TSTP Solution File: SWC008+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC008+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n026.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 11:00:42 EDT 2023

% Result   : Theorem 16.98s 5.56s
% Output   : CNFRefutation 16.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   79
% Syntax   : Number of formulae    :   99 (  10 unt;  75 typ;   0 def)
%            Number of atoms       :   82 (  23 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  107 (  49   ~;  41   |;   9   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   56 (  56 usr;   7 con; 0-2 aty)
%            Number of variables   :   30 (;  25   !;   5   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > cons > app > #nlpp > tl > hd > nil > #skF_36 > #skF_25 > #skF_5 > #skF_44 > #skF_21 > #skF_16 > #skF_6 > #skF_49 > #skF_18 > #skF_24 > #skF_35 > #skF_19 > #skF_31 > #skF_22 > #skF_37 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_51 > #skF_28 > #skF_10 > #skF_41 > #skF_2 > #skF_38 > #skF_43 > #skF_1 > #skF_8 > #skF_39 > #skF_23 > #skF_33 > #skF_26 > #skF_50 > #skF_13 > #skF_17 > #skF_11 > #skF_14 > #skF_27 > #skF_12 > #skF_7 > #skF_46 > #skF_42 > #skF_45 > #skF_9 > #skF_30 > #skF_4 > #skF_20 > #skF_47

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_36',type,
    '#skF_36': $i > $i ).

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

tff('#skF_25',type,
    '#skF_25': $i > $i ).

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

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

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

tff('#skF_44',type,
    '#skF_44': $i > $i ).

tff('#skF_21',type,
    '#skF_21': $i > $i ).

tff('#skF_16',type,
    '#skF_16': $i > $i ).

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

tff('#skF_49',type,
    '#skF_49': $i ).

tff('#skF_18',type,
    '#skF_18': $i > $i ).

tff('#skF_24',type,
    '#skF_24': $i > $i ).

tff('#skF_35',type,
    '#skF_35': $i > $i ).

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

tff('#skF_19',type,
    '#skF_19': $i > $i ).

tff('#skF_31',type,
    '#skF_31': $i > $i ).

tff('#skF_22',type,
    '#skF_22': $i > $i ).

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

tff('#skF_37',type,
    '#skF_37': $i > $i ).

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

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

tff('#skF_40',type,
    '#skF_40': $i > $i ).

tff('#skF_48',type,
    '#skF_48': $i ).

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

tff('#skF_34',type,
    '#skF_34': $i > $i ).

tff('#skF_29',type,
    '#skF_29': $i > $i ).

tff('#skF_15',type,
    '#skF_15': $i > $i ).

tff('#skF_32',type,
    '#skF_32': $i > $i ).

tff('#skF_51',type,
    '#skF_51': $i ).

tff('#skF_28',type,
    '#skF_28': $i > $i ).

tff('#skF_10',type,
    '#skF_10': $i > $i ).

tff('#skF_41',type,
    '#skF_41': $i > $i ).

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

tff('#skF_38',type,
    '#skF_38': $i > $i ).

tff('#skF_43',type,
    '#skF_43': $i > $i ).

tff(hd,type,
    hd: $i > $i ).

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

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

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

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

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

tff('#skF_39',type,
    '#skF_39': $i > $i ).

tff('#skF_23',type,
    '#skF_23': $i > $i ).

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

tff('#skF_33',type,
    '#skF_33': $i > $i ).

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

tff('#skF_26',type,
    '#skF_26': $i > $i ).

tff('#skF_50',type,
    '#skF_50': $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

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

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

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

tff('#skF_17',type,
    '#skF_17': $i > $i ).

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

tff('#skF_11',type,
    '#skF_11': $i > $i ).

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

tff('#skF_14',type,
    '#skF_14': $i > $i ).

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

tff(tl,type,
    tl: $i > $i ).

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

tff('#skF_27',type,
    '#skF_27': $i > $i ).

tff('#skF_12',type,
    '#skF_12': $i > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff('#skF_46',type,
    '#skF_46': $i > $i ).

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

tff('#skF_42',type,
    '#skF_42': $i > $i ).

tff('#skF_45',type,
    '#skF_45': $i > $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

tff('#skF_30',type,
    '#skF_30': $i > $i ).

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

tff('#skF_20',type,
    '#skF_20': $i > $i ).

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

tff('#skF_47',type,
    '#skF_47': $i > $i ).

tff(f_1024,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ~ frontsegP(X,W)
                      | ~ equalelemsP(W)
                      | ? [Y] :
                          ( ssList(Y)
                          & ? [Z] :
                              ( ssList(Z)
                              & ? [X1] :
                                  ( ssList(X1)
                                  & ( app(app(Y,Z),X1) = V )
                                  & ( app(Y,X1) = U ) ) ) )
                      | ? [X2] :
                          ( ssList(X2)
                          & neq(W,X2)
                          & frontsegP(X,X2)
                          & segmentP(X2,W)
                          & equalelemsP(X2) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_859,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(U,nil) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

tff(f_108,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( frontsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ( app(V,W) = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).

tff(f_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(c_396,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_437,plain,
    ! [U_1277] :
      ( ( app(U_1277,nil) = U_1277 )
      | ~ ssList(U_1277) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_448,plain,
    app('#skF_51',nil) = '#skF_51',
    inference(resolution,[status(thm)],[c_396,c_437]) ).

tff(c_390,plain,
    frontsegP('#skF_51','#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_398,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_30,plain,
    ! [U_34,V_40] :
      ( ssList('#skF_6'(U_34,V_40))
      | ~ frontsegP(U_34,V_40)
      | ~ ssList(V_40)
      | ~ ssList(U_34) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_168,plain,
    ssList(nil),
    inference(cnfTransformation,[status(thm)],[f_319]) ).

