TSTP Solution File: SWC023+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC023+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 : n019.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 11:00:48 EDT 2023

% Result   : Theorem 6.56s 2.60s
% Output   : CNFRefutation 6.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   78
% Syntax   : Number of formulae    :  125 (  29 unt;  76 typ;   0 def)
%            Number of atoms       :   96 (  23 equ)
%            Maximal formula atoms :   17 (   1 avg)
%            Number of connectives :   88 (  41   ~;  35   |;   4   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   2 avg)
%            Maximal term depth    :    1 (   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    :   57 (  57 usr;   8 con; 0-2 aty)
%            Number of variables   :   14 (;  13   !;   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_52 > #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_52',type,
    '#skF_52': $i ).

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 )
                      | ~ neq(V,nil)
                      | ? [Y] :
                          ( ssList(Y)
                          & neq(Y,nil)
                          & frontsegP(V,Y)
                          & frontsegP(U,Y) )
                      | ( ! [Z] :
                            ( ssList(Z)
                           => ( ~ neq(Z,nil)
                              | ~ frontsegP(X,Z)
                              | ~ frontsegP(W,Z) ) )
                        & ( ( nil != X )
                          | ( nil != W ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

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(c_394,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_406,plain,
    ( ssList('#skF_52')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_429,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_406]) ).

tff(c_414,plain,
    ( ssList('#skF_52')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_445,plain,
    ( ssList('#skF_52')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_429,c_414]) ).

tff(c_446,plain,
    '#skF_51' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_445]) ).

tff(c_390,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_386,plain,
    neq('#skF_49',nil),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_419,plain,
    neq('#skF_51',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_386]) ).

tff(c_430,plain,
    neq('#skF_51','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_429,c_419]) ).

tff(c_459,plain,
    neq('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_446,c_430]) ).

tff(c_462,plain,
    ! [V_1165] :
      ( ~ neq(V_1165,V_1165)
      | ~ ssList(V_1165) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_465,plain,
    ~ ssList('#skF_50'),
    inference(resolution,[status(thm)],[c_459,c_462]) ).

tff(c_469,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_465]) ).

tff(c_470,plain,
    ssList('#skF_52'),
    inference(splitRight,[status(thm)],[c_445]) ).

tff(c_471,plain,
    '#skF_51' != '#skF_50',
    inference(splitRight,[status(thm)],[c_445]) ).

tff(c_410,plain,
    ( frontsegP('#skF_51','#skF_52')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_479,plain,
    ( frontsegP('#skF_51','#skF_52')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_429,c_410]) ).

tff(c_480,plain,
    frontsegP('#skF_51','#skF_52'),
    inference(negUnitSimplification,[status(thm)],[c_471,c_479]) ).

tff(c_408,plain,
    ( frontsegP('#skF_50','#skF_52')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_494,plain,
    ( frontsegP('#skF_50','#skF_52')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_429,c_408]) ).

tff(c_495,plain,
    frontsegP('#skF_50','#skF_52'),
    inference(negUnitSimplification,[status(thm)],[c_471,c_494]) ).

tff(c_412,plain,
    ( neq('#skF_52',nil)
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_485,plain,
    ( neq('#skF_52','#skF_50')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_429,c_429,c_412]) ).

tff(c_486,plain,
    neq('#skF_52','#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_471,c_485]) ).

tff(c_388,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_384,plain,
    ! [Y_1163] :
      ( ~ frontsegP('#skF_48',Y_1163)
      | ~ frontsegP('#skF_49',Y_1163)
      | ~ neq(Y_1163,nil)
      | ~ ssList(Y_1163) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_420,plain,
    ! [Y_1163] :
      ( ~ frontsegP('#skF_50',Y_1163)
      | ~ frontsegP('#skF_51',Y_1163)
      | ~ neq(Y_1163,nil)
      | ~ ssList(Y_1163) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_388,c_384]) ).

tff(c_508,plain,
    ! [Y_1183] :
      ( ~ frontsegP('#skF_50',Y_1183)
      | ~ frontsegP('#skF_51',Y_1183)
      | ~ neq(Y_1183,'#skF_50')
      | ~ ssList(Y_1183) ),
    inference(demodulation,[status(thm),theory(equality)],[c_429,c_420]) ).

