TSTP Solution File: DAT036_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT036_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n021.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 10:37:01 EDT 2023

% Result   : Theorem 6.33s 2.55s
% Output   : CNFRefutation 6.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   63 (  31 unt;  11 typ;   0 def)
%            Number of atoms       :   74 (  36 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   42 (  20   ~;  16   |;   0   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number arithmetic     :   95 (  21 atm;  24 fun;  26 num;  24 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :   49 (;  49   !;   0   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty > #skF_1

%Foreground sorts:
tff(collection,type,
    collection: $tType ).

%Background operators:
tff('#skE_2',type,
    '#skE_2': $int ).

tff('#skE_1',type,
    '#skE_1': $int ).

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

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

%Foreground operators:
tff(empty,type,
    empty: collection ).

tff(count,type,
    count: collection > $int ).

tff('#skF_1',type,
    '#skF_1': collection ).

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

tff(remove,type,
    remove: ( $int * collection ) > collection ).

tff(add,type,
    add: ( $int * collection ) > collection ).

tff(f_142,negated_conjecture,
    ~ ! [U: collection,Va: $int,Wa: $int] :
        ( $greater(Wa,0)
       => $greatereq($sum(count(U),Wa),count(add(Va,add(Va,U)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_71,axiom,
    ! [Za: $int,X1: collection,X2a: $int] :
      ( ( in(Za,X1)
        | ( Za = X2a ) )
    <=> in(Za,add(X2a,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4) ).

tff(f_122,axiom,
    ! [X10a: $int,X11: collection] :
      ( in(X10a,X11)
    <=> ( count(add(X10a,X11)) = count(X11) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4) ).

tff(f_135,axiom,
    ! [X16a: $int,X17: collection] :
      ( in(X16a,X17)
     => ( X17 = add(X16a,remove(X16a,X17)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7) ).

tff(f_126,axiom,
    ! [X12a: $int,X13: collection] :
      ( in(X12a,X13)
    <=> ( count(remove(X12a,X13)) = $difference(count(X13),1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5) ).

tff(f_109,axiom,
    ! [X6: collection] : $greatereq(count(X6),0),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax1) ).

tff(f_118,axiom,
    ! [X8a: $int,X9: collection] :
      ( ~ in(X8a,X9)
    <=> ( count(add(X8a,X9)) = $sum(count(X9),1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3) ).

tff(c_47,plain,
    ~ $greatereq($sum(count('#skF_1'),'#skF_3'),count(add('#skF_2',add('#skF_2','#skF_1')))),
    inference(cnfTransformation,[status(thm)],[f_142]) ).

tff(c_55,plain,
    $less($sum('#skF_3',count('#skF_1')),count(add('#skF_2',add('#skF_2','#skF_1')))),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).

tff(c_108,plain,
    count('#skF_1') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_55]) ).

tff(c_72,plain,
    ! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_251,plain,
    ! [X10_60a: $int,X11_61: collection] :
      ( ( count(add(X10_60a,X11_61)) = count(X11_61) )
      | ~ in(X10_60a,X11_61) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_414,plain,
    ! [X2_78a: $int,X1_79: collection] : ( count(add(X2_78a,add(X2_78a,X1_79))) = count(add(X2_78a,X1_79)) ),
    inference(resolution,[status(thm)],[c_72,c_251]) ).

tff(c_111,plain,
    count(add('#skF_2',add('#skF_2','#skF_1'))) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_55]) ).

tff(c_439,plain,
    count(add('#skF_2','#skF_1')) = '#skE_2',
    inference(superposition,[status(thm),theory(equality)],[c_414,c_111]) ).

tff(c_442,plain,
    count(add('#skF_2','#skF_1')) = '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_439]) ).

