TSTP Solution File: SWC032+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC032+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 : n022.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 11:00:51 EDT 2023

% Result   : Theorem 8.17s 2.83s
% Output   : CNFRefutation 8.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   80
% Syntax   : Number of formulae    :  115 (  20 unt;  76 typ;   0 def)
%            Number of atoms       :   90 (  59 equ)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives :   82 (  31   ~;  30   |;  10   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   3 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    :   57 (  57 usr;   8 con; 0-2 aty)
%            Number of variables   :   22 (;  17   !;   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_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_1036,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ! [Y] :
                          ( ssList(Y)
                         => ( ( app(W,Y) != X )
                            | ~ strictorderedP(W)
                            | ? [Z] :
                                ( ssItem(Z)
                                & ? [X1] :
                                    ( ssList(X1)
                                    & ( app(cons(Z,nil),X1) = Y )
                                    & ? [X2] :
                                        ( ssItem(X2)
                                        & ? [X3] :
                                            ( ssList(X3)
                                            & ( app(X3,cons(X2,nil)) = W )
                                            & lt(X2,Z) ) ) ) ) ) )
                      | ( ( nil != X )
                        & ( nil = W ) )
                      | ( ( ( nil != V )
                          | ( nil = U ) )
                        & ( ( nil != U )
                          | ( nil = V ) ) ) ) ) ) ) ),
    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_779,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssList(V)
            & ( tl(U) = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).

tff(f_855,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( nil = app(U,V) )
          <=> ( ( nil = V )
              & ( nil = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).

tff(c_384,plain,
    ( ( nil != '#skF_50' )
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

tff(c_433,plain,
    nil != '#skF_50',
    inference(splitLeft,[status(thm)],[c_384]) ).

tff(c_394,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

tff(c_396,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

tff(c_412,plain,
    ( ( nil = '#skF_49' )
    | ( nil = '#skF_48' ) ),
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

tff(c_415,plain,
    ( ( nil = '#skF_51' )
    | ( nil = '#skF_48' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_412]) ).

tff(c_419,plain,
    ( ( nil = '#skF_51' )
    | ( nil = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_415]) ).

tff(c_434,plain,
    nil = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_433,c_419]) ).

tff(c_435,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_433]) ).

tff(c_400,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

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

tff(c_511,plain,
    ! [U_1652] :
      ( ( app(U_1652,'#skF_51') = U_1652 )
      | ~ ssList(U_1652) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_356]) ).

tff(c_522,plain,
    app('#skF_50','#skF_51') = '#skF_50',
    inference(resolution,[status(thm)],[c_400,c_511]) ).

tff(c_392,plain,
    ssList('#skF_52'),
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

tff(c_334,plain,
    ! [U_1047] :
      ( ( tl(U_1047) = '#skF_47'(U_1047) )
      | ( nil = U_1047 )
      | ~ ssList(U_1047) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_828,plain,
    ! [U_1699] :
      ( ( tl(U_1699) = '#skF_47'(U_1699) )
      | ( U_1699 = '#skF_51' )
      | ~ ssList(U_1699) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_334]) ).

tff(c_934,plain,
    ( ( tl('#skF_52') = '#skF_47'('#skF_52') )
    | ( '#skF_52' = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_392,c_828]) ).

tff(c_1005,plain,
    '#skF_52' = '#skF_51',
    inference(splitLeft,[status(thm)],[c_934]) ).

tff(c_390,plain,
    app('#skF_50','#skF_52') = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

tff(c_1009,plain,
    app('#skF_50','#skF_51') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1005,c_390]) ).

tff(c_1013,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_522,c_1009]) ).

tff(c_1015,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_435,c_1013]) ).

tff(c_1017,plain,
    '#skF_52' != '#skF_51',
    inference(splitRight,[status(thm)],[c_934]) ).

tff(c_354,plain,
    ! [V_1079,U_1077] :
      ( ( nil = V_1079 )
      | ( app(U_1077,V_1079) != nil )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(cnfTransformation,[status(thm)],[f_855]) ).

tff(c_2433,plain,
    ! [V_1762,U_1763] :
      ( ( V_1762 = '#skF_51' )
      | ( app(U_1763,V_1762) != '#skF_51' )
      | ~ ssList(V_1762)
      | ~ ssList(U_1763) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_434,c_354]) ).

tff(c_2445,plain,
    ( ( '#skF_52' = '#skF_51' )
    | ~ ssList('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_390,c_2433]) ).

tff(c_2462,plain,
    '#skF_52' = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_2445]) ).

tff(c_2464,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1017,c_2462]) ).

tff(c_2466,plain,
    nil = '#skF_50',
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_2465,plain,
    nil = '#skF_51',
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_2481,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_2466,c_2465]) ).

tff(c_406,plain,
    ( ( nil != '#skF_48' )
    | ( nil != '#skF_49' ) ),
    inference(cnfTransformation,[status(thm)],[f_1036]) ).

tff(c_414,plain,
    ( ( nil != '#skF_48' )
    | ( nil != '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_406]) ).

tff(c_418,plain,
    ( ( nil != '#skF_50' )
    | ( nil != '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_414]) ).

tff(c_2513,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2481,c_2466,c_2466,c_418]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC032+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14  % 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
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35  % CPULimit : 300
% 0.20/0.35  % WCLimit  : 300
% 0.20/0.35  % DateTime : Thu Aug  3 21:27:48 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 8.17/2.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.17/2.84  
% 8.17/2.84  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.17/2.87  
% 8.17/2.87  Inference rules
% 8.17/2.87  ----------------------
% 8.17/2.87  #Ref     : 0
% 8.17/2.87  #Sup     : 468
% 8.17/2.87  #Fact    : 0
% 8.17/2.87  #Define  : 0
% 8.17/2.87  #Split   : 11
% 8.17/2.87  #Chain   : 0
% 8.17/2.87  #Close   : 0
% 8.17/2.87  
% 8.17/2.87  Ordering : KBO
% 8.17/2.87  
% 8.17/2.87  Simplification rules
% 8.17/2.87  ----------------------
% 8.17/2.87  #Subsume      : 44
% 8.17/2.87  #Demod        : 274
% 8.17/2.87  #Tautology    : 136
% 8.17/2.87  #SimpNegUnit  : 20
% 8.17/2.87  #BackRed      : 37
% 8.17/2.87  
% 8.17/2.87  #Partial instantiations: 0
% 8.17/2.87  #Strategies tried      : 1
% 8.17/2.87  
% 8.17/2.87  Timing (in seconds)
% 8.17/2.87  ----------------------
% 8.17/2.87  Preprocessing        : 0.90
% 8.17/2.87  Parsing              : 0.41
% 8.17/2.87  CNF conversion       : 0.12
% 8.17/2.87  Main loop            : 0.91
% 8.17/2.87  Inferencing          : 0.26
% 8.17/2.87  Reduction            : 0.30
% 8.17/2.87  Demodulation         : 0.21
% 8.17/2.87  BG Simplification    : 0.08
% 8.17/2.87  Subsumption          : 0.18
% 8.17/2.87  Abstraction          : 0.04
% 8.17/2.87  MUC search           : 0.00
% 8.17/2.87  Cooper               : 0.00
% 8.17/2.87  Total                : 1.86
% 8.17/2.87  Index Insertion      : 0.00
% 8.17/2.87  Index Deletion       : 0.00
% 8.17/2.87  Index Matching       : 0.00
% 8.17/2.87  BG Taut test         : 0.00
%------------------------------------------------------------------------------