TSTP Solution File: SWC277+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC277+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 : n012.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   : Theorem 9.49s 3.20s
% Output   : CNFRefutation 9.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  121 (  24 unt;  75 typ;   0 def)
%            Number of atoms       :   94 (  28 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   83 (  35   ~;  31   |;   3   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   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   :   22 (;  20   !;   2   ?;   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_1004,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ~ segmentP(X,W)
                      | totalorderedP(U)
                      | ( ~ singletonP(W)
                        & neq(X,nil) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f_779,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssList(V)
            & ( tl(U) = V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).

tff(f_712,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax66) ).

tff(f_692,axiom,
    ! [U] :
      ( ssList(U)
     => ( segmentP(nil,U)
      <=> ( nil = U ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).

tff(f_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(f_311,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> ( U != V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

tff(f_96,axiom,
    ! [U] :
      ( ssList(U)
     => ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & ( cons(V,nil) = U ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).

tff(f_711,axiom,
    ! [U] :
      ( ssItem(U)
     => totalorderedP(cons(U,nil)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax65) ).

tff(c_396,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1004]) ).

tff(c_390,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1004]) ).

tff(c_386,plain,
    ~ totalorderedP('#skF_48'),
    inference(cnfTransformation,[status(thm)],[f_1004]) ).

tff(c_405,plain,
    ~ totalorderedP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_386]) ).

tff(c_394,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1004]) ).

tff(c_865,plain,
    ! [U_1199] :
      ( ( tl(U_1199) = '#skF_47'(U_1199) )
      | ( nil = U_1199 )
      | ~ ssList(U_1199) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_969,plain,
    ( ( tl('#skF_51') = '#skF_47'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_394,c_865]) ).

tff(c_971,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_969]) ).

tff(c_970,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_396,c_865]) ).

tff(c_1015,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_971,c_970]) ).

tff(c_1016,plain,
    '#skF_51' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_1015]) ).

tff(c_294,plain,
    totalorderedP(nil),
    inference(cnfTransformation,[status(thm)],[f_712]) ).

tff(c_1002,plain,
    totalorderedP('#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_971,c_294]) ).

tff(c_1037,plain,
    totalorderedP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_1016,c_1002]) ).

tff(c_1038,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_405,c_1037]) ).

tff(c_1040,plain,
    '#skF_51' != '#skF_50',
    inference(splitRight,[status(thm)],[c_1015]) ).

tff(c_388,plain,
    segmentP('#skF_51','#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1004]) ).

tff(c_278,plain,
    ! [U_1031] :
      ( ( nil = U_1031 )
      | ~ segmentP(nil,U_1031)
      | ~ ssList(U_1031) ),
    inference(cnfTransformation,[status(thm)],[f_692]) ).

tff(c_1547,plain,
    ! [U_1230] :
      ( ( U_1230 = '#skF_51' )
      | ~ segmentP('#skF_51',U_1230)
      | ~ ssList(U_1230) ),
    inference(demodulation,[status(thm),theory(equality)],[c_971,c_971,c_278]) ).

tff(c_1558,plain,
    ( ( '#skF_51' = '#skF_50' )
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_388,c_1547]) ).

tff(c_1569,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_1558]) ).

tff(c_1571,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1040,c_1569]) ).

tff(c_1573,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_969]) ).

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

tff(c_2051,plain,
    ! [U_1245,V_1246] :
      ( neq(U_1245,V_1246)
      | ( V_1246 = U_1245 )
      | ~ ssList(V_1246)
      | ~ ssList(U_1245) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_384,plain,
    ( ~ neq('#skF_51',nil)
    | singletonP('#skF_50') ),
    inference(cnfTransformation,[status(thm)],[f_1004]) ).

tff(c_414,plain,
    ~ neq('#skF_51',nil),
    inference(splitLeft,[status(thm)],[c_384]) ).

tff(c_2062,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList(nil)
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_2051,c_414]) ).

tff(c_2069,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_168,c_2062]) ).

