TSTP Solution File: SEU107+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU107+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 : n031.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 10:57:37 EDT 2023

% Result   : Theorem 7.47s 2.75s
% Output   : CNFRefutation 7.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   65 (  15 unt;  31 typ;   0 def)
%            Number of atoms       :   81 (  10 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   79 (  32   ~;  34   |;   7   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  25   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-3 aty)
%            Number of variables   :   41 (;  39   !;   2   ?;   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_difference > #nlpp > powerset > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_1 > #skF_5 > #skF_10 > #skF_2 > #skF_3 > #skF_8 > #skF_6

%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_2',type,
    '#skF_2': $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(f_175,negated_conjecture,
    ~ ! [A] :
        ( ( ~ empty(A)
          & preboolean(A) )
       => in(empty_set,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).

tff(f_68,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

tff(f_167,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_103,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_214,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_189,axiom,
    ! [A,B] :
      ( ( set_difference(A,B) = empty_set )
    <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

tff(f_165,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).

tff(f_65,axiom,
    ! [A,B,C] :
      ( ( ~ empty(A)
        & preboolean(A)
        & element(B,A)
        & element(C,A) )
     => element(prebool_difference(A,B,C),A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).

tff(f_185,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(c_90,plain,
    ~ empty('#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_88,plain,
    preboolean('#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_16,plain,
    ! [A_12] : element('#skF_1'(A_12),A_12),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_84,plain,
    ! [A_30] : subset(A_30,A_30),
    inference(cnfTransformation,[status(thm)],[f_167]) ).

tff(c_42,plain,
    empty('#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_150,plain,
    ! [A_69] :
      ( ( empty_set = A_69 )
      | ~ empty(A_69) ),
    inference(cnfTransformation,[status(thm)],[f_214]) ).

tff(c_167,plain,
    empty_set = '#skF_5',
    inference(resolution,[status(thm)],[c_42,c_150]) ).

tff(c_98,plain,
    ! [A_36,B_37] :
      ( ( set_difference(A_36,B_37) = empty_set )
      | ~ subset(A_36,B_37) ),
    inference(cnfTransformation,[status(thm)],[f_189]) ).

tff(c_312,plain,
    ! [A_104,B_105] :
      ( ( set_difference(A_104,B_105) = '#skF_5' )
      | ~ subset(A_104,B_105) ),
    inference(demodulation,[status(thm),theory(equality)],[c_167,c_98]) ).

tff(c_333,plain,
    ! [A_30] : ( set_difference(A_30,A_30) = '#skF_5' ),
    inference(resolution,[status(thm)],[c_84,c_312]) ).

tff(c_729,plain,
    ! [A_147,B_148,C_149] :
      ( ( prebool_difference(A_147,B_148,C_149) = set_difference(B_148,C_149) )
      | ~ element(C_149,A_147)
      | ~ element(B_148,A_147)
      | ~ preboolean(A_147)
      | empty(A_147) ),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_934,plain,
    ! [A_175,B_176] :
      ( ( prebool_difference(A_175,B_176,'#skF_1'(A_175)) = set_difference(B_176,'#skF_1'(A_175)) )
      | ~ element(B_176,A_175)
      | ~ preboolean(A_175)
      | empty(A_175) ),
    inference(resolution,[status(thm)],[c_16,c_729]) ).

tff(c_14,plain,
    ! [A_9,B_10,C_11] :
      ( element(prebool_difference(A_9,B_10,C_11),A_9)
      | ~ element(C_11,A_9)
      | ~ element(B_10,A_9)
      | ~ preboolean(A_9)
      | empty(A_9) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_940,plain,
    ! [B_176,A_175] :
      ( element(set_difference(B_176,'#skF_1'(A_175)),A_175)
      | ~ element('#skF_1'(A_175),A_175)
      | ~ element(B_176,A_175)
      | ~ preboolean(A_175)
      | empty(A_175)
      | ~ element(B_176,A_175)
      | ~ preboolean(A_175)
      | empty(A_175) ),
    inference(superposition,[status(thm),theory(equality)],[c_934,c_14]) ).

