TSTP Solution File: SWC239+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC239+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 : n025.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 11:01:45 EDT 2023

% Result   : Theorem 24.07s 11.80s
% Output   : CNFRefutation 24.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   87
% Syntax   : Number of formulae    :  141 (  19 unt;  77 typ;   0 def)
%            Number of atoms       :  212 (  78 equ)
%            Maximal formula atoms :   25 (   3 avg)
%            Number of connectives :  261 ( 113   ~; 118   |;  10   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   88 (  69   >;  19   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   58 (  58 usr;   8 con; 0-3 aty)
%            Number of variables   :   69 (;  63   !;   6   ?;   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_52 > #skF_48 > #skF_3 > #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_52',type,
    '#skF_52': ( $i * $i * $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_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_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(f_1046,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ( nil = U )
                      | ? [Y] :
                          ( ssItem(Y)
                          & ? [Z] :
                              ( ssList(Z)
                              & ? [X1] :
                                  ( ssList(X1)
                                  & ( app(app(Z,cons(Y,nil)),X1) = U )
                                  & ! [X2] :
                                      ( ssItem(X2)
                                     => ( ~ memberP(Z,X2)
                                        | ~ memberP(X1,X2)
                                        | ~ lt(Y,X2)
                                        | leq(Y,X2) ) ) ) ) )
                      | ( ! [X3] :
                            ( ssItem(X3)
                           => ( ( cons(X3,nil) != W )
                              | ~ memberP(X,X3)
                              | ? [X4] :
                                  ( ssItem(X4)
                                  & ( X3 != X4 )
                                  & memberP(X,X4)
                                  & leq(X3,X4) ) ) )
                        & ( ( nil != X )
                          | ( nil != W ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_859,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(U,nil) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

tff(f_413,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(nil,U) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).

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

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_879,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( nil != U )
           => ( tl(app(U,V)) = app(tl(U),V) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).

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

tff(f_392,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( tl(cons(V,U)) = U ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).

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

tff(c_392,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1046]) ).

tff(c_489,plain,
    ! [U_1433] :
      ( ( app(U_1433,nil) = U_1433 )
      | ~ ssList(U_1433) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_502,plain,
    app('#skF_50',nil) = '#skF_50',
    inference(resolution,[status(thm)],[c_392,c_489]) ).

tff(c_386,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1046]) ).

tff(c_384,plain,
    nil != '#skF_48',
    inference(cnfTransformation,[status(thm)],[f_1046]) ).

tff(c_432,plain,
    nil != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_384]) ).

tff(c_402,plain,
    ( ( cons('#skF_53',nil) = '#skF_50' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1046]) ).

tff(c_433,plain,
    cons('#skF_53',nil) = '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_432,c_402]) ).

tff(c_404,plain,
    ( ssItem('#skF_53')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1046]) ).

tff(c_436,plain,
    ssItem('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_432,c_404]) ).

tff(c_472,plain,
    ! [U_1432] :
      ( ( app(nil,U_1432) = U_1432 )
      | ~ ssList(U_1432) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_484,plain,
    app(nil,'#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_392,c_472]) ).

tff(c_1434,plain,
    ! [U_1515] :
      ( ( tl(U_1515) = '#skF_47'(U_1515) )
      | ( nil = U_1515 )
      | ~ ssList(U_1515) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_1515,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_392,c_1434]) ).

tff(c_1547,plain,
    tl('#skF_50') = '#skF_47'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_432,c_1515]) ).

tff(c_188,plain,
    ! [U_892] :
      ( ssList(tl(U_892))
      | ( nil = U_892 )
      | ~ ssList(U_892) ),
    inference(cnfTransformation,[status(thm)],[f_385]) ).

tff(c_1581,plain,
    ( ssList('#skF_47'('#skF_50'))
    | ( nil = '#skF_50' )
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_1547,c_188]) ).

tff(c_1585,plain,
    ( ssList('#skF_47'('#skF_50'))
    | ( nil = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_1581]) ).

tff(c_1586,plain,
    ssList('#skF_47'('#skF_50')),
    inference(negUnitSimplification,[status(thm)],[c_432,c_1585]) ).

