TSTP Solution File: SWC198+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC198+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 : n017.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 11:01:35 EDT 2023

% Result   : Theorem 15.47s 5.06s
% Output   : CNFRefutation 15.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   82
% Syntax   : Number of formulae    :  110 (  13 unt;  77 typ;   0 def)
%            Number of atoms       :   87 (  25 equ)
%            Maximal formula atoms :   19 (   2 avg)
%            Number of connectives :   95 (  41   ~;  36   |;   7   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   86 (  69   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   58 (  58 usr;   8 con; 0-2 aty)
%            Number of variables   :   31 (;  27   !;   4   ?;   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_52 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_53 > #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_52',type,
    '#skF_52': $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_53',type,
    '#skF_53': $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_1030,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ? [Y] :
                          ( ssItem(Y)
                          & ! [Z] :
                              ( ssItem(Z)
                             => ( ~ memberP(U,Z)
                                | ( Y = Z ) ) ) )
                      | ( ! [X1] :
                            ( ssItem(X1)
                           => ( ( cons(X1,nil) != W )
                              | ~ memberP(X,X1)
                              | ? [X2] :
                                  ( ssItem(X2)
                                  & ( X1 != X2 )
                                  & memberP(X,X2)
                                  & leq(X1,X2) ) ) )
                        & ( ( nil != X )
                          | ( nil != W ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_517,axiom,
    ! [U] :
      ( ssItem(U)
     => ~ memberP(nil,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).

tff(f_72,axiom,
    ? [U] :
      ( ssItem(U)
      & ? [V] :
          ( ssItem(V)
          & ( U != V ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax2) ).

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

tff(f_512,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ! [W] :
              ( ssList(W)
             => ( memberP(cons(V,W),U)
              <=> ( ( U = V )
                  | memberP(W,U) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).

tff(c_416,plain,
    ! [Y_1223] :
      ( ssItem('#skF_52'(Y_1223))
      | ~ ssItem(Y_1223) ),
    inference(cnfTransformation,[status(thm)],[f_1030]) ).

tff(c_384,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1030]) ).

tff(c_414,plain,
    ! [Y_1223] :
      ( memberP('#skF_48','#skF_52'(Y_1223))
      | ~ ssItem(Y_1223) ),
    inference(cnfTransformation,[status(thm)],[f_1030]) ).

tff(c_521,plain,
    ! [Y_1249] :
      ( memberP('#skF_50','#skF_52'(Y_1249))
      | ~ ssItem(Y_1249) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_414]) ).

tff(c_402,plain,
    ( ssItem('#skF_53')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1030]) ).

tff(c_430,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_402]) ).

tff(c_228,plain,
    ! [U_948] :
      ( ~ memberP(nil,U_948)
      | ~ ssItem(U_948) ),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

tff(c_461,plain,
    ! [U_948] :
      ( ~ memberP('#skF_50',U_948)
      | ~ ssItem(U_948) ),
    inference(demodulation,[status(thm),theory(equality)],[c_430,c_228]) ).

tff(c_527,plain,
    ! [Y_1250] :
      ( ~ ssItem('#skF_52'(Y_1250))
      | ~ ssItem(Y_1250) ),
    inference(resolution,[status(thm)],[c_521,c_461]) ).

tff(c_531,plain,
    ! [Y_1223] : ~ ssItem(Y_1223),
    inference(resolution,[status(thm)],[c_416,c_527]) ).

tff(c_8,plain,
    ssItem('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_535,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_531,c_8]) ).

tff(c_536,plain,
    ssItem('#skF_53'),
    inference(splitRight,[status(thm)],[c_402]) ).

tff(c_608,plain,
    ! [Y_1267] :
      ( ( '#skF_52'(Y_1267) != Y_1267 )
      | ~ ssItem(Y_1267) ),
    inference(cnfTransformation,[status(thm)],[f_1030]) ).

tff(c_622,plain,
    '#skF_52'('#skF_53') != '#skF_53',
    inference(resolution,[status(thm)],[c_536,c_608]) ).

tff(c_420,plain,
    ! [Y_1223] :
      ( memberP('#skF_50','#skF_52'(Y_1223))
      | ~ ssItem(Y_1223) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_414]) ).