tff(c_3153,plain,
    ! [B_350,A_351] :
      ( element(set_difference(B_350,'#skF_1'(A_351)),A_351)
      | ~ element(B_350,A_351)
      | ~ preboolean(A_351)
      | empty(A_351) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_940]) ).

tff(c_3237,plain,
    ! [A_351] :
      ( element('#skF_5',A_351)
      | ~ element('#skF_1'(A_351),A_351)
      | ~ preboolean(A_351)
      | empty(A_351) ),
    inference(superposition,[status(thm),theory(equality)],[c_333,c_3153]) ).

tff(c_3292,plain,
    ! [A_352] :
      ( element('#skF_5',A_352)
      | ~ preboolean(A_352)
      | empty(A_352) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_3237]) ).

tff(c_547,plain,
    ! [A_120,B_121] :
      ( in(A_120,B_121)
      | empty(B_121)
      | ~ element(A_120,B_121) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_86,plain,
    ~ in(empty_set,'#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_170,plain,
    ~ in('#skF_5','#skF_11'),
    inference(demodulation,[status(thm),theory(equality)],[c_167,c_86]) ).

tff(c_558,plain,
    ( empty('#skF_11')
    | ~ element('#skF_5','#skF_11') ),
    inference(resolution,[status(thm)],[c_547,c_170]) ).

tff(c_564,plain,
    ~ element('#skF_5','#skF_11'),
    inference(negUnitSimplification,[status(thm)],[c_90,c_558]) ).

tff(c_3329,plain,
    ( ~ preboolean('#skF_11')
    | empty('#skF_11') ),
    inference(resolution,[status(thm)],[c_3292,c_564]) ).

tff(c_3360,plain,
    empty('#skF_11'),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_3329]) ).

tff(c_3362,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_90,c_3360]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SEU107+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15  % 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
% 0.16/0.37  % Computer : n031.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 12:18:14 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 7.47/2.75  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.47/2.76  
% 7.47/2.76  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.47/2.79  
% 7.47/2.79  Inference rules
% 7.47/2.79  ----------------------
% 7.47/2.79  #Ref     : 5
% 7.47/2.79  #Sup     : 737
% 7.47/2.79  #Fact    : 0
% 7.47/2.79  #Define  : 0
% 7.47/2.79  #Split   : 3
% 7.47/2.79  #Chain   : 0
% 7.47/2.79  #Close   : 0
% 7.47/2.79  
% 7.47/2.79  Ordering : KBO
% 7.47/2.79  
% 7.47/2.79  Simplification rules
% 7.47/2.79  ----------------------
% 7.47/2.79  #Subsume      : 201
% 7.47/2.79  #Demod        : 212
% 7.47/2.79  #Tautology    : 179
% 7.47/2.79  #SimpNegUnit  : 91
% 7.47/2.79  #BackRed      : 14
% 7.47/2.79  
% 7.47/2.79  #Partial instantiations: 0
% 7.47/2.79  #Strategies tried      : 1
% 7.47/2.79  
% 7.47/2.79  Timing (in seconds)
% 7.47/2.79  ----------------------
% 7.47/2.79  Preprocessing        : 0.56
% 7.47/2.79  Parsing              : 0.30
% 7.47/2.79  CNF conversion       : 0.04
% 7.47/2.79  Main loop            : 1.08
% 7.47/2.79  Inferencing          : 0.38
% 7.47/2.79  Reduction            : 0.31
% 7.47/2.79  Demodulation         : 0.20
% 7.47/2.79  BG Simplification    : 0.04
% 7.47/2.79  Subsumption          : 0.28
% 7.47/2.79  Abstraction          : 0.04
% 7.47/2.79  MUC search           : 0.00
% 7.47/2.79  Cooper               : 0.00
% 7.47/2.79  Total                : 1.69
% 7.47/2.79  Index Insertion      : 0.00
% 7.47/2.79  Index Deletion       : 0.00
% 7.47/2.79  Index Matching       : 0.00
% 7.47/2.79  BG Taut test         : 0.00
%------------------------------------------------------------------------------