TSTP Solution File: SWC013+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC013+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 : n027.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 11:00:44 EDT 2023

% Result   : Theorem 9.80s 3.17s
% Output   : CNFRefutation 9.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   81
% Syntax   : Number of formulae    :  135 (  34 unt;  75 typ;   0 def)
%            Number of atoms       :  135 (  44 equ)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives :  137 (  62   ~;  50   |;  12   &)
%                                         (   1 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   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    :   56 (  56 usr;   7 con; 0-2 aty)
%            Number of variables   :   24 (;  19   !;   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_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_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_1031,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ( ( ~ neq(V,nil)
                          | ? [Y] :
                              ( ssList(Y)
                              & ( W != Y )
                              & ? [Z] :
                                  ( ssItem(Z)
                                  & ( cons(Z,nil) = Y )
                                  & ( hd(X) = Z )
                                  & neq(nil,X) ) )
                          | ? [X1] :
                              ( ssList(X1)
                              & ( U = X1 )
                              & ? [X2] :
                                  ( ssItem(X2)
                                  & ( cons(X2,nil) = X1 )
                                  & ( hd(V) = X2 )
                                  & neq(nil,V) ) ) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_371,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssItem(hd(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).

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_311,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> ( U != V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).

tff(f_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(f_318,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ssList(cons(V,U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).

tff(c_390,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_388,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_4805,plain,
    ! [U_1489] :
      ( ssItem(hd(U_1489))
      | ( nil = U_1489 )
      | ~ ssList(U_1489) ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_2329,plain,
    ! [U_1393] :
      ( ( tl(U_1393) = '#skF_47'(U_1393) )
      | ( nil = U_1393 )
      | ~ ssList(U_1393) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_2437,plain,
    ( ( tl('#skF_51') = '#skF_47'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_2329]) ).

tff(c_2439,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_2437]) ).

tff(c_386,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_406,plain,
    neq('#skF_49',nil),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_411,plain,
    neq('#skF_51',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).

tff(c_2472,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_2439,c_411]) ).

tff(c_164,plain,
    ! [V_858] :
      ( ~ neq(V_858,V_858)
      | ~ ssList(V_858) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_2625,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_2472,c_164]) ).

tff(c_2630,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_2625]) ).

tff(c_2632,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_2437]) ).

tff(c_168,plain,
    ssList(nil),
    inference(cnfTransformation,[status(thm)],[f_319]) ).

tff(c_4649,plain,
    ! [U_1468,V_1469] :
      ( neq(U_1468,V_1469)
      | ( V_1469 = U_1468 )
      | ~ ssList(V_1469)
      | ~ ssList(U_1468) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_807,plain,
    ! [U_1298] :
      ( ( tl(U_1298) = '#skF_47'(U_1298) )
      | ( nil = U_1298 )
      | ~ ssList(U_1298) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_915,plain,
    ( ( tl('#skF_51') = '#skF_47'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_807]) ).

tff(c_917,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_915]) ).

tff(c_948,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_917,c_411]) ).

tff(c_1199,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_948,c_164]) ).

tff(c_1204,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_1199]) ).

tff(c_1206,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_915]) ).

tff(c_184,plain,
    ! [U_888] :
      ( ssItem(hd(U_888))
      | ( nil = U_888 )
      | ~ ssList(U_888) ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_1941,plain,
    ! [V_1328,U_1329] :
      ( ssList(cons(V_1328,U_1329))
      | ~ ssItem(V_1328)
      | ~ ssList(U_1329) ),
    inference(cnfTransformation,[status(thm)],[f_318]) ).

tff(c_398,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) = '#skF_50' )
    | ~ ssList(cons(hd('#skF_51'),nil))
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_415,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) = '#skF_50' )
    | ~ ssList(cons(hd('#skF_51'),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_398]) ).

tff(c_431,plain,
    ~ ssList(cons(hd('#skF_51'),nil)),
    inference(splitLeft,[status(thm)],[c_415]) ).

tff(c_1953,plain,
    ( ~ ssItem(hd('#skF_51'))
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_1941,c_431]) ).

tff(c_1959,plain,
    ~ ssItem(hd('#skF_51')),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_1953]) ).

tff(c_1962,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_184,c_1959]) ).

tff(c_1965,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_1962]) ).

tff(c_1967,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1206,c_1965]) ).