tff(c_61,plain,
    ! [X10_16a: $int,X11_17: collection] :
      ( in(X10_16a,X11_17)
      | ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_272,plain,
    ! [X16_62a: $int,X17_63: collection] :
      ( ( add(X16_62a,remove(X16_62a,X17_63)) = X17_63 )
      | ~ in(X16_62a,X17_63) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_288,plain,
    ! [X10_16a: $int,X11_17: collection] :
      ( ( add(X10_16a,remove(X10_16a,X11_17)) = X11_17 )
      | ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
    inference(resolution,[status(thm)],[c_61,c_272]) ).

tff(c_35,plain,
    ! [X12_18a: $int,X13_19: collection] :
      ( ( count(remove(X12_18a,X13_19)) = $difference(count(X13_19),1) )
      | ~ in(X12_18a,X13_19) ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_702,plain,
    ! [X12_94a: $int,X13_95: collection] :
      ( ( count(remove(X12_94a,X13_95)) = $sum($uminus(1),count(X13_95)) )
      | ~ in(X12_94a,X13_95) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).

tff(c_1828,plain,
    ! [X2_147a: $int,X1_148: collection] : ( count(remove(X2_147a,add(X2_147a,X1_148))) = $sum($uminus(1),count(add(X2_147a,X1_148))) ),
    inference(resolution,[status(thm)],[c_72,c_702]) ).

tff(c_18,plain,
    ! [X6_12: collection] : $greatereq(count(X6_12),0),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_67,plain,
    ! [X6_12: collection] : ~ $less(count(X6_12),0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_18]) ).

tff(c_1860,plain,
    ! [X2_147a: $int,X1_148: collection] : ~ $less($sum($uminus(1),count(add(X2_147a,X1_148))),0),
    inference(superposition,[status(thm),theory(equality)],[c_1828,c_67]) ).

tff(c_1932,plain,
    ! [X2_149a: $int,X1_150: collection] : ~ $less(count(add(X2_149a,X1_150)),1),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1860]) ).

tff(c_2209,plain,
    ! [X11_175: collection,X10_176a: $int] :
      ( ~ $less(count(X11_175),1)
      | ( count(add(X10_176a,X11_175)) != count(X11_175) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_288,c_1932]) ).

tff(c_2227,plain,
    ( ~ $less(count('#skF_1'),1)
    | ( count('#skF_1') != '#skE_2' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_442,c_2209]) ).

tff(c_2246,plain,
    ( ~ $less('#skE_1',1)
    | ( '#skE_2' != '#skE_1' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_108,c_2227]) ).

tff(c_2291,plain,
    '#skE_2' != '#skE_1',
    inference(splitLeft,[status(thm)],[c_2246]) ).

tff(c_452,plain,
    count(add('#skF_2','#skF_1')) = '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_439]) ).

tff(c_25,plain,
    ! [X8_14a: $int,X9_15: collection] :
      ( ( count(add(X8_14a,X9_15)) = $sum(count(X9_15),1) )
      | in(X8_14a,X9_15) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_503,plain,
    ! [X8_85a: $int,X9_86: collection] :
      ( ( count(add(X8_85a,X9_86)) = $sum(1,count(X9_86)) )
      | in(X8_85a,X9_86) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).

tff(c_62,plain,
    ! [X10_16a: $int,X11_17: collection] :
      ( ( count(add(X10_16a,X11_17)) = count(X11_17) )
      | ~ in(X10_16a,X11_17) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_3500,plain,
    ! [X8_211a: $int,X9_212: collection] :
      ( ( count(add(X8_211a,X9_212)) = count(X9_212) )
      | ( count(add(X8_211a,X9_212)) = $sum(1,count(X9_212)) ) ),
    inference(resolution,[status(thm)],[c_503,c_62]) ).

tff(c_3545,plain,
    ( ( $sum(1,count('#skF_1')) = '#skE_2' )
    | ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3500,c_442]) ).

tff(c_3618,plain,
    ( ( '#skE_2' = $sum(1,'#skE_1') )
    | ( '#skE_2' = '#skE_1' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_452,c_108,c_108,c_3545]) ).

