.43/2.30  #Subsume      : 17
% 5.43/2.30  #Demod        : 175
% 5.43/2.30  #Tautology    : 146
% 5.43/2.30  #SimpNegUnit  : 52
% 5.43/2.30  #BackRed      : 12
% 5.43/2.30  
% 5.43/2.30  #Partial instantiations: 0
% 5.43/2.30  #Strategies tried      : 1
% 5.43/2.30  
% 5.43/2.30  Timing (in seconds)
% 5.43/2.30  ----------------------
% 5.43/2.31  Preprocessing        : 0.59
% 5.43/2.31  Parsing              : 0.30
% 5.43/2.31  CNF conversion       : 0.05
% 5.43/2.31  Main loop            : 0.67
% 5.43/2.31  Inferencing          : 0.24
% 5.43/2.31  Reduction            : 0.22
% 5.43/2.31  Demodulation         : 0.15
% 5.43/2.31  BG Simplification    : 0.03
% 5.43/2.31  Subsumption          : 0.14
% 5.43/2.31  Abstraction          : 0.03
% 5.43/2.31  MUC search           : 0.00
% 5.43/2.31  Cooper               : 0.00
% 5.43/2.31  Total                : 1.31
% 5.43/2.31  Index Insertion      : 0.00
% 5.43/2.31  Index Deletion       : 0.00
% 5.43/2.31  Index Matching       : 0.00
% 5.43/2.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------