tff(c_1968,plain,
    ( ~ ssItem(hd('#skF_51'))
    | ~ neq(nil,'#skF_51')
    | ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
    inference(splitRight,[status(thm)],[c_415]) ).

tff(c_1981,plain,
    ~ neq(nil,'#skF_51'),
    inference(splitLeft,[status(thm)],[c_1968]) ).

tff(c_4652,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_4649,c_1981]) ).

tff(c_4663,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_4652]) ).

tff(c_4665,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2632,c_4663]) ).

tff(c_4666,plain,
    ( ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
    inference(splitRight,[status(thm)],[c_1968]) ).

tff(c_4793,plain,
    ~ ssItem(hd('#skF_51')),
    inference(splitLeft,[status(thm)],[c_4666]) ).

tff(c_4808,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_4805,c_4793]) ).

tff(c_4811,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_4808]) ).

tff(c_4837,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_4811,c_411]) ).

tff(c_4857,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_4837,c_164]) ).

tff(c_4862,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_4857]) ).

tff(c_4863,plain,
    cons(hd('#skF_51'),nil) = '#skF_50',
    inference(splitRight,[status(thm)],[c_4666]) ).

tff(c_4864,plain,
    ssItem(hd('#skF_51')),
    inference(splitRight,[status(thm)],[c_4666]) ).

tff(c_4667,plain,
    neq(nil,'#skF_51'),
    inference(splitRight,[status(thm)],[c_1968]) ).

tff(c_384,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_396,plain,
    ( ~ neq(nil,'#skF_49')
    | ~ ssItem(hd('#skF_49'))
    | ( cons(hd('#skF_49'),nil) != '#skF_48' )
    | ~ ssList(cons(hd('#skF_49'),nil))
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_412,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) != '#skF_48' )
    | ~ ssList(cons(hd('#skF_51'),nil))
    | ~ neq('#skF_51',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_386,c_386,c_386,c_396]) ).

tff(c_417,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) != '#skF_48' )
    | ~ ssList(cons(hd('#skF_51'),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_412]) ).

tff(c_419,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) != '#skF_50' )
    | ~ ssList(cons(hd('#skF_51'),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_417]) ).

tff(c_5023,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_4863,c_4863,c_4864,c_4667,c_419]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC013+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
% 0.14/0.35  % Computer : n027.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 21:59:54 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 9.80/3.17  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.80/3.18  
% 9.80/3.18  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.80/3.21  
% 9.80/3.21  Inference rules
% 9.80/3.21  ----------------------
% 9.80/3.21  #Ref     : 0
% 9.80/3.21  #Sup     : 999
% 9.80/3.21  #Fact    : 0
% 9.80/3.21  #Define  : 0
% 9.80/3.21  #Split   : 22
% 9.80/3.21  #Chain   : 0
% 9.80/3.21  #Close   : 0
% 9.80/3.21  
% 9.80/3.21  Ordering : KBO
% 9.80/3.21  
% 9.80/3.21  Simplification rules
% 9.80/3.21  ----------------------
% 9.80/3.21  #Subsume      : 19
% 9.80/3.21  #Demod        : 547
% 9.80/3.21  #Tautology    : 248
% 9.80/3.21  #SimpNegUnit  : 21
% 9.80/3.21  #BackRed      : 234
% 9.80/3.21  
% 9.80/3.21  #Partial instantiations: 0
% 9.80/3.21  #Strategies tried      : 1
% 9.80/3.21  
% 9.80/3.21  Timing (in seconds)
% 9.80/3.21  ----------------------
% 9.80/3.21  Preprocessing        : 0.89
% 9.80/3.21  Parsing              : 0.41
% 9.80/3.21  CNF conversion       : 0.11
% 9.80/3.21  Main loop            : 1.27
% 9.80/3.21  Inferencing          : 0.42
% 9.80/3.21  Reduction            : 0.37
% 9.80/3.21  Demodulation         : 0.25
% 9.80/3.21  BG Simplification    : 0.09
% 9.80/3.21  Subsumption          : 0.26
% 9.80/3.21  Abstraction          : 0.05
% 9.80/3.21  MUC search           : 0.00
% 9.80/3.21  Cooper               : 0.00
% 9.80/3.21  Total                : 2.21
% 9.80/3.21  Index Insertion      : 0.00
% 9.80/3.21  Index Deletion       : 0.00
% 9.80/3.21  Index Matching       : 0.00
% 9.80/3.21  BG Taut test         : 0.00
%------------------------------------------------------------------------------