TSTP Solution File: SWC415+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC415+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 : n016.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 11:02:34 EDT 2023

% Result   : Theorem 8.05s 2.87s
% Output   : CNFRefutation 8.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   80
% Syntax   : Number of formulae    :  118 (  24 unt;  75 typ;   0 def)
%            Number of atoms       :   94 (  33 equ)
%            Maximal formula atoms :   17 (   2 avg)
%            Number of connectives :   94 (  43   ~;  32   |;   8   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   3 avg)
%            Maximal term depth    :    2 (   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   :   16 (;  13   !;   3   ?;   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_1021,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 )
                              & ( tl(X) = Y )
                              & neq(nil,X) )
                          | ? [Z] :
                              ( ssList(Z)
                              & ( tl(V) = Z )
                              & ( U = Z )
                              & neq(nil,V) ) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_769,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssItem(V)
            & ( hd(U) = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).

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_385,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssList(tl(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).

tff(c_388,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1021]) ).

tff(c_1146,plain,
    ! [U_1286] :
      ( ( hd(U_1286) = '#skF_46'(U_1286) )
      | ( nil = U_1286 )
      | ~ ssList(U_1286) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_1254,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_1146]) ).

tff(c_1366,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_1254]) ).

tff(c_386,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1021]) ).

tff(c_406,plain,
    neq('#skF_49',nil),
    inference(cnfTransformation,[status(thm)],[f_1021]) ).

tff(c_414,plain,
    neq('#skF_51',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).

tff(c_1398,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_1366,c_414]) ).

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

tff(c_1473,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_1398,c_164]) ).

tff(c_1478,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_1473]) ).

tff(c_1480,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_1254]) ).

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

tff(c_2789,plain,
    ! [U_1352,V_1353] :
      ( neq(U_1352,V_1353)
      | ( V_1353 = U_1352 )
      | ~ ssList(V_1353)
      | ~ ssList(U_1352) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_718,plain,
    ! [U_1221] :
      ( ssList(tl(U_1221))
      | ( nil = U_1221 )
      | ~ ssList(U_1221) ),
    inference(cnfTransformation,[status(thm)],[f_385]) ).

tff(c_398,plain,
    ( ~ neq(nil,'#skF_51')
    | ( tl('#skF_51') = '#skF_50' )
    | ~ ssList(tl('#skF_51'))
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1021]) ).

tff(c_419,plain,
    ( ~ neq(nil,'#skF_51')
    | ( tl('#skF_51') = '#skF_50' )
    | ~ ssList(tl('#skF_51')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_398]) ).

tff(c_433,plain,
    ~ ssList(tl('#skF_51')),
    inference(splitLeft,[status(thm)],[c_419]) ).

tff(c_727,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_718,c_433]) ).

tff(c_732,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_727]) ).

tff(c_760,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_732,c_414]) ).

tff(c_781,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_760,c_164]) ).

tff(c_786,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_781]) ).

tff(c_787,plain,
    ( ~ neq(nil,'#skF_51')
    | ( tl('#skF_51') = '#skF_50' ) ),
    inference(splitRight,[status(thm)],[c_419]) ).

tff(c_797,plain,
    ~ neq(nil,'#skF_51'),
    inference(splitLeft,[status(thm)],[c_787]) ).

tff(c_2796,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_2789,c_797]) ).

tff(c_2805,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_2796]) ).

tff(c_2807,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1480,c_2805]) ).

tff(c_2808,plain,
    tl('#skF_51') = '#skF_50',
    inference(splitRight,[status(thm)],[c_787]) ).

tff(c_2809,plain,
    neq(nil,'#skF_51'),
    inference(splitRight,[status(thm)],[c_787]) ).

tff(c_384,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1021]) ).

tff(c_394,plain,
    ssList('#skF_48'),
    inference(cnfTransformation,[status(thm)],[f_1021]) ).

tff(c_396,plain,
    ( ~ neq(nil,'#skF_49')
    | ( tl('#skF_49') != '#skF_48' )
    | ~ ssList('#skF_48')
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1021]) ).

tff(c_411,plain,
    ( ~ neq(nil,'#skF_49')
    | ( tl('#skF_49') != '#skF_48' )
    | ~ neq('#skF_51',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_396]) ).

tff(c_413,plain,
    ( ~ neq(nil,'#skF_51')
    | ( tl('#skF_51') != '#skF_48' )
    | ~ neq('#skF_51',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_386,c_411]) ).

tff(c_417,plain,
    ( ~ neq(nil,'#skF_51')
    | ( tl('#skF_51') != '#skF_48' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_413]) ).

tff(c_421,plain,
    ( ~ neq(nil,'#skF_51')
    | ( tl('#skF_51') != '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_417]) ).

tff(c_2819,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2808,c_2809,c_421]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC415+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 : n016.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 21:55:23 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 8.05/2.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.05/2.87  
% 8.05/2.87  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.05/2.90  
% 8.05/2.91  Inference rules
% 8.05/2.91  ----------------------
% 8.05/2.91  #Ref     : 0
% 8.05/2.91  #Sup     : 507
% 8.05/2.91  #Fact    : 0
% 8.05/2.91  #Define  : 0
% 8.05/2.91  #Split   : 17
% 8.05/2.91  #Chain   : 0
% 8.05/2.91  #Close   : 0
% 8.05/2.91  
% 8.05/2.91  Ordering : KBO
% 8.05/2.91  
% 8.05/2.91  Simplification rules
% 8.05/2.91  ----------------------
% 8.05/2.91  #Subsume      : 9
% 8.05/2.91  #Demod        : 322
% 8.05/2.91  #Tautology    : 157
% 8.05/2.91  #SimpNegUnit  : 14
% 8.05/2.91  #BackRed      : 139
% 8.05/2.91  
% 8.05/2.91  #Partial instantiations: 0
% 8.05/2.91  #Strategies tried      : 1
% 8.05/2.91  
% 8.05/2.91  Timing (in seconds)
% 8.05/2.91  ----------------------
% 8.05/2.91  Preprocessing        : 0.89
% 8.05/2.91  Parsing              : 0.42
% 8.05/2.91  CNF conversion       : 0.10
% 8.05/2.91  Main loop            : 0.94
% 8.05/2.91  Inferencing          : 0.29
% 8.05/2.91  Reduction            : 0.29
% 8.05/2.91  Demodulation         : 0.20
% 8.05/2.91  BG Simplification    : 0.08
% 8.05/2.91  Subsumption          : 0.20
% 8.05/2.91  Abstraction          : 0.04
% 8.05/2.91  MUC search           : 0.00
% 8.05/2.91  Cooper               : 0.00
% 8.05/2.91  Total                : 1.88
% 8.05/2.91  Index Insertion      : 0.00
% 8.05/2.91  Index Deletion       : 0.00
% 8.05/2.91  Index Matching       : 0.00
% 8.05/2.91  BG Taut test         : 0.00
%------------------------------------------------------------------------------