TSTP Solution File: SWC279-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC279-1 : 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 : n028.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 11:01:54 EDT 2023

% Result   : Unsatisfiable 167.88s 147.61s
% Output   : CNFRefutation 167.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  134 (  30 unt;  76 typ;   0 def)
%            Number of atoms       :  154 (  20 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  195 (  99   ~;  96   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   82 (  65   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   57 (  57 usr;  11 con; 0-2 aty)
%            Number of variables   :   48 (;  48   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > skaf48 > skaf47 > skaf46 > skaf45 > skaf43 > skaf42 > cons > app > #nlpp > tl > skaf83 > skaf82 > skaf81 > skaf80 > skaf79 > skaf78 > skaf77 > skaf76 > skaf75 > skaf74 > skaf73 > skaf72 > skaf71 > skaf70 > skaf69 > skaf68 > skaf67 > skaf66 > skaf65 > skaf64 > skaf63 > skaf62 > skaf61 > skaf60 > skaf59 > skaf58 > skaf57 > skaf56 > skaf55 > skaf54 > skaf53 > skaf52 > skaf51 > skaf50 > skaf49 > skaf44 > hd > skac3 > skac2 > sk8 > sk7 > sk6 > sk5 > sk4 > sk3 > sk2 > sk1 > nil

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(skaf56,type,
    skaf56: $i > $i ).

tff(segmentP,type,
    segmentP: ( $i * $i ) > $o ).

tff(totalorderedP,type,
    totalorderedP: $i > $o ).

tff(equalelemsP,type,
    equalelemsP: $i > $o ).

tff(skaf74,type,
    skaf74: $i > $i ).

tff(skaf61,type,
    skaf61: $i > $i ).

tff(skaf51,type,
    skaf51: $i > $i ).

tff(skaf83,type,
    skaf83: $i > $i ).

tff(skac2,type,
    skac2: $i ).

tff(skaf63,type,
    skaf63: $i > $i ).

tff(skaf62,type,
    skaf62: $i > $i ).

tff(sk2,type,
    sk2: $i ).

tff(skaf52,type,
    skaf52: $i > $i ).

tff(skaf50,type,
    skaf50: $i > $i ).

tff(skaf42,type,
    skaf42: ( $i * $i ) > $i ).

tff(skaf44,type,
    skaf44: $i > $i ).

tff(singletonP,type,
    singletonP: $i > $o ).

tff(skaf67,type,
    skaf67: $i > $i ).

tff(skaf75,type,
    skaf75: $i > $i ).

tff(sk1,type,
    sk1: $i ).

tff(skaf58,type,
    skaf58: $i > $i ).

tff(skaf46,type,
    skaf46: ( $i * $i ) > $i ).

tff(frontsegP,type,
    frontsegP: ( $i * $i ) > $o ).

tff(skaf70,type,
    skaf70: $i > $i ).

tff(totalorderP,type,
    totalorderP: $i > $o ).

tff(ssItem,type,
    ssItem: $i > $o ).

tff(sk6,type,
    sk6: $i ).

tff(skaf82,type,
    skaf82: $i > $i ).

tff(skaf47,type,
    skaf47: ( $i * $i ) > $i ).

tff(skaf76,type,
    skaf76: $i > $i ).

tff(skac3,type,
    skac3: $i ).

tff(skaf80,type,
    skaf80: $i > $i ).

tff(skaf59,type,
    skaf59: $i > $i ).

tff(skaf53,type,
    skaf53: $i > $i ).

tff(skaf45,type,
    skaf45: ( $i * $i ) > $i ).

tff(hd,type,
    hd: $i > $i ).

tff(app,type,
    app: ( $i * $i ) > $i ).

tff(skaf72,type,
    skaf72: $i > $i ).

tff(duplicatefreeP,type,
    duplicatefreeP: $i > $o ).

tff(skaf64,type,
    skaf64: $i > $i ).

tff(sk4,type,
    sk4: $i ).

tff(sk8,type,
    sk8: $i ).

tff(gt,type,
    gt: ( $i * $i ) > $o ).

