TSTP Solution File: SWV401+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV401+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 : n027.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 5.80s 2.45s
% Output   : CNFRefutation 6.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   69 (  25 unt;  18 typ;   0 def)
%            Number of atoms       :   88 (  14 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   76 (  39   ~;  26   |;   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   :   67 (;  67   !;   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)
              & less_than(X,W) )
           => pair_in_list(update_slb(U,X),V,W) )
       => ! [Y,Z,X1,X2,X3] :
            ( ( pair_in_list(insert_slb(U,pair(X2,X3)),Y,Z)
              & less_than(X1,Z) )
           => pair_in_list(update_slb(insert_slb(U,pair(X2,X3)),X1),Y,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l37_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_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(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_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(c_54,plain,
    less_than('#skF_4','#skF_3'),
    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_3075,plain,
    ! [U_221,V_222,X_223,W_224] :
      ( ( update_slb(insert_slb(U_221,pair(V_222,X_223)),W_224) = insert_slb(update_slb(U_221,W_224),pair(V_222,X_223)) )
      | ~ less_than(W_224,X_223) ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

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_911,plain,
    ! [X_140,W_141,Y_139,V_138,U_137] :
      ( ( W_141 = V_138 )
      | pair_in_list(U_137,W_141,Y_139)
      | ~ pair_in_list(insert_slb(U_137,pair(V_138,X_140)),W_141,Y_139) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_924,plain,
    ( ( '#skF_5' = '#skF_2' )
    | pair_in_list('#skF_1','#skF_2','#skF_3') ),
    inference(resolution,[status(thm)],[c_56,c_911]) ).

tff(c_925,plain,
    pair_in_list('#skF_1','#skF_2','#skF_3'),
    inference(splitLeft,[status(thm)],[c_924]) ).

tff(c_58,plain,
    ! [X_58,V_56,W_57] :
      ( pair_in_list(update_slb('#skF_1',X_58),V_56,W_57)
      | ~ less_than(X_58,W_57)
      | ~ pair_in_list('#skF_1',V_56,W_57) ),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

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_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_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_1732,plain,
    ! [U_173,V_174,X_175,W_176] :
      ( ( update_slb(insert_slb(U_173,pair(V_174,X_175)),W_176) = insert_slb(update_slb(U_173,W_176),pair(V_174,W_176)) )
      | ~ strictly_less_than(X_175,W_176) ),
    inference(cnfTransformation,[status(thm)],[f_145]) ).

tff(c_52,plain,
    ~ pair_in_list(update_slb(insert_slb('#skF_1',pair('#skF_5','#skF_6')),'#skF_4'),'#skF_2','#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_1765,plain,
    ( ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_4')),'#skF_2','#skF_3')
    | ~ strictly_less_than('#skF_6','#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_1732,c_52]) ).

tff(c_1813,plain,
    ~ strictly_less_than('#skF_6','#skF_4'),
    inference(splitLeft,[status(thm)],[c_1765]) ).

tff(c_1817,plain,
    ( less_than('#skF_4','#skF_6')
    | ~ less_than('#skF_6','#skF_4') ),
    inference(resolution,[status(thm)],[c_8,c_1813]) ).

tff(c_1818,plain,
    ~ less_than('#skF_6','#skF_4'),
    inference(splitLeft,[status(thm)],[c_1817]) ).

tff(c_1880,plain,
    less_than('#skF_4','#skF_6'),
    inference(resolution,[status(thm)],[c_4,c_1818]) ).

tff(c_1968,plain,
    ! [U_186,V_187,X_188,W_189] :
      ( ( update_slb(insert_slb(U_186,pair(V_187,X_188)),W_189) = insert_slb(update_slb(U_186,W_189),pair(V_187,X_188)) )
      | ~ less_than(W_189,X_188) ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_1986,plain,
    ( ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_6')),'#skF_2','#skF_3')
    | ~ less_than('#skF_4','#skF_6') ),
    inference(superposition,[status(thm),theory(equality)],[c_1968,c_52]) ).

tff(c_2000,plain,
    ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_6')),'#skF_2','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_1880,c_1986]) ).

tff(c_2032,plain,
    ~ pair_in_list(update_slb('#skF_1','#skF_4'),'#skF_2','#skF_3'),
    inference(resolution,[status(thm)],[c_36,c_2000]) ).

tff(c_2035,plain,
    ( ~ less_than('#skF_4','#skF_3')
    | ~ pair_in_list('#skF_1','#skF_2','#skF_3') ),
    inference(resolution,[status(thm)],[c_58,c_2032]) ).

tff(c_2039,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_925,c_54,c_2035]) ).

tff(c_2040,plain,
    less_than('#skF_4','#skF_6'),
    inference(splitRight,[status(thm)],[c_1817]) ).

tff(c_2133,plain,
    ! [U_191,V_192,X_193,W_194] :
      ( ( update_slb(insert_slb(U_191,pair(V_192,X_193)),W_194) = insert_slb(update_slb(U_191,W_194),pair(V_192,X_193)) )
      | ~ less_than(W_194,X_193) ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_2151,plain,
    ( ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_6')),'#skF_2','#skF_3')
    | ~ less_than('#skF_4','#skF_6') ),
    inference(superposition,[status(thm),theory(equality)],[c_2133,c_52]) ).

tff(c_2165,plain,
    ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_6')),'#skF_2','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_2040,c_2151]) ).

