TSTP Solution File: DAT047_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT047_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 : n029.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 10:37:02 EDT 2023

% Result   : Theorem 4.59s 2.43s
% Output   : CNFRefutation 4.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   53 (  25 unt;   8 typ;   0 def)
%            Number of atoms       :   66 (  47 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   43 (  22   ~;  15   |;   0   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number arithmetic     :   94 (   0 atm;  15 fun;  53 num;  26 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (   6 usr;   7 con; 0-2 aty)
%            Number of variables   :   48 (;  48   !;   0   ?;  48   :)

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

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

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

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

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

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

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

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

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

tff(f_139,negated_conjecture,
    count(add(5,remove(3,add(3,empty)))) != 1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_113,axiom,
    ! [X7: collection] :
      ( ( X7 = empty )
    <=> ( count(X7) = 0 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2) ).

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(f_60,axiom,
    ! [Ua: $int] : ~ in(Ua,empty),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1) ).

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_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_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(c_48,plain,
    count(add(5,remove(3,add(3,empty)))) != 1,
    inference(cnfTransformation,[status(thm)],[f_139]) ).

tff(c_105,plain,
    count(add(5,remove(3,add(3,empty)))) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_48]) ).

tff(c_109,plain,
    '#skE_1' != 1,
    inference(demodulation,[status(thm),theory(equality)],[c_105,c_48]) ).

tff(c_59,plain,
    count(empty) = 0,
    inference(cnfTransformation,[status(thm)],[f_113]) ).

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_360,plain,
    ! [X8_62a: $int,X9_63: collection] :
      ( ( count(add(X8_62a,X9_63)) = $sum(1,count(X9_63)) )
      | in(X8_62a,X9_63) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).

tff(c_69,plain,
    ! [U_1a: $int] : ~ in(U_1a,empty),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_385,plain,
    ! [X8_62a: $int] : ( count(add(X8_62a,empty)) = $sum(1,count(empty)) ),
    inference(resolution,[status(thm)],[c_360,c_69]) ).

tff(c_399,plain,
    ! [X8_62a: $int] : ( count(add(X8_62a,empty)) = $sum(1,0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_59,c_385]) ).

tff(c_401,plain,
    ! [X8_62a: $int] : ( count(add(X8_62a,empty)) = 1 ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_399]) ).

tff(c_108,plain,
    count(add(5,remove(3,add(3,empty)))) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_48]) ).

tff(c_54,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_195,plain,
    ! [X16_45a: $int,X17_46: collection] :
      ( ( add(X16_45a,remove(X16_45a,X17_46)) = X17_46 )
      | ~ in(X16_45a,X17_46) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_706,plain,
    ! [X10_83a: $int,X11_84: collection] :
      ( ( add(X10_83a,remove(X10_83a,X11_84)) = X11_84 )
      | ( count(add(X10_83a,X11_84)) != count(X11_84) ) ),
    inference(resolution,[status(thm)],[c_54,c_195]) ).

tff(c_65,plain,
    ! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_217,plain,
    ! [X10_48a: $int,X11_49: collection] :
      ( ( count(add(X10_48a,X11_49)) = count(X11_49) )
      | ~ in(X10_48a,X11_49) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_423,plain,
    ! [X2_65a: $int,X1_66: collection] : ( count(add(X2_65a,add(X2_65a,X1_66))) = count(add(X2_65a,X1_66)) ),
    inference(resolution,[status(thm)],[c_65,c_217]) ).

tff(c_58,plain,
    ! [X7_13: collection] :
      ( ( empty = X7_13 )
      | ( count(X7_13) != 0 ) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_552,plain,
    ! [X2_75a: $int,X1_76: collection] :
      ( ( add(X2_75a,add(X2_75a,X1_76)) = empty )
      | ( count(add(X2_75a,X1_76)) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_423,c_58]) ).

tff(c_579,plain,
    ! [X2_75a: $int,X1_76: collection] :
      ( in(X2_75a,empty)
      | ( count(add(X2_75a,X1_76)) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_552,c_65]) ).

tff(c_604,plain,
    ! [X2_75a: $int,X1_76: collection] : ( count(add(X2_75a,X1_76)) != 0 ),
    inference(negUnitSimplification,[status(thm)],[c_69,c_579]) ).

tff(c_765,plain,
    ! [X11_85: collection,X10_86a: $int] :
      ( ( count(X11_85) != 0 )
      | ( count(add(X10_86a,X11_85)) != count(X11_85) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_706,c_604]) ).

tff(c_785,plain,
    ( ( count(remove(3,add(3,empty))) != 0 )
    | ( count(remove(3,add(3,empty))) != '#skE_1' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_108,c_765]) ).

tff(c_1066,plain,
    count(remove(3,add(3,empty))) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_785]) ).

tff(c_1100,plain,
    ( ( remove(3,add(3,empty)) = empty )
    | ( '#skE_2' != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1066,c_58]) ).

tff(c_1109,plain,
    '#skE_2' != 0,
    inference(splitLeft,[status(thm)],[c_1100]) ).

