TSTP Solution File: SWC003-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC003-1 : 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 : 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 11:00:40 EDT 2023

% Result   : Unsatisfiable 36.79s 20.93s
% Output   : CNFRefutation 36.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  126 (  19 unt;  75 typ;   0 def)
%            Number of atoms       :  114 (  30 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  136 (  73   ~;  63   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 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    :   56 (  56 usr;  10 con; 0-2 aty)
%            Number of variables   :   25 (;  25   !;   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 > 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(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_1653,axiom,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file(unknown,unknown) ).

tff(f_1649,axiom,
    sk2 = sk4,
    file(unknown,unknown) ).

tff(f_1730,axiom,
    ( ssItem(sk5)
    | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ssList(nil),
    file(unknown,unknown) ).

tff(f_437,axiom,
    ! [U,V] :
      ( ( cons(U,V) != nil )
      | ~ ssItem(U)
      | ~ ssList(V) ),
    file(unknown,unknown) ).

tff(f_342,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ssList(cons(U,V)) ),
    file(unknown,unknown) ).

tff(f_1734,axiom,
    ( ssList(sk6)
    | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_1738,axiom,
    ( ssList(sk7)
    | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

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

tff(f_1746,axiom,
    ( ( app(sk6,sk7) = sk3 )
    | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_1742,axiom,
    ( ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 )
    | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_1726,axiom,
    ! [A,B,C] :
      ( ~ ssList(A)
      | ~ ssList(B)
      | ~ ssList(C)
      | ( app(app(A,B),C) != sk2 )
      | ( app(A,C) != sk1 )
      | ~ neq(B,nil)
      | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_456,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | neq(V,U)
      | ( V = U ) ),
    file(unknown,unknown) ).

tff(c_384,plain,
    neq(sk2,nil),
    inference(cnfTransformation,[status(thm)],[f_1653]) ).

tff(c_380,plain,
    sk4 = sk2,
    inference(cnfTransformation,[status(thm)],[f_1649]) ).

tff(c_404,plain,
    ( ~ neq(sk4,nil)
    | ssItem(sk5) ),
    inference(cnfTransformation,[status(thm)],[f_1730]) ).

tff(c_424,plain,
    ( ~ neq(sk2,nil)
    | ssItem(sk5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_404]) ).

tff(c_432,plain,
    ssItem(sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_424]) ).

tff(c_16,plain,
    ssList(nil),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_1360,plain,
    ! [V_458,U_459] :
      ( ~ ssList(V_458)
      | ~ ssItem(U_459)
      | ( cons(U_459,V_458) != nil ) ),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_1831,plain,
    ! [U_485] :
      ( ~ ssItem(U_485)
      | ( cons(U_485,nil) != nil ) ),
    inference(resolution,[status(thm)],[c_16,c_1360]) ).

tff(c_1907,plain,
    cons(sk5,nil) != nil,
    inference(resolution,[status(thm)],[c_432,c_1831]) ).

tff(c_172,plain,
    ! [U_82,V_83] :
      ( ssList(cons(U_82,V_83))
      | ~ ssList(V_83)
      | ~ ssItem(U_82) ),
    inference(cnfTransformation,[status(thm)],[f_342]) ).

tff(c_406,plain,
    ( ~ neq(sk4,nil)
    | ssList(sk6) ),
    inference(cnfTransformation,[status(thm)],[f_1734]) ).

tff(c_429,plain,
    ( ~ neq(sk2,nil)
    | ssList(sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_406]) ).

tff(c_442,plain,
    ssList(sk6),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_429]) ).

tff(c_408,plain,
    ( ~ neq(sk4,nil)
    | ssList(sk7) ),
    inference(cnfTransformation,[status(thm)],[f_1738]) ).

tff(c_425,plain,
    ( ~ neq(sk2,nil)
    | ssList(sk7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_408]) ).

tff(c_434,plain,
    ssList(sk7),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_425]) ).

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

tff(c_412,plain,
    ( ~ neq(sk4,nil)
    | ( app(sk6,sk7) = sk3 ) ),
    inference(cnfTransformation,[status(thm)],[f_1746]) ).

tff(c_423,plain,
    ( ~ neq(sk4,nil)
    | ( app(sk6,sk7) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_412]) ).

tff(c_430,plain,
    ( ~ neq(sk2,nil)
    | ( app(sk6,sk7) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_423]) ).

tff(c_444,plain,
    app(sk6,sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_430]) ).

tff(c_410,plain,
    ( ~ neq(sk4,nil)
    | ( app(app(sk6,cons(sk5,nil)),sk7) = sk4 ) ),
    inference(cnfTransformation,[status(thm)],[f_1742]) ).

tff(c_426,plain,
    ( ~ neq(sk2,nil)
    | ( app(app(sk6,cons(sk5,nil)),sk7) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_410]) ).

tff(c_436,plain,
    app(app(sk6,cons(sk5,nil)),sk7) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_426]) ).

