TSTP Solution File: SWC402+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC402+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 : n010.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 11:02:30 EDT 2023

% Result   : Theorem 21.74s 9.17s
% Output   : CNFRefutation 21.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  114 (  15 unt;  78 typ;   0 def)
%            Number of atoms       :  129 (  24 equ)
%            Maximal formula atoms :   29 (   3 avg)
%            Number of connectives :  167 (  74   ~;  66   |;  14   &)
%                                         (   2 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   5 avg)
%            Maximal term depth    :    5 (   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   :   49 (;  40   !;   9   ?;   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_1058,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(app(Y,W),Z) != X )
                            | ~ totalorderedP(W)
                            | ? [X1] :
                                ( ssItem(X1)
                                & ? [X2] :
                                    ( ssList(X2)
                                    & ( app(X2,cons(X1,nil)) = Y )
                                    & ? [X3] :
                                        ( ssItem(X3)
                                        & ? [X4] :
                                            ( ssList(X4)
                                            & ( app(cons(X3,nil),X4) = W )
                                            & leq(X1,X3) ) ) ) )
                            | ? [X5] :
                                ( ssItem(X5)
                                & ? [X6] :
                                    ( ssList(X6)
                                    & ( app(cons(X5,nil),X6) = Z )
                                    & ? [X7] :
                                        ( ssItem(X7)
                                        & ? [X8] :
                                            ( ssList(X8)
                                            & ( app(X8,cons(X7,nil)) = W )
                                            & leq(X7,X5) ) ) ) ) ) )
                    | ! [X9] :
                        ( ~ ssItem(X9)
                        | ~ memberP(U,X9)
                        | memberP(V,X9) )
                    | ( ( nil != X )
                      & ( nil = W ) ) ) ) ) ),
    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(f_399,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).

tff(f_96,axiom,
    ! [U] :
      ( ssList(U)
     => ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & ( cons(V,nil) = U ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).

tff(f_442,axiom,
    ! [U] :
      ( ssItem(U)
     => leq(U,U) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax31) ).

tff(c_390,plain,
    ssItem('#skF_54'),
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_404,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_388,plain,
    memberP('#skF_48','#skF_54'),
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_419,plain,
    memberP('#skF_50','#skF_54'),
    inference(demodulation,[status(thm),theory(equality)],[c_404,c_388]) ).

tff(c_402,plain,
    ssList('#skF_52'),
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_410,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_41474,plain,
    ! [W_4548,U_4549,V_4550] :
      ( ~ memberP(W_4548,U_4549)
      | memberP(app(V_4550,W_4548),U_4549)
      | ~ ssList(W_4548)
      | ~ ssList(V_4550)
      | ~ ssItem(U_4549) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_192,plain,
    ! [U_896,V_898] :
      ( ssList(app(U_896,V_898))
      | ~ ssList(V_898)
      | ~ ssList(U_896) ),
    inference(cnfTransformation,[status(thm)],[f_399]) ).

tff(c_400,plain,
    ssList('#skF_53'),
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_398,plain,
    app(app('#skF_52','#skF_50'),'#skF_53') = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_34536,plain,
    ! [U_4317] :
      ( ( cons('#skF_5'(U_4317),nil) = U_4317 )
      | ~ singletonP(U_4317)
      | ~ ssList(U_4317) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_202,plain,
    ! [U_917] :
      ( leq(U_917,U_917)
      | ~ ssItem(U_917) ),
    inference(cnfTransformation,[status(thm)],[f_442]) ).

tff(c_448,plain,
    ! [X1_3128,X3_3129,X4_3130,X2_3131] :
      ( ~ leq(X1_3128,X3_3129)
      | ( app(cons(X3_3129,nil),X4_3130) != '#skF_50' )
      | ~ ssList(X4_3130)
      | ~ ssItem(X3_3129)
      | ( app(X2_3131,cons(X1_3128,nil)) != '#skF_52' )
      | ~ ssList(X2_3131)
      | ~ ssItem(X1_3128) ),
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_451,plain,
    ! [U_917,X4_3130,X2_3131] :
      ( ( app(cons(U_917,nil),X4_3130) != '#skF_50' )
      | ~ ssList(X4_3130)
      | ( app(X2_3131,cons(U_917,nil)) != '#skF_52' )
      | ~ ssList(X2_3131)
      | ~ ssItem(U_917) ),
    inference(resolution,[status(thm)],[c_202,c_448]) ).

tff(c_34608,plain,
    ! [U_4323,X4_4324,X2_4325] :
      ( ( app(U_4323,X4_4324) != '#skF_50' )
      | ~ ssList(X4_4324)
      | ( app(X2_4325,cons('#skF_5'(U_4323),nil)) != '#skF_52' )
      | ~ ssList(X2_4325)
      | ~ ssItem('#skF_5'(U_4323))
      | ~ singletonP(U_4323)
      | ~ ssList(U_4323) ),
    inference(superposition,[status(thm),theory(equality)],[c_34536,c_451]) ).

tff(c_34640,plain,
    ! [X2_4325] :
      ( ( '#skF_51' != '#skF_50' )
      | ~ ssList('#skF_53')
      | ( app(X2_4325,cons('#skF_5'(app('#skF_52','#skF_50')),nil)) != '#skF_52' )
      | ~ ssList(X2_4325)
      | ~ ssItem('#skF_5'(app('#skF_52','#skF_50')))
      | ~ singletonP(app('#skF_52','#skF_50'))
      | ~ ssList(app('#skF_52','#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_398,c_34608]) ).

