TSTP Solution File: SWC378+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC378+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 : n008.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 11:02:23 EDT 2023

% Result   : Theorem 43.05s 27.76s
% Output   : CNFRefutation 43.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   80
% Syntax   : Number of formulae    :  122 (  14 unt;  78 typ;   0 def)
%            Number of atoms       :  145 (   8 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  188 (  87   ~;  91   |;   2   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    2 (   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    :   59 (  59 usr;  10 con; 0-2 aty)
%            Number of variables   :   44 (;  44   !;   0   ?;   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_54 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_53 > #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_54',type,
    '#skF_54': $i ).

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_53',type,
    '#skF_53': $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_1022,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ~ ssList(X)
                    | ( V != X )
                    | ( U != W )
                    | ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ~ ssList(Z)
                            | ( app(Y,Z) != X )
                            | ( app(Z,Y) != W ) ) )
                    | ! [X1] :
                        ( ~ ssItem(X1)
                        | ( ~ memberP(V,X1)
                          & ~ memberP(U,X1) )
                        | ( memberP(V,X1)
                          & memberP(U,X1) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f_498,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( memberP(app(V,W),U)
              <=> ( memberP(V,U)
                  | memberP(W,U) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).

tff(c_388,plain,
    ssItem('#skF_54'),
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_400,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_398,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_384,plain,
    ( ~ memberP('#skF_48','#skF_54')
    | ~ memberP('#skF_49','#skF_54') ),
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_414,plain,
    ( ~ memberP('#skF_50','#skF_54')
    | ~ memberP('#skF_51','#skF_54') ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_398,c_384]) ).

tff(c_439,plain,
    ~ memberP('#skF_51','#skF_54'),
    inference(splitLeft,[status(thm)],[c_414]) ).

tff(c_386,plain,
    ( memberP('#skF_48','#skF_54')
    | memberP('#skF_49','#skF_54') ),
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_413,plain,
    ( memberP('#skF_50','#skF_54')
    | memberP('#skF_51','#skF_54') ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_398,c_386]) ).

tff(c_448,plain,
    memberP('#skF_50','#skF_54'),
    inference(negUnitSimplification,[status(thm)],[c_439,c_413]) ).

tff(c_394,plain,
    ssList('#skF_53'),
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_396,plain,
    ssList('#skF_52'),
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_390,plain,
    app('#skF_53','#skF_52') = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_44242,plain,
    ! [W_2159,U_2160,V_2161] :
      ( memberP(W_2159,U_2160)
      | memberP(V_2161,U_2160)
      | ~ memberP(app(V_2161,W_2159),U_2160)
      | ~ ssList(W_2159)
      | ~ ssList(V_2161)
      | ~ ssItem(U_2160) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_44509,plain,
    ! [U_2160] :
      ( memberP('#skF_52',U_2160)
      | memberP('#skF_53',U_2160)
      | ~ memberP('#skF_50',U_2160)
      | ~ ssList('#skF_52')
      | ~ ssList('#skF_53')
      | ~ ssItem(U_2160) ),
    inference(superposition,[status(thm),theory(equality)],[c_390,c_44242]) ).

tff(c_44732,plain,
    ! [U_2162] :
      ( memberP('#skF_52',U_2162)
      | memberP('#skF_53',U_2162)
      | ~ memberP('#skF_50',U_2162)
      | ~ ssItem(U_2162) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_396,c_44509]) ).

tff(c_392,plain,
    app('#skF_52','#skF_53') = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1022]) ).

tff(c_32619,plain,
    ! [V_2034,U_2035,W_2036] :
      ( ~ memberP(V_2034,U_2035)
      | memberP(app(V_2034,W_2036),U_2035)
      | ~ ssList(W_2036)
      | ~ ssList(V_2034)
      | ~ ssItem(U_2035) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_32847,plain,
    ! [U_2035] :
      ( ~ memberP('#skF_52',U_2035)
      | memberP('#skF_51',U_2035)
      | ~ ssList('#skF_53')
      | ~ ssList('#skF_52')
      | ~ ssItem(U_2035) ),
    inference(superposition,[status(thm),theory(equality)],[c_392,c_32619]) ).