tff(c_402,plain,
    ! [B_332,A_331,C_333] :
      ( ~ neq(sk4,nil)
      | ~ neq(B_332,nil)
      | ( app(A_331,C_333) != sk1 )
      | ( app(app(A_331,B_332),C_333) != sk2 )
      | ~ ssList(C_333)
      | ~ ssList(B_332)
      | ~ ssList(A_331) ),
    inference(cnfTransformation,[status(thm)],[f_1726]) ).

tff(c_427,plain,
    ! [B_332,A_331,C_333] :
      ( ~ neq(sk2,nil)
      | ~ neq(B_332,nil)
      | ( app(A_331,C_333) != sk1 )
      | ( app(app(A_331,B_332),C_333) != sk2 )
      | ~ ssList(C_333)
      | ~ ssList(B_332)
      | ~ ssList(A_331) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_402]) ).

tff(c_48389,plain,
    ! [B_2677,A_2678,C_2679] :
      ( ~ neq(B_2677,nil)
      | ( app(A_2678,C_2679) != sk1 )
      | ( app(app(A_2678,B_2677),C_2679) != sk2 )
      | ~ ssList(C_2679)
      | ~ ssList(B_2677)
      | ~ ssList(A_2678) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_427]) ).

tff(c_48534,plain,
    ( ~ neq(cons(sk5,nil),nil)
    | ( app(sk6,sk7) != sk1 )
    | ~ ssList(sk7)
    | ~ ssList(cons(sk5,nil))
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_436,c_48389]) ).

tff(c_48688,plain,
    ( ~ neq(cons(sk5,nil),nil)
    | ~ ssList(cons(sk5,nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_442,c_434,c_444,c_48534]) ).

tff(c_55293,plain,
    ~ ssList(cons(sk5,nil)),
    inference(splitLeft,[status(thm)],[c_48688]) ).

tff(c_55296,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sk5) ),
    inference(resolution,[status(thm)],[c_172,c_55293]) ).

tff(c_55300,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_432,c_16,c_55296]) ).

tff(c_55302,plain,
    ssList(cons(sk5,nil)),
    inference(splitRight,[status(thm)],[c_48688]) ).

tff(c_200,plain,
    ! [V_102,U_101] :
      ( ( V_102 = U_101 )
      | neq(V_102,U_101)
      | ~ ssList(V_102)
      | ~ ssList(U_101) ),
    inference(cnfTransformation,[status(thm)],[f_456]) ).

tff(c_55301,plain,
    ~ neq(cons(sk5,nil),nil),
    inference(splitRight,[status(thm)],[c_48688]) ).

tff(c_55412,plain,
    ( ( cons(sk5,nil) = nil )
    | ~ ssList(cons(sk5,nil))
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_200,c_55301]) ).

tff(c_55418,plain,
    cons(sk5,nil) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_55302,c_55412]) ).

tff(c_55420,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1907,c_55418]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC003-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n010.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 21:05:43 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 36.79/20.93  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.79/20.94  
% 36.79/20.94  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.79/20.97  
% 36.79/20.97  Inference rules
% 36.79/20.97  ----------------------
% 36.79/20.97  #Ref     : 0
% 36.79/20.97  #Sup     : 12308
% 36.79/20.97  #Fact    : 0
% 36.79/20.97  #Define  : 0
% 36.79/20.97  #Split   : 53
% 36.79/20.97  #Chain   : 0
% 36.79/20.97  #Close   : 0
% 36.79/20.97  
% 36.79/20.97  Ordering : KBO
% 36.79/20.97  
% 36.79/20.97  Simplification rules
% 36.79/20.97  ----------------------
% 36.79/20.97  #Subsume      : 2474
% 36.79/20.97  #Demod        : 14613
% 36.79/20.97  #Tautology    : 4267
% 36.79/20.97  #SimpNegUnit  : 245
% 36.79/20.97  #BackRed      : 133
% 36.79/20.97  
% 36.79/20.97  #Partial instantiations: 0
% 36.79/20.97  #Strategies tried      : 1
% 36.79/20.97  
% 36.79/20.97  Timing (in seconds)
% 36.79/20.97  ----------------------
% 36.79/20.98  Preprocessing        : 0.95
% 36.79/20.98  Parsing              : 0.47
% 36.79/20.98  CNF conversion       : 0.07
% 36.79/20.98  Main loop            : 18.94
% 36.79/20.98  Inferencing          : 3.92
% 36.79/20.98  Reduction            : 9.55
% 36.79/20.98  Demodulation         : 7.19
% 36.79/20.98  BG Simplification    : 0.13
% 36.79/20.98  Subsumption          : 4.12
% 36.79/20.98  Abstraction          : 0.21
% 36.79/20.98  MUC search           : 0.00
% 36.79/20.98  Cooper               : 0.00
% 36.79/20.98  Total                : 19.95
% 36.79/20.98  Index Insertion      : 0.00
% 36.79/20.98  Index Deletion       : 0.00
% 36.79/20.98  Index Matching       : 0.00
% 36.79/20.98  BG Taut test         : 0.00
%------------------------------------------------------------------------------