tff(skaf71,type,
    skaf71: $i > $i ).

tff(skaf78,type,
    skaf78: $i > $i ).

tff(sk5,type,
    sk5: $i ).

tff(skaf79,type,
    skaf79: $i > $i ).

tff(rearsegP,type,
    rearsegP: ( $i * $i ) > $o ).

tff(memberP,type,
    memberP: ( $i * $i ) > $o ).

tff(skaf73,type,
    skaf73: $i > $i ).

tff(ssList,type,
    ssList: $i > $o ).

tff(cons,type,
    cons: ( $i * $i ) > $i ).

tff(skaf54,type,
    skaf54: $i > $i ).

tff(skaf77,type,
    skaf77: $i > $i ).

tff(sk3,type,
    sk3: $i ).

tff(skaf66,type,
    skaf66: $i > $i ).

tff(strictorderP,type,
    strictorderP: $i > $o ).

tff(skaf81,type,
    skaf81: $i > $i ).

tff(geq,type,
    geq: ( $i * $i ) > $o ).

tff(skaf60,type,
    skaf60: $i > $i ).

tff(leq,type,
    leq: ( $i * $i ) > $o ).

tff(lt,type,
    lt: ( $i * $i ) > $o ).

tff(skaf69,type,
    skaf69: $i > $i ).

tff(tl,type,
    tl: $i > $i ).

tff(neq,type,
    neq: ( $i * $i ) > $o ).

tff(skaf43,type,
    skaf43: ( $i * $i ) > $i ).

tff(skaf48,type,
    skaf48: ( $i * $i ) > $i ).

tff(skaf65,type,
    skaf65: $i > $i ).

tff(skaf57,type,
    skaf57: $i > $i ).

tff(sk7,type,
    sk7: $i ).

tff(nil,type,
    nil: $i ).

tff(skaf49,type,
    skaf49: $i > $i ).

tff(skaf55,type,
    skaf55: $i > $i ).

tff(skaf68,type,
    skaf68: $i > $i ).

tff(strictorderedP,type,
    strictorderedP: $i > $o ).

tff(cyclefreeP,type,
    cyclefreeP: $i > $o ).

tff(f_1706,axiom,
    ( ~ leq(sk8,sk5)
    | memberP(sk7,sk8) ),
    file(unknown,unknown) ).

tff(f_1691,axiom,
    ssItem(sk5),
    file(unknown,unknown) ).

tff(f_1693,axiom,
    ssList(sk7),
    file(unknown,unknown) ).

tff(f_1694,axiom,
    app(app(sk6,cons(sk5,nil)),sk7) = sk1,
    file(unknown,unknown) ).

tff(f_1692,axiom,
    ssList(sk6),
    file(unknown,unknown) ).

tff(f_1695,axiom,
    ssItem(sk8),
    file(unknown,unknown) ).

tff(f_1702,axiom,
    ( memberP(sk6,sk8)
    | ~ leq(sk5,sk8) ),
    file(unknown,unknown) ).

tff(f_1698,axiom,
    ( memberP(sk6,sk8)
    | memberP(sk7,sk8) ),
    file(unknown,unknown) ).

tff(f_1650,axiom,
    sk1 = sk3,
    file(unknown,unknown) ).

tff(f_1690,axiom,
    ! [A,B,C,D] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk3 )
      | ~ ssItem(D)
      | leq(D,A)
      | ~ memberP(B,D) ),
    file(unknown,unknown) ).

tff(f_1670,axiom,
    ! [A,B,C,D] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(B,cons(A,nil)),C) != sk3 )
      | ~ ssItem(D)
      | leq(A,D)
      | ~ memberP(C,D) ),
    file(unknown,unknown) ).

tff(f_1711,axiom,
    ( ~ leq(sk8,sk5)
    | ~ leq(sk5,sk8) ),
    file(unknown,unknown) ).

tff(c_402,plain,
    ( memberP(sk7,sk8)
    | ~ leq(sk8,sk5) ),
    inference(cnfTransformation,[status(thm)],[f_1706]) ).