tff(c_2071,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1573,c_2069]) ).

tff(c_2072,plain,
    singletonP('#skF_50'),
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_24,plain,
    ! [U_30] :
      ( ssItem('#skF_5'(U_30))
      | ~ singletonP(U_30)
      | ~ ssList(U_30) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_3398,plain,
    ! [U_1333] :
      ( ( cons('#skF_5'(U_1333),nil) = U_1333 )
      | ~ singletonP(U_1333)
      | ~ ssList(U_1333) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_292,plain,
    ! [U_1035] :
      ( totalorderedP(cons(U_1035,nil))
      | ~ ssItem(U_1035) ),
    inference(cnfTransformation,[status(thm)],[f_711]) ).

tff(c_4779,plain,
    ! [U_1382] :
      ( totalorderedP(U_1382)
      | ~ ssItem('#skF_5'(U_1382))
      | ~ singletonP(U_1382)
      | ~ ssList(U_1382) ),
    inference(superposition,[status(thm),theory(equality)],[c_3398,c_292]) ).

tff(c_4841,plain,
    ! [U_1383] :
      ( totalorderedP(U_1383)
      | ~ singletonP(U_1383)
      | ~ ssList(U_1383) ),
    inference(resolution,[status(thm)],[c_24,c_4779]) ).

tff(c_4844,plain,
    ( ~ singletonP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_4841,c_405]) ).

tff(c_4848,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_2072,c_4844]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC277+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
% 0.19/0.35  % Computer : n012.cluster.edu
% 0.19/0.35  % Model    : x86_64 x86_64
% 0.19/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35  % Memory   : 8042.1875MB
% 0.19/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35  % CPULimit : 300
% 0.19/0.35  % WCLimit  : 300
% 0.19/0.35  % DateTime : Thu Aug  3 21:32:37 EDT 2023
% 0.19/0.35  % CPUTime  : 
% 9.49/3.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.74/3.21  
% 9.74/3.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.74/3.24  
% 9.74/3.24  Inference rules
% 9.74/3.24  ----------------------
% 9.74/3.24  #Ref     : 0
% 9.74/3.24  #Sup     : 974
% 9.74/3.24  #Fact    : 0
% 9.74/3.24  #Define  : 0
% 9.74/3.24  #Split   : 25
% 9.74/3.24  #Chain   : 0
% 9.74/3.24  #Close   : 0
% 9.74/3.24  
% 9.74/3.24  Ordering : KBO
% 9.74/3.24  
% 9.74/3.24  Simplification rules
% 9.74/3.24  ----------------------
% 9.74/3.24  #Subsume      : 57
% 9.74/3.24  #Demod        : 554
% 9.74/3.24  #Tautology    : 238
% 9.74/3.24  #SimpNegUnit  : 44
% 9.74/3.24  #BackRed      : 200
% 9.74/3.24  
% 9.74/3.24  #Partial instantiations: 0
% 9.74/3.24  #Strategies tried      : 1
% 9.74/3.24  
% 9.74/3.24  Timing (in seconds)
% 9.74/3.24  ----------------------
% 9.74/3.25  Preprocessing        : 0.89
% 9.74/3.25  Parsing              : 0.42
% 9.74/3.25  CNF conversion       : 0.11
% 9.74/3.25  Main loop            : 1.23
% 9.74/3.25  Inferencing          : 0.44
% 9.74/3.25  Reduction            : 0.36
% 9.74/3.25  Demodulation         : 0.25
% 9.74/3.25  BG Simplification    : 0.08
% 9.74/3.25  Subsumption          : 0.24
% 9.74/3.25  Abstraction          : 0.05
% 9.74/3.25  MUC search           : 0.00
% 9.74/3.25  Cooper               : 0.00
% 9.74/3.25  Total                : 2.18
% 9.74/3.25  Index Insertion      : 0.00
% 9.74/3.25  Index Deletion       : 0.00
% 9.74/3.25  Index Matching       : 0.00
% 9.74/3.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------