tff(c_2386,plain,
    ~ pair_in_list(update_slb('#skF_1','#skF_4'),'#skF_2','#skF_3'),
    inference(resolution,[status(thm)],[c_36,c_2165]) ).

tff(c_2454,plain,
    ( ~ less_than('#skF_4','#skF_3')
    | ~ pair_in_list('#skF_1','#skF_2','#skF_3') ),
    inference(resolution,[status(thm)],[c_58,c_2386]) ).

tff(c_2458,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_925,c_54,c_2454]) ).

tff(c_2459,plain,
    ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_5','#skF_4')),'#skF_2','#skF_3'),
    inference(splitRight,[status(thm)],[c_1765]) ).

tff(c_2763,plain,
    ~ pair_in_list(update_slb('#skF_1','#skF_4'),'#skF_2','#skF_3'),
    inference(resolution,[status(thm)],[c_36,c_2459]) ).

tff(c_2766,plain,
    ( ~ less_than('#skF_4','#skF_3')
    | ~ pair_in_list('#skF_1','#skF_2','#skF_3') ),
    inference(resolution,[status(thm)],[c_58,c_2763]) ).

tff(c_2770,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_925,c_54,c_2766]) ).

tff(c_2772,plain,
    ~ pair_in_list('#skF_1','#skF_2','#skF_3'),
    inference(splitRight,[status(thm)],[c_924]) ).

tff(c_2771,plain,
    '#skF_5' = '#skF_2',
    inference(splitRight,[status(thm)],[c_924]) ).

tff(c_2774,plain,
    pair_in_list(insert_slb('#skF_1',pair('#skF_2','#skF_6')),'#skF_2','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_2771,c_56]) ).

tff(c_2786,plain,
    ! [U_205,V_206,Y_207,X_208,W_209] :
      ( ( Y_207 = X_208 )
      | pair_in_list(U_205,W_209,Y_207)
      | ~ pair_in_list(insert_slb(U_205,pair(V_206,X_208)),W_209,Y_207) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_2789,plain,
    ( ( '#skF_6' = '#skF_3' )
    | pair_in_list('#skF_1','#skF_2','#skF_3') ),
    inference(resolution,[status(thm)],[c_2774,c_2786]) ).

tff(c_2798,plain,
    '#skF_6' = '#skF_3',
    inference(negUnitSimplification,[status(thm)],[c_2772,c_2789]) ).

tff(c_2773,plain,
    ~ pair_in_list(update_slb(insert_slb('#skF_1',pair('#skF_2','#skF_6')),'#skF_4'),'#skF_2','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_2771,c_52]) ).

tff(c_2802,plain,
    ~ pair_in_list(update_slb(insert_slb('#skF_1',pair('#skF_2','#skF_3')),'#skF_4'),'#skF_2','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_2798,c_2773]) ).

tff(c_3081,plain,
    ( ~ pair_in_list(insert_slb(update_slb('#skF_1','#skF_4'),pair('#skF_2','#skF_3')),'#skF_2','#skF_3')
    | ~ less_than('#skF_4','#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_3075,c_2802]) ).

tff(c_3088,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_34,c_3081]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV401+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
% 0.14/0.34  % Computer : n027.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
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 22:53:09 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 5.80/2.45  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.22/2.46  
% 6.22/2.46  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.22/2.49  
% 6.22/2.49  Inference rules
% 6.22/2.49  ----------------------
% 6.22/2.49  #Ref     : 0
% 6.22/2.49  #Sup     : 650
% 6.22/2.49  #Fact    : 70
% 6.22/2.49  #Define  : 0
% 6.22/2.49  #Split   : 3
% 6.22/2.49  #Chain   : 0
% 6.22/2.49  #Close   : 0
% 6.22/2.49  
% 6.22/2.49  Ordering : KBO
% 6.22/2.49  
% 6.22/2.49  Simplification rules
% 6.22/2.49  ----------------------
% 6.22/2.49  #Subsume      : 297
% 6.22/2.49  #Demod        : 221
% 6.22/2.49  #Tautology    : 141
% 6.22/2.49  #SimpNegUnit  : 2
% 6.22/2.49  #BackRed      : 4
% 6.22/2.49  
% 6.22/2.49  #Partial instantiations: 0
% 6.22/2.49  #Strategies tried      : 1
% 6.22/2.49  
% 6.22/2.49  Timing (in seconds)
% 6.22/2.49  ----------------------
% 6.22/2.49  Preprocessing        : 0.55
% 6.22/2.49  Parsing              : 0.28
% 6.22/2.49  CNF conversion       : 0.04
% 6.22/2.49  Main loop            : 0.89
% 6.22/2.49  Inferencing          : 0.27
% 6.22/2.49  Reduction            : 0.24
% 6.22/2.49  Demodulation         : 0.17
% 6.22/2.49  BG Simplification    : 0.03
% 6.22/2.49  Subsumption          : 0.29
% 6.22/2.49  Abstraction          : 0.04
% 6.22/2.49  MUC search           : 0.00
% 6.22/2.49  Cooper               : 0.00
% 6.22/2.49  Total                : 1.49
% 6.22/2.49  Index Insertion      : 0.00
% 6.22/2.49  Index Deletion       : 0.00
% 6.22/2.49  Index Matching       : 0.00
% 6.22/2.49  BG Taut test         : 0.00
%------------------------------------------------------------------------------