tff(c_34674,plain,
    ! [X2_4325] :
      ( ( '#skF_51' != '#skF_50' )
      | ( app(X2_4325,cons('#skF_5'(app('#skF_52','#skF_50')),nil)) != '#skF_52' )
      | ~ ssList(X2_4325)
      | ~ ssItem('#skF_5'(app('#skF_52','#skF_50')))
      | ~ singletonP(app('#skF_52','#skF_50'))
      | ~ ssList(app('#skF_52','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_34640]) ).

tff(c_35915,plain,
    ~ ssList(app('#skF_52','#skF_50')),
    inference(splitLeft,[status(thm)],[c_34674]) ).

tff(c_35918,plain,
    ( ~ ssList('#skF_50')
    | ~ ssList('#skF_52') ),
    inference(resolution,[status(thm)],[c_192,c_35915]) ).

tff(c_35922,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_410,c_35918]) ).

tff(c_35924,plain,
    ssList(app('#skF_52','#skF_50')),
    inference(splitRight,[status(thm)],[c_34674]) ).

tff(c_40733,plain,
    ! [V_4535,U_4536,W_4537] :
      ( ~ memberP(V_4535,U_4536)
      | memberP(app(V_4535,W_4537),U_4536)
      | ~ ssList(W_4537)
      | ~ ssList(V_4535)
      | ~ ssItem(U_4536) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_40859,plain,
    ! [U_4536] :
      ( ~ memberP(app('#skF_52','#skF_50'),U_4536)
      | memberP('#skF_51',U_4536)
      | ~ ssList('#skF_53')
      | ~ ssList(app('#skF_52','#skF_50'))
      | ~ ssItem(U_4536) ),
    inference(superposition,[status(thm),theory(equality)],[c_398,c_40733]) ).

tff(c_40937,plain,
    ! [U_4536] :
      ( ~ memberP(app('#skF_52','#skF_50'),U_4536)
      | memberP('#skF_51',U_4536)
      | ~ ssItem(U_4536) ),
    inference(demodulation,[status(thm),theory(equality)],[c_35924,c_400,c_40859]) ).

tff(c_41478,plain,
    ! [U_4549] :
      ( memberP('#skF_51',U_4549)
      | ~ memberP('#skF_50',U_4549)
      | ~ ssList('#skF_50')
      | ~ ssList('#skF_52')
      | ~ ssItem(U_4549) ),
    inference(resolution,[status(thm)],[c_41474,c_40937]) ).

tff(c_47444,plain,
    ! [U_4636] :
      ( memberP('#skF_51',U_4636)
      | ~ memberP('#skF_50',U_4636)
      | ~ ssItem(U_4636) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_410,c_41478]) ).

tff(c_406,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_386,plain,
    ~ memberP('#skF_49','#skF_54'),
    inference(cnfTransformation,[status(thm)],[f_1058]) ).

tff(c_420,plain,
    ~ memberP('#skF_51','#skF_54'),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_386]) ).

tff(c_47447,plain,
    ( ~ memberP('#skF_50','#skF_54')
    | ~ ssItem('#skF_54') ),
    inference(resolution,[status(thm)],[c_47444,c_420]) ).

tff(c_47451,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_419,c_47447]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC402+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 : n010.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 21:05:28 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 21.74/9.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.74/9.18  
% 21.74/9.18  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.96/9.21  
% 21.96/9.21  Inference rules
% 21.96/9.21  ----------------------
% 21.96/9.21  #Ref     : 6
% 21.96/9.21  #Sup     : 10683
% 21.96/9.21  #Fact    : 0
% 21.96/9.21  #Define  : 0
% 21.96/9.21  #Split   : 174
% 21.96/9.21  #Chain   : 0
% 21.96/9.21  #Close   : 0
% 21.96/9.21  
% 21.96/9.21  Ordering : KBO
% 21.96/9.21  
% 21.96/9.21  Simplification rules
% 21.96/9.21  ----------------------
% 21.96/9.21  #Subsume      : 1945
% 21.96/9.21  #Demod        : 8707
% 21.96/9.21  #Tautology    : 2695
% 21.96/9.21  #SimpNegUnit  : 771
% 21.96/9.21  #BackRed      : 335
% 21.96/9.21  
% 21.96/9.21  #Partial instantiations: 0
% 21.96/9.21  #Strategies tried      : 1
% 21.96/9.21  
% 21.96/9.21  Timing (in seconds)
% 21.96/9.21  ----------------------
% 21.96/9.21  Preprocessing        : 0.92
% 21.96/9.21  Parsing              : 0.41
% 21.96/9.21  CNF conversion       : 0.14
% 21.96/9.21  Main loop            : 7.23
% 21.96/9.21  Inferencing          : 1.72
% 21.96/9.21  Reduction            : 3.16
% 21.96/9.21  Demodulation         : 2.39
% 21.96/9.21  BG Simplification    : 0.13
% 21.96/9.21  Subsumption          : 1.73
% 21.96/9.21  Abstraction          : 0.14
% 21.96/9.21  MUC search           : 0.00
% 21.96/9.21  Cooper               : 0.00
% 21.96/9.21  Total                : 8.19
% 21.96/9.21  Index Insertion      : 0.00
% 21.96/9.21  Index Deletion       : 0.00
% 21.96/9.21  Index Matching       : 0.00
% 21.96/9.21  BG Taut test         : 0.00
%------------------------------------------------------------------------------