tff(c_474,plain,
    ~ leq(sk8,sk5),
    inference(splitLeft,[status(thm)],[c_402]) ).

tff(c_388,plain,
    ssItem(sk5),
    inference(cnfTransformation,[status(thm)],[f_1691]) ).

tff(c_392,plain,
    ssList(sk7),
    inference(cnfTransformation,[status(thm)],[f_1693]) ).

tff(c_394,plain,
    app(app(sk6,cons(sk5,nil)),sk7) = sk1,
    inference(cnfTransformation,[status(thm)],[f_1694]) ).

tff(c_390,plain,
    ssList(sk6),
    inference(cnfTransformation,[status(thm)],[f_1692]) ).

tff(c_396,plain,
    ssItem(sk8),
    inference(cnfTransformation,[status(thm)],[f_1695]) ).

tff(c_400,plain,
    ( ~ leq(sk5,sk8)
    | memberP(sk6,sk8) ),
    inference(cnfTransformation,[status(thm)],[f_1702]) ).

tff(c_774,plain,
    ~ leq(sk5,sk8),
    inference(splitLeft,[status(thm)],[c_400]) ).

tff(c_398,plain,
    ( memberP(sk7,sk8)
    | memberP(sk6,sk8) ),
    inference(cnfTransformation,[status(thm)],[f_1698]) ).

tff(c_907,plain,
    memberP(sk6,sk8),
    inference(splitLeft,[status(thm)],[c_398]) ).

tff(c_382,plain,
    sk3 = sk1,
    inference(cnfTransformation,[status(thm)],[f_1650]) ).

tff(c_386,plain,
    ! [B_332,D_334,A_331,C_333] :
      ( ~ memberP(B_332,D_334)
      | leq(D_334,A_331)
      | ~ ssItem(D_334)
      | ( app(app(B_332,cons(A_331,nil)),C_333) != sk3 )
      | ~ ssList(C_333)
      | ~ ssList(B_332)
      | ~ ssItem(A_331) ),
    inference(cnfTransformation,[status(thm)],[f_1690]) ).

tff(c_10049,plain,
    ! [B_889,D_890,A_891,C_892] :
      ( ~ memberP(B_889,D_890)
      | leq(D_890,A_891)
      | ~ ssItem(D_890)
      | ( app(app(B_889,cons(A_891,nil)),C_892) != sk1 )
      | ~ ssList(C_892)
      | ~ ssList(B_889)
      | ~ ssItem(A_891) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_386]) ).

tff(c_10061,plain,
    ! [A_891,C_892] :
      ( leq(sk8,A_891)
      | ~ ssItem(sk8)
      | ( app(app(sk6,cons(A_891,nil)),C_892) != sk1 )
      | ~ ssList(C_892)
      | ~ ssList(sk6)
      | ~ ssItem(A_891) ),
    inference(resolution,[status(thm)],[c_907,c_10049]) ).

tff(c_66806,plain,
    ! [A_3186,C_3187] :
      ( leq(sk8,A_3186)
      | ( app(app(sk6,cons(A_3186,nil)),C_3187) != sk1 )
      | ~ ssList(C_3187)
      | ~ ssItem(A_3186) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_396,c_10061]) ).

tff(c_66831,plain,
    ( leq(sk8,sk5)
    | ~ ssList(sk7)
    | ~ ssItem(sk5) ),
    inference(superposition,[status(thm),theory(equality)],[c_394,c_66806]) ).

tff(c_66846,plain,
    leq(sk8,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_66831]) ).

tff(c_66848,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_474,c_66846]) ).

tff(c_66849,plain,
    memberP(sk7,sk8),
    inference(splitRight,[status(thm)],[c_398]) ).

tff(c_384,plain,
    ! [C_329,D_330,A_327,B_328] :
      ( ~ memberP(C_329,D_330)
      | leq(A_327,D_330)
      | ~ ssItem(D_330)
      | ( app(app(B_328,cons(A_327,nil)),C_329) != sk3 )
      | ~ ssList(C_329)
      | ~ ssList(B_328)
      | ~ ssItem(A_327) ),
    inference(cnfTransformation,[status(thm)],[f_1670]) ).