tff(c_330,plain,
    ! [U_1045] :
      ( ( hd(U_1045) = '#skF_46'(U_1045) )
      | ( nil = U_1045 )
      | ~ ssList(U_1045) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_1605,plain,
    ( ( hd('#skF_47'('#skF_50')) = '#skF_46'('#skF_47'('#skF_50')) )
    | ( '#skF_47'('#skF_50') = nil ) ),
    inference(resolution,[status(thm)],[c_1586,c_330]) ).

tff(c_1661,plain,
    '#skF_47'('#skF_50') = nil,
    inference(splitLeft,[status(thm)],[c_1605]) ).

tff(c_1665,plain,
    tl('#skF_50') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_1661,c_1547]) ).

tff(c_15500,plain,
    ! [U_1998,V_1999] :
      ( ( app(tl(U_1998),V_1999) = tl(app(U_1998,V_1999)) )
      | ( nil = U_1998 )
      | ~ ssList(V_1999)
      | ~ ssList(U_1998) ),
    inference(cnfTransformation,[status(thm)],[f_879]) ).

tff(c_15604,plain,
    ! [V_1999] :
      ( ( tl(app('#skF_50',V_1999)) = app(nil,V_1999) )
      | ( nil = '#skF_50' )
      | ~ ssList(V_1999)
      | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_1665,c_15500]) ).

tff(c_15627,plain,
    ! [V_1999] :
      ( ( tl(app('#skF_50',V_1999)) = app(nil,V_1999) )
      | ( nil = '#skF_50' )
      | ~ ssList(V_1999) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_15604]) ).

tff(c_15628,plain,
    ! [V_1999] :
      ( ( tl(app('#skF_50',V_1999)) = app(nil,V_1999) )
      | ~ ssList(V_1999) ),
    inference(negUnitSimplification,[status(thm)],[c_432,c_15627]) ).

tff(c_422,plain,
    ! [Y_1403,Z_1411,X1_1415] :
      ( ssItem('#skF_52'(Y_1403,Z_1411,X1_1415))
      | ( app(app(Z_1411,cons(Y_1403,nil)),X1_1415) != '#skF_48' )
      | ~ ssList(X1_1415)
      | ~ ssList(Z_1411)
      | ~ ssItem(Y_1403) ),
    inference(cnfTransformation,[status(thm)],[f_1046]) ).

tff(c_428,plain,
    ! [Y_1403,Z_1411,X1_1415] :
      ( ssItem('#skF_52'(Y_1403,Z_1411,X1_1415))
      | ( app(app(Z_1411,cons(Y_1403,nil)),X1_1415) != '#skF_50' )
      | ~ ssList(X1_1415)
      | ~ ssList(Z_1411)
      | ~ ssItem(Y_1403) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_422]) ).

tff(c_16328,plain,
    ! [Y_2012,U_2013,X1_2014] :
      ( ssItem('#skF_52'(Y_2012,tl(U_2013),X1_2014))
      | ( app(tl(app(U_2013,cons(Y_2012,nil))),X1_2014) != '#skF_50' )
      | ~ ssList(X1_2014)
      | ~ ssList(tl(U_2013))
      | ~ ssItem(Y_2012)
      | ( nil = U_2013 )
      | ~ ssList(cons(Y_2012,nil))
      | ~ ssList(U_2013) ),
    inference(superposition,[status(thm),theory(equality)],[c_15500,c_428]) ).

tff(c_16332,plain,
    ! [Y_2012,X1_2014] :
      ( ssItem('#skF_52'(Y_2012,tl('#skF_50'),X1_2014))
      | ( app(app(nil,cons(Y_2012,nil)),X1_2014) != '#skF_50' )
      | ~ ssList(X1_2014)
      | ~ ssList(tl('#skF_50'))
      | ~ ssItem(Y_2012)
      | ( nil = '#skF_50' )
      | ~ ssList(cons(Y_2012,nil))
      | ~ ssList('#skF_50')
      | ~ ssList(cons(Y_2012,nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15628,c_16328]) ).

