TSTP Solution File: SWC068+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC068+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/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 : n020.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 11:01:01 EDT 2023

% Result   : Theorem 20.93s 8.36s
% Output   : CNFRefutation 21.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   81
% Syntax   : Number of formulae    :  120 (  21 unt;  75 typ;   0 def)
%            Number of atoms       :  107 (  27 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  117 (  55   ~;  44   |;   4   &)
%                                         (   1 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 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   :   32 (;  31   !;   1   ?;   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_1010,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( app(X,X) != W )
                      | ( V != X )
                      | ( U != W )
                      | ? [Y] :
                          ( ssList(Y)
                          & neq(Y,nil)
                          & segmentP(V,Y)
                          & segmentP(U,Y) )
                      | ( ( nil = V )
                        & ( nil = U ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(f_311,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> ( U != V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

tff(f_667,axiom,
    ! [U] :
      ( ssList(U)
     => segmentP(U,U) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).

tff(f_859,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(U,nil) = U ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).

tff(f_682,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( segmentP(U,V)
                   => segmentP(app(app(W,U),X),V) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).

tff(c_390,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1010]) ).

tff(c_388,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1010]) ).

tff(c_384,plain,
    ( ( nil != '#skF_48' )
    | ( nil != '#skF_49' ) ),
    inference(cnfTransformation,[status(thm)],[f_1010]) ).

tff(c_406,plain,
    ( ( nil != '#skF_50' )
    | ( nil != '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_388,c_384]) ).

tff(c_419,plain,
    nil != '#skF_51',
    inference(splitLeft,[status(thm)],[c_406]) ).

tff(c_394,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1010]) ).

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

tff(c_2373,plain,
    ! [U_1268,V_1269] :
      ( neq(U_1268,V_1269)
      | ( V_1269 = U_1268 )
      | ~ ssList(V_1269)
      | ~ ssList(U_1268) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_428,plain,
    ! [U_1157] :
      ( segmentP(U_1157,U_1157)
      | ~ ssList(U_1157) ),
    inference(cnfTransformation,[status(thm)],[f_667]) ).

tff(c_386,plain,
    ! [Y_1148] :
      ( ~ segmentP('#skF_48',Y_1148)
      | ~ segmentP('#skF_49',Y_1148)
      | ~ neq(Y_1148,nil)
      | ~ ssList(Y_1148) ),
    inference(cnfTransformation,[status(thm)],[f_1010]) ).

tff(c_405,plain,
    ! [Y_1148] :
      ( ~ segmentP('#skF_50',Y_1148)
      | ~ segmentP('#skF_51',Y_1148)
      | ~ neq(Y_1148,nil)
      | ~ ssList(Y_1148) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_388,c_386]) ).

tff(c_432,plain,
    ( ~ segmentP('#skF_50','#skF_51')
    | ~ neq('#skF_51',nil)
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_428,c_405]) ).

tff(c_435,plain,
    ( ~ segmentP('#skF_50','#skF_51')
    | ~ neq('#skF_51',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_432]) ).

tff(c_444,plain,
    ~ neq('#skF_51',nil),
    inference(splitLeft,[status(thm)],[c_435]) ).

tff(c_2387,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList(nil)
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_2373,c_444]) ).

tff(c_2398,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_168,c_2387]) ).

tff(c_2400,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_419,c_2398]) ).

tff(c_2401,plain,
    ~ segmentP('#skF_50','#skF_51'),
    inference(splitRight,[status(thm)],[c_435]) ).

tff(c_270,plain,
    ! [U_1014] :
      ( segmentP(U_1014,U_1014)
      | ~ ssList(U_1014) ),
    inference(cnfTransformation,[status(thm)],[f_667]) ).

tff(c_396,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1010]) ).

tff(c_2439,plain,
    ! [U_1281] :
      ( ( app(U_1281,nil) = U_1281 )
      | ~ ssList(U_1281) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_2452,plain,
    app('#skF_50',nil) = '#skF_50',
    inference(resolution,[status(thm)],[c_396,c_2439]) ).

tff(c_392,plain,
    app('#skF_51','#skF_51') = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1010]) ).

tff(c_45448,plain,
    ! [W_2604,U_2605,X_2606,V_2607] :
      ( segmentP(app(app(W_2604,U_2605),X_2606),V_2607)
      | ~ segmentP(U_2605,V_2607)
      | ~ ssList(X_2606)
      | ~ ssList(W_2604)
      | ~ ssList(V_2607)
      | ~ ssList(U_2605) ),
    inference(cnfTransformation,[status(thm)],[f_682]) ).