tff(c_449,plain,
    app('#skF_50',nil) = '#skF_50',
    inference(resolution,[status(thm)],[c_398,c_437]) ).

tff(c_6486,plain,
    ! [V_1603,U_1604] :
      ( ( app(V_1603,'#skF_6'(U_1604,V_1603)) = U_1604 )
      | ~ frontsegP(U_1604,V_1603)
      | ~ ssList(V_1603)
      | ~ ssList(U_1604) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_394,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_392,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_386,plain,
    ! [Y_1253,X1_1259,Z_1257] :
      ( ( app(Y_1253,X1_1259) != '#skF_48' )
      | ( app(app(Y_1253,Z_1257),X1_1259) != '#skF_49' )
      | ~ ssList(X1_1259)
      | ~ ssList(Z_1257)
      | ~ ssList(Y_1253) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_407,plain,
    ! [Y_1253,X1_1259,Z_1257] :
      ( ( app(Y_1253,X1_1259) != '#skF_50' )
      | ( app(app(Y_1253,Z_1257),X1_1259) != '#skF_51' )
      | ~ ssList(X1_1259)
      | ~ ssList(Z_1257)
      | ~ ssList(Y_1253) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_392,c_386]) ).

tff(c_6619,plain,
    ! [V_1608,X1_1609,U_1610] :
      ( ( app(V_1608,X1_1609) != '#skF_50' )
      | ( app(U_1610,X1_1609) != '#skF_51' )
      | ~ ssList(X1_1609)
      | ~ ssList('#skF_6'(U_1610,V_1608))
      | ~ ssList(V_1608)
      | ~ frontsegP(U_1610,V_1608)
      | ~ ssList(V_1608)
      | ~ ssList(U_1610) ),
    inference(superposition,[status(thm),theory(equality)],[c_6486,c_407]) ).

tff(c_6737,plain,
    ! [U_1610] :
      ( ( app(U_1610,nil) != '#skF_51' )
      | ~ ssList(nil)
      | ~ ssList('#skF_6'(U_1610,'#skF_50'))
      | ~ frontsegP(U_1610,'#skF_50')
      | ~ ssList('#skF_50')
      | ~ ssList(U_1610) ),
    inference(superposition,[status(thm),theory(equality)],[c_449,c_6619]) ).

tff(c_13245,plain,
    ! [U_1714] :
      ( ( app(U_1714,nil) != '#skF_51' )
      | ~ ssList('#skF_6'(U_1714,'#skF_50'))
      | ~ frontsegP(U_1714,'#skF_50')
      | ~ ssList(U_1714) ),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_168,c_6737]) ).

tff(c_13249,plain,
    ! [U_34] :
      ( ( app(U_34,nil) != '#skF_51' )
      | ~ frontsegP(U_34,'#skF_50')
      | ~ ssList('#skF_50')
      | ~ ssList(U_34) ),
    inference(resolution,[status(thm)],[c_30,c_13245]) ).

tff(c_13253,plain,
    ! [U_1715] :
      ( ( app(U_1715,nil) != '#skF_51' )
      | ~ frontsegP(U_1715,'#skF_50')
      | ~ ssList(U_1715) ),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_13249]) ).

tff(c_13279,plain,
    ( ( app('#skF_51',nil) != '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_390,c_13253]) ).

tff(c_13301,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_448,c_13279]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC008+1 : TPTP v8.1.2. Released v2.4.0.
% 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
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Aug  3 21:44:31 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 16.98/5.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.98/5.57  
% 16.98/5.57  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.98/5.60  
% 16.98/5.60  Inference rules
% 16.98/5.60  ----------------------
% 16.98/5.60  #Ref     : 2
% 16.98/5.60  #Sup     : 2814
% 16.98/5.60  #Fact    : 0
% 16.98/5.60  #Define  : 0
% 16.98/5.60  #Split   : 35
% 16.98/5.60  #Chain   : 0
% 16.98/5.60  #Close   : 0
% 16.98/5.60  
% 16.98/5.60  Ordering : KBO
% 16.98/5.60  
% 16.98/5.60  Simplification rules
% 16.98/5.60  ----------------------
% 16.98/5.60  #Subsume      : 433
% 16.98/5.60  #Demod        : 2221
% 16.98/5.60  #Tautology    : 644
% 16.98/5.60  #SimpNegUnit  : 169
% 16.98/5.60  #BackRed      : 59
% 16.98/5.60  
% 16.98/5.60  #Partial instantiations: 0
% 16.98/5.60  #Strategies tried      : 1
% 16.98/5.60  
% 16.98/5.60  Timing (in seconds)
% 16.98/5.60  ----------------------
% 16.98/5.60  Preprocessing        : 0.98
% 16.98/5.60  Parsing              : 0.45
% 16.98/5.60  CNF conversion       : 0.13
% 16.98/5.60  Main loop            : 3.48
% 16.98/5.60  Inferencing          : 0.97
% 16.98/5.60  Reduction            : 1.26
% 16.98/5.60  Demodulation         : 0.90
% 16.98/5.60  BG Simplification    : 0.12
% 16.98/5.60  Subsumption          : 0.87
% 16.98/5.60  Abstraction          : 0.08
% 16.98/5.60  MUC search           : 0.00
% 16.98/5.60  Cooper               : 0.00
% 16.98/5.60  Total                : 4.51
% 16.98/5.60  Index Insertion      : 0.00
% 16.98/5.60  Index Deletion       : 0.00
% 16.98/5.60  Index Matching       : 0.00
% 16.98/5.60  BG Taut test         : 0.00
%------------------------------------------------------------------------------