tff(c_511,plain,
    ( ~ frontsegP('#skF_50','#skF_52')
    | ~ frontsegP('#skF_51','#skF_52')
    | ~ ssList('#skF_52') ),
    inference(resolution,[status(thm)],[c_486,c_508]) ).

tff(c_518,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_470,c_480,c_495,c_511]) ).

tff(c_519,plain,
    ssList('#skF_52'),
    inference(splitRight,[status(thm)],[c_406]) ).

tff(c_392,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_524,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_410]) ).

tff(c_527,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_524,c_419]) ).

tff(c_547,plain,
    ! [V_1186] :
      ( ~ neq(V_1186,V_1186)
      | ~ ssList(V_1186) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_550,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_527,c_547]) ).

tff(c_554,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_550]) ).

tff(c_555,plain,
    frontsegP('#skF_51','#skF_52'),
    inference(splitRight,[status(thm)],[c_410]) ).

tff(c_520,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_406]) ).

tff(c_400,plain,
    ( frontsegP('#skF_50','#skF_52')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1024]) ).

tff(c_562,plain,
    frontsegP('#skF_50','#skF_52'),
    inference(negUnitSimplification,[status(thm)],[c_520,c_400]) ).

tff(c_556,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_410]) ).

tff(c_558,plain,
    neq('#skF_52',nil),
    inference(negUnitSimplification,[status(thm)],[c_556,c_412]) ).

tff(c_576,plain,
    ! [Y_1198] :
      ( ~ frontsegP('#skF_50',Y_1198)
      | ~ frontsegP('#skF_51',Y_1198)
      | ~ neq(Y_1198,nil)
      | ~ ssList(Y_1198) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_388,c_384]) ).

tff(c_579,plain,
    ( ~ frontsegP('#skF_50','#skF_52')
    | ~ frontsegP('#skF_51','#skF_52')
    | ~ ssList('#skF_52') ),
    inference(resolution,[status(thm)],[c_558,c_576]) ).

tff(c_586,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_519,c_555,c_562,c_579]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC023+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 : n019.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 21:27:47 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.56/2.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.56/2.61  
% 6.56/2.61  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.56/2.64  
% 6.56/2.64  Inference rules
% 6.56/2.64  ----------------------
% 6.56/2.64  #Ref     : 0
% 6.56/2.64  #Sup     : 18
% 6.56/2.64  #Fact    : 0
% 6.56/2.64  #Define  : 0
% 6.56/2.64  #Split   : 3
% 6.56/2.64  #Chain   : 0
% 6.56/2.64  #Close   : 0
% 6.56/2.64  
% 6.56/2.64  Ordering : KBO
% 6.56/2.64  
% 6.56/2.64  Simplification rules
% 6.56/2.64  ----------------------
% 6.56/2.64  #Subsume      : 8
% 6.56/2.64  #Demod        : 76
% 6.56/2.64  #Tautology    : 29
% 6.56/2.64  #SimpNegUnit  : 10
% 6.56/2.64  #BackRed      : 24
% 6.56/2.64  
% 6.56/2.64  #Partial instantiations: 0
% 6.56/2.64  #Strategies tried      : 1
% 6.56/2.64  
% 6.56/2.64  Timing (in seconds)
% 6.56/2.64  ----------------------
% 6.96/2.65  Preprocessing        : 0.97
% 6.96/2.65  Parsing              : 0.42
% 6.96/2.65  CNF conversion       : 0.12
% 6.96/2.65  Main loop            : 0.51
% 6.96/2.65  Inferencing          : 0.10
% 6.96/2.65  Reduction            : 0.19
% 6.96/2.65  Demodulation         : 0.13
% 6.96/2.65  BG Simplification    : 0.08
% 6.96/2.65  Subsumption          : 0.13
% 6.96/2.65  Abstraction          : 0.02
% 6.96/2.65  MUC search           : 0.00
% 6.96/2.65  Cooper               : 0.00
% 6.96/2.65  Total                : 1.54
% 6.96/2.65  Index Insertion      : 0.00
% 6.96/2.65  Index Deletion       : 0.00
% 6.96/2.65  Index Matching       : 0.00
% 6.96/2.65  BG Taut test         : 0.00
%------------------------------------------------------------------------------