tff(c_76134,plain,
    ! [C_3679,D_3680,A_3681,B_3682] :
      ( ~ memberP(C_3679,D_3680)
      | leq(A_3681,D_3680)
      | ~ ssItem(D_3680)
      | ( app(app(B_3682,cons(A_3681,nil)),C_3679) != sk1 )
      | ~ ssList(C_3679)
      | ~ ssList(B_3682)
      | ~ ssItem(A_3681) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_384]) ).

tff(c_76146,plain,
    ! [A_3681,B_3682] :
      ( leq(A_3681,sk8)
      | ~ ssItem(sk8)
      | ( app(app(B_3682,cons(A_3681,nil)),sk7) != sk1 )
      | ~ ssList(sk7)
      | ~ ssList(B_3682)
      | ~ ssItem(A_3681) ),
    inference(resolution,[status(thm)],[c_66849,c_76134]) ).

tff(c_135649,plain,
    ! [A_5997,B_5998] :
      ( leq(A_5997,sk8)
      | ( app(app(B_5998,cons(A_5997,nil)),sk7) != sk1 )
      | ~ ssList(B_5998)
      | ~ ssItem(A_5997) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_396,c_76146]) ).

tff(c_135689,plain,
    ( leq(sk5,sk8)
    | ~ ssList(sk6)
    | ~ ssItem(sk5) ),
    inference(superposition,[status(thm),theory(equality)],[c_394,c_135649]) ).

tff(c_135707,plain,
    leq(sk5,sk8),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_390,c_135689]) ).

tff(c_135709,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_774,c_135707]) ).

tff(c_135710,plain,
    memberP(sk6,sk8),
    inference(splitRight,[status(thm)],[c_400]) ).

tff(c_144518,plain,
    ! [B_6484,D_6485,A_6486,C_6487] :
      ( ~ memberP(B_6484,D_6485)
      | leq(D_6485,A_6486)
      | ~ ssItem(D_6485)
      | ( app(app(B_6484,cons(A_6486,nil)),C_6487) != sk1 )
      | ~ ssList(C_6487)
      | ~ ssList(B_6484)
      | ~ ssItem(A_6486) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_386]) ).

tff(c_144530,plain,
    ! [A_6486,C_6487] :
      ( leq(sk8,A_6486)
      | ~ ssItem(sk8)
      | ( app(app(sk6,cons(A_6486,nil)),C_6487) != sk1 )
      | ~ ssList(C_6487)
      | ~ ssList(sk6)
      | ~ ssItem(A_6486) ),
    inference(resolution,[status(thm)],[c_135710,c_144518]) ).

tff(c_204262,plain,
    ! [A_8810,C_8811] :
      ( leq(sk8,A_8810)
      | ( app(app(sk6,cons(A_8810,nil)),C_8811) != sk1 )
      | ~ ssList(C_8811)
      | ~ ssItem(A_8810) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_396,c_144530]) ).

tff(c_204287,plain,
    ( leq(sk8,sk5)
    | ~ ssList(sk7)
    | ~ ssItem(sk5) ),
    inference(superposition,[status(thm),theory(equality)],[c_394,c_204262]) ).

tff(c_204302,plain,
    leq(sk8,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_204287]) ).

tff(c_204304,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_474,c_204302]) ).

tff(c_204306,plain,
    leq(sk8,sk5),
    inference(splitRight,[status(thm)],[c_402]) ).

tff(c_204309,plain,
    ~ leq(sk5,sk8),
    inference(splitLeft,[status(thm)],[c_400]) ).

tff(c_204305,plain,
    memberP(sk7,sk8),
    inference(splitRight,[status(thm)],[c_402]) ).