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_610,plain,
    ! [X12_77a: $int,X13_78: collection] :
      ( ( count(remove(X12_77a,X13_78)) = $sum($uminus(1),count(X13_78)) )
      | ~ in(X12_77a,X13_78) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).

tff(c_2495,plain,
    ! [X2_155a: $int,X1_156: collection] : ( count(remove(X2_155a,add(X2_155a,X1_156))) = $sum($uminus(1),count(add(X2_155a,X1_156))) ),
    inference(resolution,[status(thm)],[c_65,c_610]) ).

tff(c_2529,plain,
    $sum($uminus(1),count(add(3,empty))) = '#skE_2',
    inference(superposition,[status(thm),theory(equality)],[c_2495,c_1066]) ).

tff(c_2596,plain,
    '#skE_2' = $sum($uminus(1),1),
    inference(demodulation,[status(thm),theory(equality)],[c_401,c_2529]) ).

tff(c_2598,plain,
    '#skE_2' = 0,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2596]) ).

tff(c_2622,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1109,c_2598]) ).

tff(c_2625,plain,
    remove(3,add(3,empty)) = empty,
    inference(splitRight,[status(thm)],[c_1100]) ).

tff(c_2639,plain,
    count(add(5,empty)) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_2625,c_108]) ).

tff(c_2640,plain,
    '#skE_1' = 1,
    inference(demodulation,[status(thm),theory(equality)],[c_401,c_2639]) ).

tff(c_2642,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_109,c_2640]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : DAT047_1 : TPTP v8.1.2. Released v5.0.0.
% 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
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.34  % CPULimit : 300
% 0.20/0.34  % WCLimit  : 300
% 0.20/0.34  % DateTime : Thu Aug  3 13:30:52 EDT 2023
% 0.20/0.34  % CPUTime  : 
% 4.59/2.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.59/2.44  
% 4.59/2.44  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.59/2.47  
% 4.59/2.47  Inference rules
% 4.59/2.47  ----------------------
% 4.59/2.47  #Ref     : 0
% 4.59/2.47  #Sup     : 525
% 4.59/2.47  #Fact    : 0
% 4.59/2.47  #Define  : 2
% 4.59/2.47  #Split   : 9
% 4.59/2.47  #Chain   : 0
% 4.59/2.47  #Close   : 0
% 4.59/2.47  
% 4.59/2.47  Ordering : LPO
% 4.59/2.47  
% 4.59/2.47  Simplification rules
% 4.59/2.47  ----------------------
% 4.59/2.47  #Subsume      : 153
% 4.59/2.47  #Demod        : 287
% 4.59/2.47  #Tautology    : 204
% 4.59/2.47  #SimpNegUnit  : 26
% 4.59/2.47  #BackRed      : 5
% 4.59/2.47  
% 4.59/2.47  #Partial instantiations: 0
% 4.59/2.47  #Strategies tried      : 1
% 4.59/2.47  
% 4.59/2.47  Timing (in seconds)
% 4.59/2.47  ----------------------
% 4.59/2.47  Preprocessing        : 0.58
% 4.59/2.47  Parsing              : 0.32
% 4.59/2.47  CNF conversion       : 0.03
% 4.59/2.47  Main loop            : 0.76
% 4.59/2.47  Inferencing          : 0.24
% 4.59/2.47  Reduction            : 0.20
% 4.59/2.47  Demodulation         : 0.14
% 4.59/2.47  BG Simplification    : 0.09
% 4.59/2.47  Subsumption          : 0.16
% 4.59/2.47  Abstraction          : 0.03
% 4.59/2.47  MUC search           : 0.00
% 4.59/2.47  Cooper               : 0.02
% 4.59/2.47  Total                : 1.39
% 4.59/2.47  Index Insertion      : 0.00
% 4.59/2.47  Index Deletion       : 0.00
% 4.59/2.47  Index Matching       : 0.00
% 4.59/2.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------