TSTP Solution File: SWV403+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV403+1 : 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 : 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 11:04:01 EDT 2023

% Result   : Theorem 6.94s 2.63s
% Output   : CNFRefutation 7.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   72 (  27 unt;  18 typ;   0 def)
%            Number of atoms       :   95 (  13 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   79 (  38   ~;  30   |;   4   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  10   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :   71 (;  71   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ pair_in_list > strictly_less_than > less_than > contains_slb > isnonempty_slb > update_slb > remove_slb > pair > lookup_slb > insert_slb > #nlpp > create_slb > bottom > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_169,negated_conjecture,
    ~ ! [U] :
        ( ! [V,W,X] :
            ( ( pair_in_list(U,V,W)
              & strictly_less_than(W,X) )
           => pair_in_list(update_slb(U,X),V,X) )
       => ! [Y,Z,X1,X2,X3] :
            ( ( pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z)
              & strictly_less_than(Z,X1) )
           => pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_co) ).

tff(f_121,axiom,
    ! [U,V,W,X,Y] :
      ( pair_in_list(insert_slb(U,pair(V,X)),W,Y)
    <=> ( pair_in_list(U,W,Y)
        | ( ( V = W )
          & ( X = Y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax23) ).

tff(f_145,axiom,
    ! [U,V,W,X] :
      ( strictly_less_than(X,W)
     => ( update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,W)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax29) ).

tff(f_69,axiom,
    ! [U,V] :
      ( strictly_less_than(U,V)
    <=> ( less_than(U,V)
        & ~ less_than(V,U) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).

tff(f_149,axiom,
    ! [U,V,W,X] :
      ( less_than(W,X)
     => ( update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax30) ).

tff(f_60,axiom,
    ! [U,V] :
      ( less_than(U,V)
      | less_than(V,U) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).

tff(c_54,plain,
    strictly_less_than('#skF_3','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_34,plain,
    ! [U_20,W_22,Y_24] : pair_in_list(insert_slb(U_20,pair(W_22,Y_24)),W_22,Y_24),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_4346,plain,
    ! [U_243,V_244,X_245,W_246] :
      ( ( update_slb(insert_slb(U_243,pair(V_244,X_245)),W_246) = insert_slb(update_slb(U_243,W_246),pair(V_244,W_246)) )
      | ~ strictly_less_than(X_245,W_246) ),
    inference(cnfTransformation,[status(thm)],[f_145]) ).

tff(c_93,plain,
    ! [V_72,U_73] :
      ( ~ less_than(V_72,U_73)
      | ~ strictly_less_than(U_73,V_72) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_97,plain,
    ~ less_than('#skF_4','#skF_3'),
    inference(resolution,[status(thm)],[c_54,c_93]) ).

tff(c_87,plain,
    ! [U_67,V_68] :
      ( less_than(U_67,V_68)
      | ~ strictly_less_than(U_67,V_68) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_91,plain,
    less_than('#skF_3','#skF_4'),
    inference(resolution,[status(thm)],[c_54,c_87]) ).

tff(c_56,plain,
    pair_in_list(insert_slb('#skF_1',pair('#skF_5','#skF_6')),'#skF_2','#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_752,plain,
    ! [W_136,V_133,Y_134,X_135,U_132] :
      ( ( Y_134 = X_135 )
      | pair_in_list(U_132,W_136,Y_134)
      | ~ pair_in_list(insert_slb(U_132,pair(V_133,X_135)),W_136,Y_134) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_765,plain,
    ( ( '#skF_6' = '#skF_3' )
    | pair_in_list('#skF_1','#skF_2','#skF_3') ),
    inference(resolution,[status(thm)],[c_56,c_752]) ).

tff(c_766,plain,
    pair_in_list('#skF_1','#skF_2','#skF_3'),
    inference(splitLeft,[status(thm)],[c_765]) ).

tff(c_8,plain,
    ! [U_7,V_8] :
      ( strictly_less_than(U_7,V_8)
      | less_than(V_8,U_7)
      | ~ less_than(U_7,V_8) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_327,plain,
    ! [X_105,V_106,W_107] :
      ( pair_in_list(update_slb('#skF_1',X_105),V_106,X_105)
      | ~ strictly_less_than(W_107,X_105)
      | ~ pair_in_list('#skF_1',V_106,W_107) ),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_767,plain,
    ! [V_137,V_138,U_139] :
      ( pair_in_list(update_slb('#skF_1',V_137),V_138,V_137)
      | ~ pair_in_list('#skF_1',V_138,U_139)
      | less_than(V_137,U_139)
      | ~ less_than(U_139,V_137) ),
    inference(resolution,[status(thm)],[c_8,c_327]) ).