tff(c_32993,plain,
    ! [U_2035] :
      ( ~ memberP('#skF_52',U_2035)
      | memberP('#skF_51',U_2035)
      | ~ ssItem(U_2035) ),
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_394,c_32847]) ).

tff(c_62673,plain,
    ! [U_2500] :
      ( memberP('#skF_51',U_2500)
      | memberP('#skF_53',U_2500)
      | ~ memberP('#skF_50',U_2500)
      | ~ ssItem(U_2500) ),
    inference(resolution,[status(thm)],[c_44732,c_32993]) ).

tff(c_35417,plain,
    ! [W_2055,U_2056,V_2057] :
      ( ~ memberP(W_2055,U_2056)
      | memberP(app(V_2057,W_2055),U_2056)
      | ~ ssList(W_2055)
      | ~ ssList(V_2057)
      | ~ ssItem(U_2056) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_35648,plain,
    ! [U_2056] :
      ( ~ memberP('#skF_53',U_2056)
      | memberP('#skF_51',U_2056)
      | ~ ssList('#skF_53')
      | ~ ssList('#skF_52')
      | ~ ssItem(U_2056) ),
    inference(superposition,[status(thm),theory(equality)],[c_392,c_35417]) ).

tff(c_35794,plain,
    ! [U_2056] :
      ( ~ memberP('#skF_53',U_2056)
      | memberP('#skF_51',U_2056)
      | ~ ssItem(U_2056) ),
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_394,c_35648]) ).

tff(c_62682,plain,
    ! [U_2501] :
      ( memberP('#skF_51',U_2501)
      | ~ memberP('#skF_50',U_2501)
      | ~ ssItem(U_2501) ),
    inference(resolution,[status(thm)],[c_62673,c_35794]) ).

tff(c_62685,plain,
    ( ~ memberP('#skF_50','#skF_54')
    | ~ ssItem('#skF_54') ),
    inference(resolution,[status(thm)],[c_62682,c_439]) ).

tff(c_62689,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_448,c_62685]) ).

tff(c_62690,plain,
    ~ memberP('#skF_50','#skF_54'),
    inference(splitRight,[status(thm)],[c_414]) ).

tff(c_62691,plain,
    memberP('#skF_51','#skF_54'),
    inference(splitRight,[status(thm)],[c_414]) ).

tff(c_86513,plain,
    ! [W_3021,U_3022,V_3023] :
      ( memberP(W_3021,U_3022)
      | memberP(V_3023,U_3022)
      | ~ memberP(app(V_3023,W_3021),U_3022)
      | ~ ssList(W_3021)
      | ~ ssList(V_3023)
      | ~ ssItem(U_3022) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_86777,plain,
    ! [U_3022] :
      ( memberP('#skF_53',U_3022)
      | memberP('#skF_52',U_3022)
      | ~ memberP('#skF_51',U_3022)
      | ~ ssList('#skF_53')
      | ~ ssList('#skF_52')
      | ~ ssItem(U_3022) ),
    inference(superposition,[status(thm),theory(equality)],[c_392,c_86513]) ).

tff(c_87231,plain,
    ! [U_3028] :
      ( memberP('#skF_53',U_3028)
      | memberP('#skF_52',U_3028)
      | ~ memberP('#skF_51',U_3028)
      | ~ ssItem(U_3028) ),
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_394,c_86777]) ).

tff(c_76117,plain,
    ! [W_2904,U_2905,V_2906] :
      ( ~ memberP(W_2904,U_2905)
      | memberP(app(V_2906,W_2904),U_2905)
      | ~ ssList(W_2904)
      | ~ ssList(V_2906)
      | ~ ssItem(U_2905) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_76342,plain,
    ! [U_2905] :
      ( ~ memberP('#skF_52',U_2905)
      | memberP('#skF_50',U_2905)
      | ~ ssList('#skF_52')
      | ~ ssList('#skF_53')
      | ~ ssItem(U_2905) ),
    inference(superposition,[status(thm),theory(equality)],[c_390,c_76117]) ).

tff(c_76489,plain,
    ! [U_2905] :
      ( ~ memberP('#skF_52',U_2905)
      | memberP('#skF_50',U_2905)
      | ~ ssItem(U_2905) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_396,c_76342]) ).