tff(c_213955,plain,
    ! [C_9326,D_9327,A_9328,B_9329] :
      ( ~ memberP(C_9326,D_9327)
      | leq(A_9328,D_9327)
      | ~ ssItem(D_9327)
      | ( app(app(B_9329,cons(A_9328,nil)),C_9326) != sk1 )
      | ~ ssList(C_9326)
      | ~ ssList(B_9329)
      | ~ ssItem(A_9328) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_384]) ).

tff(c_213967,plain,
    ! [A_9328,B_9329] :
      ( leq(A_9328,sk8)
      | ~ ssItem(sk8)
      | ( app(app(B_9329,cons(A_9328,nil)),sk7) != sk1 )
      | ~ ssList(sk7)
      | ~ ssList(B_9329)
      | ~ ssItem(A_9328) ),
    inference(resolution,[status(thm)],[c_204305,c_213955]) ).

tff(c_272421,plain,
    ! [A_11644,B_11645] :
      ( leq(A_11644,sk8)
      | ( app(app(B_11645,cons(A_11644,nil)),sk7) != sk1 )
      | ~ ssList(B_11645)
      | ~ ssItem(A_11644) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_396,c_213967]) ).

tff(c_272461,plain,
    ( leq(sk5,sk8)
    | ~ ssList(sk6)
    | ~ ssItem(sk5) ),
    inference(superposition,[status(thm),theory(equality)],[c_394,c_272421]) ).

tff(c_272479,plain,
    leq(sk5,sk8),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_390,c_272461]) ).

tff(c_272481,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_204309,c_272479]) ).

tff(c_272483,plain,
    leq(sk5,sk8),
    inference(splitRight,[status(thm)],[c_400]) ).

tff(c_404,plain,
    ( ~ leq(sk5,sk8)
    | ~ leq(sk8,sk5) ),
    inference(cnfTransformation,[status(thm)],[f_1711]) ).

tff(c_272784,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_204306,c_272483,c_404]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC279-1 : 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
% 0.14/0.36  % Computer : n028.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 21:53:24 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 167.88/147.61  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 167.88/147.62  
% 167.88/147.62  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 167.92/147.65  
% 167.92/147.65  Inference rules
% 167.92/147.65  ----------------------
% 167.92/147.65  #Ref     : 0
% 167.92/147.65  #Sup     : 63309
% 167.92/147.65  #Fact    : 0
% 167.92/147.65  #Define  : 0
% 167.92/147.65  #Split   : 326
% 167.92/147.65  #Chain   : 0
% 167.92/147.66  #Close   : 0
% 167.92/147.66  
% 167.92/147.66  Ordering : KBO
% 167.92/147.66  
% 167.92/147.66  Simplification rules
% 167.92/147.66  ----------------------
% 167.92/147.66  #Subsume      : 15987
% 167.92/147.66  #Demod        : 56086
% 167.92/147.66  #Tautology    : 13224
% 167.92/147.66  #SimpNegUnit  : 2208
% 167.92/147.66  #BackRed      : 483
% 167.92/147.66  
% 167.92/147.66  #Partial instantiations: 0
% 167.92/147.66  #Strategies tried      : 1
% 167.92/147.66  
% 167.92/147.66  Timing (in seconds)
% 167.92/147.66  ----------------------
% 167.92/147.66  Preprocessing        : 0.88
% 167.92/147.66  Parsing              : 0.46
% 167.92/147.66  CNF conversion       : 0.06
% 167.92/147.66  Main loop            : 145.66
% 167.92/147.66  Inferencing          : 24.48
% 167.92/147.66  Reduction            : 71.06
% 167.92/147.66  Demodulation         : 51.56
% 167.92/147.66  BG Simplification    : 0.40
% 167.92/147.66  Subsumption          : 40.45
% 167.92/147.66  Abstraction          : 1.08
% 167.92/147.66  MUC search           : 0.00
% 167.92/147.66  Cooper               : 0.00
% 167.92/147.66  Total                : 146.61
% 167.92/147.66  Index Insertion      : 0.00
% 167.92/147.66  Index Deletion       : 0.00
% 167.92/147.66  Index Matching       : 0.00
% 167.92/147.66  BG Taut test         : 0.00
%------------------------------------------------------------------------------