tff(c_770,plain,
    ! [V_137] :
      ( pair_in_list(update_slb('#skF_1',V_137),'#skF_2',V_137)
      | less_than(V_137,'#skF_3')
      | ~ less_than('#skF_3',V_137) ),
    inference(resolution,[status(thm)],[c_766,c_767]) ).

tff(c_36,plain,
    ! [V_21,U_20,Y_24,X_23,W_22] :
      ( ~ pair_in_list(U_20,W_22,Y_24)
      | pair_in_list(insert_slb(U_20,pair(V_21,X_23)),W_22,Y_24) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_2137,plain,
    ! [U_175,V_176,X_177,W_178] :
      ( ( update_slb(insert_slb(U_175,pair(V_176,X_177)),W_178) = insert_slb(update_slb(U_175,W_178),pair(V_176,X_177)) )
      | ~ less_than(W_178,X_177) ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_52,plain,
    ~ pair_in_list(update_slb(insert_slb('#skF_1',pair('#skF_5','#skF_6')),'#skF_4'),'#skF_2','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_2143,plain,
    ( ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_6')),'#skF_2','#skF_4')
    | ~ less_than('#skF_4','#skF_6') ),
    inference(superposition,[status(thm),theory(equality)],[c_2137,c_52]) ).

tff(c_2149,plain,
    ~ less_than('#skF_4','#skF_6'),
    inference(splitLeft,[status(thm)],[c_2143]) ).

tff(c_4,plain,
    ! [V_5,U_4] :
      ( less_than(V_5,U_4)
      | less_than(U_4,V_5) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_2931,plain,
    ! [U_192,V_193,X_194,W_195] :
      ( ( update_slb(insert_slb(U_192,pair(V_193,X_194)),W_195) = insert_slb(update_slb(U_192,W_195),pair(V_193,W_195)) )
      | ~ strictly_less_than(X_194,W_195) ),
    inference(cnfTransformation,[status(thm)],[f_145]) ).

tff(c_2970,plain,
    ( ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_4')),'#skF_2','#skF_4')
    | ~ strictly_less_than('#skF_6','#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_2931,c_52]) ).

tff(c_3032,plain,
    ~ strictly_less_than('#skF_6','#skF_4'),
    inference(splitLeft,[status(thm)],[c_2970]) ).

tff(c_3035,plain,
    ( less_than('#skF_4','#skF_6')
    | ~ less_than('#skF_6','#skF_4') ),
    inference(resolution,[status(thm)],[c_8,c_3032]) ).

tff(c_3038,plain,
    ~ less_than('#skF_6','#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_2149,c_3035]) ).

tff(c_3107,plain,
    less_than('#skF_4','#skF_6'),
    inference(resolution,[status(thm)],[c_4,c_3038]) ).

tff(c_3139,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2149,c_3107]) ).

tff(c_3140,plain,
    ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_4')),'#skF_2','#skF_4'),
    inference(splitRight,[status(thm)],[c_2970]) ).

tff(c_3788,plain,
    ~ pair_in_list(update_slb('#skF_1','#skF_4'),'#skF_2','#skF_4'),
    inference(resolution,[status(thm)],[c_36,c_3140]) ).

tff(c_3794,plain,
    ( less_than('#skF_4','#skF_3')
    | ~ less_than('#skF_3','#skF_4') ),
    inference(resolution,[status(thm)],[c_770,c_3788]) ).

tff(c_3801,plain,
    less_than('#skF_4','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_91,c_3794]) ).

tff(c_3803,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_97,c_3801]) ).

tff(c_3804,plain,
    ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_6')),'#skF_2','#skF_4'),
    inference(splitRight,[status(thm)],[c_2143]) ).

tff(c_3874,plain,
    ~ pair_in_list(update_slb('#skF_1','#skF_4'),'#skF_2','#skF_4'),
    inference(resolution,[status(thm)],[c_36,c_3804]) ).