tff(c_45684,plain,
    ! [X_2606,V_2607] :
      ( segmentP(app('#skF_50',X_2606),V_2607)
      | ~ segmentP('#skF_51',V_2607)
      | ~ ssList(X_2606)
      | ~ ssList('#skF_51')
      | ~ ssList(V_2607)
      | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_392,c_45448]) ).

tff(c_45845,plain,
    ! [X_2608,V_2609] :
      ( segmentP(app('#skF_50',X_2608),V_2609)
      | ~ segmentP('#skF_51',V_2609)
      | ~ ssList(X_2608)
      | ~ ssList(V_2609) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_394,c_45684]) ).

tff(c_45859,plain,
    ! [V_2609] :
      ( segmentP('#skF_50',V_2609)
      | ~ segmentP('#skF_51',V_2609)
      | ~ ssList(nil)
      | ~ ssList(V_2609) ),
    inference(superposition,[status(thm),theory(equality)],[c_2452,c_45845]) ).

tff(c_45866,plain,
    ! [V_2610] :
      ( segmentP('#skF_50',V_2610)
      | ~ segmentP('#skF_51',V_2610)
      | ~ ssList(V_2610) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_45859]) ).

tff(c_45874,plain,
    ( segmentP('#skF_50','#skF_51')
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_270,c_45866]) ).

tff(c_45880,plain,
    segmentP('#skF_50','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_45874]) ).

tff(c_45882,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2401,c_45880]) ).

tff(c_45884,plain,
    nil = '#skF_51',
    inference(splitRight,[status(thm)],[c_406]) ).

tff(c_45883,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_406]) ).

tff(c_45885,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_45884,c_45883]) ).

tff(c_356,plain,
    ! [U_1080] :
      ( ( app(U_1080,nil) = U_1080 )
      | ~ ssList(U_1080) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_45933,plain,
    ! [U_2624] :
      ( ( app(U_2624,'#skF_51') = U_2624 )
      | ~ ssList(U_2624) ),
    inference(demodulation,[status(thm),theory(equality)],[c_45884,c_356]) ).

tff(c_45936,plain,
    app('#skF_51','#skF_51') = '#skF_51',
    inference(resolution,[status(thm)],[c_394,c_45933]) ).

tff(c_45941,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_45936]) ).

tff(c_45943,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_45885,c_45941]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC068+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 21:34:22 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 20.93/8.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.93/8.36  
% 20.93/8.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.02/8.39  
% 21.02/8.39  Inference rules
% 21.02/8.39  ----------------------
% 21.02/8.39  #Ref     : 5
% 21.02/8.39  #Sup     : 9754
% 21.02/8.39  #Fact    : 0
% 21.02/8.39  #Define  : 0
% 21.02/8.39  #Split   : 79
% 21.02/8.39  #Chain   : 0
% 21.02/8.39  #Close   : 0
% 21.02/8.39  
% 21.02/8.39  Ordering : KBO
% 21.02/8.39  
% 21.02/8.39  Simplification rules
% 21.02/8.39  ----------------------
% 21.02/8.39  #Subsume      : 2033
% 21.02/8.39  #Demod        : 9153
% 21.02/8.39  #Tautology    : 2968
% 21.02/8.39  #SimpNegUnit  : 688
% 21.02/8.39  #BackRed      : 870
% 21.02/8.39  
% 21.02/8.39  #Partial instantiations: 0
% 21.02/8.39  #Strategies tried      : 1
% 21.02/8.39  
% 21.02/8.39  Timing (in seconds)
% 21.02/8.39  ----------------------
% 21.02/8.40  Preprocessing        : 0.86
% 21.02/8.40  Parsing              : 0.40
% 21.02/8.40  CNF conversion       : 0.11
% 21.02/8.40  Main loop            : 6.47
% 21.02/8.40  Inferencing          : 1.90
% 21.02/8.40  Reduction            : 2.37
% 21.02/8.40  Demodulation         : 1.71
% 21.02/8.40  BG Simplification    : 0.14
% 21.02/8.40  Subsumption          : 1.60
% 21.02/8.40  Abstraction          : 0.14
% 21.02/8.40  MUC search           : 0.00
% 21.02/8.40  Cooper               : 0.00
% 21.09/8.40  Total                : 7.38
% 21.09/8.40  Index Insertion      : 0.00
% 21.09/8.40  Index Deletion       : 0.00
% 21.09/8.40  Index Matching       : 0.00
% 21.09/8.40  BG Taut test         : 0.00
%------------------------------------------------------------------------------