tff(c_105781,plain,
    ! [U_3396] :
      ( memberP('#skF_50',U_3396)
      | memberP('#skF_53',U_3396)
      | ~ memberP('#skF_51',U_3396)
      | ~ ssItem(U_3396) ),
    inference(resolution,[status(thm)],[c_87231,c_76489]) ).

tff(c_77099,plain,
    ! [V_2915,U_2916,W_2917] :
      ( ~ memberP(V_2915,U_2916)
      | memberP(app(V_2915,W_2917),U_2916)
      | ~ ssList(W_2917)
      | ~ ssList(V_2915)
      | ~ ssItem(U_2916) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_77327,plain,
    ! [U_2916] :
      ( ~ memberP('#skF_53',U_2916)
      | memberP('#skF_50',U_2916)
      | ~ ssList('#skF_52')
      | ~ ssList('#skF_53')
      | ~ ssItem(U_2916) ),
    inference(superposition,[status(thm),theory(equality)],[c_390,c_77099]) ).

tff(c_77474,plain,
    ! [U_2916] :
      ( ~ memberP('#skF_53',U_2916)
      | memberP('#skF_50',U_2916)
      | ~ ssItem(U_2916) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_396,c_77327]) ).

tff(c_105790,plain,
    ! [U_3397] :
      ( memberP('#skF_50',U_3397)
      | ~ memberP('#skF_51',U_3397)
      | ~ ssItem(U_3397) ),
    inference(resolution,[status(thm)],[c_105781,c_77474]) ).

tff(c_105815,plain,
    ( memberP('#skF_50','#skF_54')
    | ~ ssItem('#skF_54') ),
    inference(resolution,[status(thm)],[c_62691,c_105790]) ).

tff(c_105837,plain,
    memberP('#skF_50','#skF_54'),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_105815]) ).

tff(c_105839,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_62690,c_105837]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC378+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 : n008.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 21:29:18 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 43.05/27.76  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.11/27.77  
% 43.11/27.77  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 43.11/27.80  
% 43.11/27.80  Inference rules
% 43.11/27.80  ----------------------
% 43.11/27.80  #Ref     : 10
% 43.11/27.80  #Sup     : 23106
% 43.11/27.80  #Fact    : 0
% 43.11/27.80  #Define  : 0
% 43.11/27.80  #Split   : 440
% 43.11/27.80  #Chain   : 0
% 43.11/27.80  #Close   : 0
% 43.11/27.80  
% 43.11/27.80  Ordering : KBO
% 43.11/27.80  
% 43.11/27.80  Simplification rules
% 43.11/27.80  ----------------------
% 43.11/27.80  #Subsume      : 3503
% 43.11/27.80  #Demod        : 21350
% 43.11/27.80  #Tautology    : 6716
% 43.11/27.80  #SimpNegUnit  : 2591
% 43.11/27.80  #BackRed      : 1149
% 43.11/27.80  
% 43.11/27.80  #Partial instantiations: 0
% 43.11/27.80  #Strategies tried      : 1
% 43.11/27.80  
% 43.11/27.80  Timing (in seconds)
% 43.11/27.80  ----------------------
% 43.11/27.81  Preprocessing        : 0.89
% 43.11/27.81  Parsing              : 0.42
% 43.11/27.81  CNF conversion       : 0.11
% 43.11/27.81  Main loop            : 25.86
% 43.11/27.81  Inferencing          : 5.17
% 43.11/27.81  Reduction            : 12.40
% 43.11/27.81  Demodulation         : 9.01
% 43.11/27.81  BG Simplification    : 0.19
% 43.11/27.81  Subsumption          : 6.34
% 43.11/27.81  Abstraction          : 0.28
% 43.11/27.81  MUC search           : 0.00
% 43.11/27.81  Cooper               : 0.00
% 43.11/27.81  Total                : 26.81
% 43.11/27.81  Index Insertion      : 0.00
% 43.11/27.81  Index Deletion       : 0.00
% 43.11/27.81  Index Matching       : 0.00
% 43.11/27.81  BG Taut test         : 0.00
%------------------------------------------------------------------------------