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

tff(c_537,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_402]) ).

tff(c_400,plain,
    ( ( cons('#skF_53',nil) = '#skF_50' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1030]) ).

tff(c_632,plain,
    cons('#skF_53',nil) = '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_537,c_400]) ).

tff(c_14143,plain,
    ! [W_1724,U_1725,V_1726] :
      ( memberP(W_1724,U_1725)
      | ( V_1726 = U_1725 )
      | ~ memberP(cons(V_1726,W_1724),U_1725)
      | ~ ssList(W_1724)
      | ~ ssItem(V_1726)
      | ~ ssItem(U_1725) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_14179,plain,
    ! [U_1725] :
      ( memberP(nil,U_1725)
      | ( U_1725 = '#skF_53' )
      | ~ memberP('#skF_50',U_1725)
      | ~ ssList(nil)
      | ~ ssItem('#skF_53')
      | ~ ssItem(U_1725) ),
    inference(superposition,[status(thm),theory(equality)],[c_632,c_14143]) ).

tff(c_14287,plain,
    ! [U_1727] :
      ( memberP(nil,U_1727)
      | ( U_1727 = '#skF_53' )
      | ~ memberP('#skF_50',U_1727)
      | ~ ssItem(U_1727) ),
    inference(demodulation,[status(thm),theory(equality)],[c_536,c_168,c_14179]) ).

tff(c_14292,plain,
    ! [U_1728] :
      ( ( U_1728 = '#skF_53' )
      | ~ memberP('#skF_50',U_1728)
      | ~ ssItem(U_1728) ),
    inference(resolution,[status(thm)],[c_14287,c_228]) ).

tff(c_14304,plain,
    ! [Y_1729] :
      ( ( '#skF_52'(Y_1729) = '#skF_53' )
      | ~ ssItem('#skF_52'(Y_1729))
      | ~ ssItem(Y_1729) ),
    inference(resolution,[status(thm)],[c_420,c_14292]) ).

tff(c_14309,plain,
    ! [Y_1730] :
      ( ( '#skF_52'(Y_1730) = '#skF_53' )
      | ~ ssItem(Y_1730) ),
    inference(resolution,[status(thm)],[c_416,c_14304]) ).

tff(c_14375,plain,
    '#skF_52'('#skF_53') = '#skF_53',
    inference(resolution,[status(thm)],[c_536,c_14309]) ).

tff(c_14406,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_622,c_14375]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC198+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 : n017.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 21:14:36 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 15.47/5.06  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.47/5.06  
% 15.47/5.06  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.47/5.09  
% 15.47/5.09  Inference rules
% 15.47/5.09  ----------------------
% 15.47/5.09  #Ref     : 2
% 15.47/5.09  #Sup     : 3022
% 15.47/5.09  #Fact    : 0
% 15.47/5.09  #Define  : 0
% 15.47/5.09  #Split   : 24
% 15.47/5.09  #Chain   : 0
% 15.47/5.09  #Close   : 0
% 15.47/5.09  
% 15.47/5.09  Ordering : KBO
% 15.47/5.09  
% 15.47/5.09  Simplification rules
% 15.47/5.09  ----------------------
% 15.47/5.09  #Subsume      : 526
% 15.47/5.09  #Demod        : 2500
% 15.47/5.09  #Tautology    : 889
% 15.47/5.09  #SimpNegUnit  : 311
% 15.47/5.09  #BackRed      : 37
% 15.47/5.09  
% 15.47/5.09  #Partial instantiations: 0
% 15.47/5.09  #Strategies tried      : 1
% 15.47/5.09  
% 15.47/5.09  Timing (in seconds)
% 15.47/5.09  ----------------------
% 15.47/5.09  Preprocessing        : 0.90
% 15.47/5.09  Parsing              : 0.41
% 15.47/5.09  CNF conversion       : 0.11
% 15.47/5.09  Main loop            : 3.12
% 15.47/5.09  Inferencing          : 0.90
% 15.47/5.09  Reduction            : 1.17
% 15.47/5.09  Demodulation         : 0.83
% 15.76/5.09  BG Simplification    : 0.10
% 15.76/5.09  Subsumption          : 0.75
% 15.76/5.09  Abstraction          : 0.08
% 15.76/5.09  MUC search           : 0.00
% 15.76/5.09  Cooper               : 0.00
% 15.76/5.09  Total                : 4.07
% 15.76/5.09  Index Insertion      : 0.00
% 15.76/5.09  Index Deletion       : 0.00
% 15.76/5.09  Index Matching       : 0.00
% 15.76/5.09  BG Taut test         : 0.00
%------------------------------------------------------------------------------