tff(c_3896,plain,
    ( less_than('#skF_4','#skF_3')
    | ~ less_than('#skF_3','#skF_4') ),
    inference(resolution,[status(thm)],[c_770,c_3874]) ).

tff(c_3902,plain,
    less_than('#skF_4','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_91,c_3896]) ).

tff(c_3904,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_97,c_3902]) ).

tff(c_3906,plain,
    ~ pair_in_list('#skF_1','#skF_2','#skF_3'),
    inference(splitRight,[status(thm)],[c_765]) ).

tff(c_3905,plain,
    '#skF_6' = '#skF_3',
    inference(splitRight,[status(thm)],[c_765]) ).

tff(c_3908,plain,
    pair_in_list(insert_slb('#skF_1',pair('#skF_5','#skF_3')),'#skF_2','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_3905,c_56]) ).

tff(c_3920,plain,
    ! [X_222,V_220,U_219,Y_221,W_223] :
      ( ( W_223 = V_220 )
      | pair_in_list(U_219,W_223,Y_221)
      | ~ pair_in_list(insert_slb(U_219,pair(V_220,X_222)),W_223,Y_221) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_3923,plain,
    ( ( '#skF_5' = '#skF_2' )
    | pair_in_list('#skF_1','#skF_2','#skF_3') ),
    inference(resolution,[status(thm)],[c_3908,c_3920]) ).

tff(c_3932,plain,
    '#skF_5' = '#skF_2',
    inference(negUnitSimplification,[status(thm)],[c_3906,c_3923]) ).

tff(c_3907,plain,
    ~ pair_in_list(update_slb(insert_slb('#skF_1',pair('#skF_5','#skF_3')),'#skF_4'),'#skF_2','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_3905,c_52]) ).

tff(c_3942,plain,
    ~ pair_in_list(update_slb(insert_slb('#skF_1',pair('#skF_2','#skF_3')),'#skF_4'),'#skF_2','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_3932,c_3907]) ).

tff(c_4364,plain,
    ( ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_2','#skF_4')),'#skF_2','#skF_4')
    | ~ strictly_less_than('#skF_3','#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_4346,c_3942]) ).

tff(c_4412,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_34,c_4364]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV403+1 : 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
% 0.17/0.35  % Computer : n029.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 22:50:38 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 6.94/2.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.94/2.63  
% 6.94/2.63  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.03/2.67  
% 7.03/2.67  Inference rules
% 7.03/2.67  ----------------------
% 7.03/2.67  #Ref     : 0
% 7.03/2.67  #Sup     : 845
% 7.03/2.67  #Fact    : 140
% 7.03/2.67  #Define  : 0
% 7.03/2.67  #Split   : 3
% 7.03/2.67  #Chain   : 0
% 7.03/2.67  #Close   : 0
% 7.03/2.67  
% 7.03/2.67  Ordering : KBO
% 7.03/2.67  
% 7.03/2.67  Simplification rules
% 7.03/2.67  ----------------------
% 7.03/2.67  #Subsume      : 436
% 7.03/2.67  #Demod        : 274
% 7.03/2.67  #Tautology    : 170
% 7.03/2.67  #SimpNegUnit  : 10
% 7.03/2.67  #BackRed      : 3
% 7.03/2.67  
% 7.03/2.67  #Partial instantiations: 0
% 7.03/2.67  #Strategies tried      : 1
% 7.03/2.67  
% 7.03/2.67  Timing (in seconds)
% 7.03/2.67  ----------------------
% 7.03/2.67  Preprocessing        : 0.56
% 7.03/2.67  Parsing              : 0.28
% 7.03/2.67  CNF conversion       : 0.04
% 7.03/2.67  Main loop            : 1.04
% 7.03/2.67  Inferencing          : 0.30
% 7.03/2.67  Reduction            : 0.25
% 7.03/2.67  Demodulation         : 0.19
% 7.03/2.67  BG Simplification    : 0.03
% 7.03/2.67  Subsumption          : 0.38
% 7.03/2.67  Abstraction          : 0.04
% 7.03/2.67  MUC search           : 0.00
% 7.03/2.67  Cooper               : 0.00
% 7.03/2.67  Total                : 1.65
% 7.03/2.67  Index Insertion      : 0.00
% 7.03/2.67  Index Deletion       : 0.00
% 7.03/2.67  Index Matching       : 0.00
% 7.03/2.67  BG Taut test         : 0.00
%------------------------------------------------------------------------------