tff(c_3620,plain,
    '#skE_2' = $sum(1,'#skE_1'),
    inference(negUnitSimplification,[status(thm)],[c_2291,c_3618]) ).

tff(c_104,plain,
    count(add('#skF_2',add('#skF_2','#skF_1'))) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_55]) ).

tff(c_103,plain,
    count('#skF_1') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_55]) ).

tff(c_77,plain,
    $less($sum('#skF_3',count('#skF_1')),count(add('#skF_2',add('#skF_2','#skF_1')))),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).

tff(c_106,plain,
    $less($sum('#skF_3','#skE_1'),'#skE_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_104,c_103,c_77]) ).

tff(c_113,plain,
    $less($sum('#skE_1','#skF_3'),'#skE_2'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_106]) ).

tff(c_3682,plain,
    $less($sum('#skE_1','#skF_3'),$sum(1,'#skE_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_3620,c_113]) ).

tff(c_3691,plain,
    $less('#skF_3',1),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3682]) ).

tff(c_49,plain,
    $greater('#skF_3',0),
    inference(cnfTransformation,[status(thm)],[f_142]) ).

tff(c_51,plain,
    $less(0,'#skF_3'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_49]) ).

tff(c_3692,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_3691,c_51]) ).

tff(c_3696,plain,
    '#skE_2' = '#skE_1',
    inference(splitRight,[status(thm)],[c_2246]) ).

tff(c_3709,plain,
    $less($sum('#skE_1','#skF_3'),'#skE_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_3696,c_113]) ).

tff(c_3719,plain,
    $less('#skF_3',0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3709]) ).

tff(c_3793,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_3719,c_51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : DAT036_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14  % 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
% 0.17/0.35  % Computer : n021.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 13:12:36 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 6.33/2.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.33/2.56  
% 6.33/2.56  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.58/2.64  
% 6.58/2.64  Inference rules
% 6.58/2.64  ----------------------
% 6.58/2.64  #Ref     : 0
% 6.58/2.64  #Sup     : 734
% 6.58/2.64  #Fact    : 1
% 6.58/2.64  #Define  : 2
% 6.58/2.64  #Split   : 11
% 6.58/2.64  #Chain   : 0
% 6.58/2.64  #Close   : 2
% 6.58/2.64  
% 6.58/2.64  Ordering : LPO
% 6.58/2.64  
% 6.58/2.64  Simplification rules
% 6.58/2.64  ----------------------
% 6.58/2.64  #Subsume      : 192
% 6.58/2.64  #Demod        : 370
% 6.58/2.64  #Tautology    : 265
% 6.58/2.64  #SimpNegUnit  : 16
% 6.58/2.64  #BackRed      : 11
% 6.58/2.64  
% 6.58/2.64  #Partial instantiations: 0
% 6.58/2.64  #Strategies tried      : 1
% 6.58/2.64  
% 6.58/2.64  Timing (in seconds)
% 6.58/2.64  ----------------------
% 6.58/2.64  Preprocessing        : 0.58
% 6.58/2.64  Parsing              : 0.31
% 6.58/2.64  CNF conversion       : 0.03
% 6.58/2.65  Main loop            : 0.93
% 6.58/2.65  Inferencing          : 0.28
% 6.58/2.65  Reduction            : 0.25
% 6.58/2.65  Demodulation         : 0.18
% 6.58/2.65  BG Simplification    : 0.12
% 6.58/2.65  Subsumption          : 0.18
% 6.58/2.65  Abstraction          : 0.04
% 6.58/2.65  MUC search           : 0.00
% 6.58/2.65  Cooper               : 0.03
% 6.58/2.65  Total                : 1.62
% 6.58/2.65  Index Insertion      : 0.00
% 6.58/2.65  Index Deletion       : 0.00
% 6.58/2.65  Index Matching       : 0.00
% 6.58/2.65  BG Taut test         : 0.00
%------------------------------------------------------------------------------