tff(c_16364,plain,
    ! [Y_2012,X1_2014] :
      ( ssItem('#skF_52'(Y_2012,nil,X1_2014))
      | ( app(app(nil,cons(Y_2012,nil)),X1_2014) != '#skF_50' )
      | ~ ssList(X1_2014)
      | ~ ssItem(Y_2012)
      | ( nil = '#skF_50' )
      | ~ ssList(cons(Y_2012,nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_168,c_1665,c_1665,c_16332]) ).

tff(c_17206,plain,
    ! [Y_2023,X1_2024] :
      ( ssItem('#skF_52'(Y_2023,nil,X1_2024))
      | ( app(app(nil,cons(Y_2023,nil)),X1_2024) != '#skF_50' )
      | ~ ssList(X1_2024)
      | ~ ssItem(Y_2023)
      | ~ ssList(cons(Y_2023,nil)) ),
    inference(negUnitSimplification,[status(thm)],[c_432,c_16364]) ).

tff(c_17216,plain,
    ! [X1_2024] :
      ( ssItem('#skF_52'('#skF_53',nil,X1_2024))
      | ( app(app(nil,'#skF_50'),X1_2024) != '#skF_50' )
      | ~ ssList(X1_2024)
      | ~ ssItem('#skF_53')
      | ~ ssList(cons('#skF_53',nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_433,c_17206]) ).

tff(c_17218,plain,
    ! [X1_2024] :
      ( ssItem('#skF_52'('#skF_53',nil,X1_2024))
      | ( app('#skF_50',X1_2024) != '#skF_50' )
      | ~ ssList(X1_2024) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_433,c_436,c_484,c_17216]) ).

tff(c_418,plain,
    ! [X1_1415,Y_1403,Z_1411] :
      ( memberP(X1_1415,'#skF_52'(Y_1403,Z_1411,X1_1415))
      | ( app(app(Z_1411,cons(Y_1403,nil)),X1_1415) != '#skF_48' )
      | ~ ssList(X1_1415)
      | ~ ssList(Z_1411)
      | ~ ssItem(Y_1403) ),
    inference(cnfTransformation,[status(thm)],[f_1046]) ).

tff(c_427,plain,
    ! [X1_1415,Y_1403,Z_1411] :
      ( memberP(X1_1415,'#skF_52'(Y_1403,Z_1411,X1_1415))
      | ( app(app(Z_1411,cons(Y_1403,nil)),X1_1415) != '#skF_50' )
      | ~ ssList(X1_1415)
      | ~ ssList(Z_1411)
      | ~ ssItem(Y_1403) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_418]) ).

tff(c_17306,plain,
    ! [X1_2035,Y_2036,U_2037] :
      ( memberP(X1_2035,'#skF_52'(Y_2036,tl(U_2037),X1_2035))
      | ( app(tl(app(U_2037,cons(Y_2036,nil))),X1_2035) != '#skF_50' )
      | ~ ssList(X1_2035)
      | ~ ssList(tl(U_2037))
      | ~ ssItem(Y_2036)
      | ( nil = U_2037 )
      | ~ ssList(cons(Y_2036,nil))
      | ~ ssList(U_2037) ),
    inference(superposition,[status(thm),theory(equality)],[c_15500,c_427]) ).

tff(c_17312,plain,
    ! [X1_2035,Y_2036] :
      ( memberP(X1_2035,'#skF_52'(Y_2036,tl('#skF_50'),X1_2035))
      | ( app(app(nil,cons(Y_2036,nil)),X1_2035) != '#skF_50' )
      | ~ ssList(X1_2035)
      | ~ ssList(tl('#skF_50'))
      | ~ ssItem(Y_2036)
      | ( nil = '#skF_50' )
      | ~ ssList(cons(Y_2036,nil))
      | ~ ssList('#skF_50')
      | ~ ssList(cons(Y_2036,nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15628,c_17306]) ).

tff(c_17339,plain,
    ! [X1_2035,Y_2036] :
      ( memberP(X1_2035,'#skF_52'(Y_2036,nil,X1_2035))
      | ( app(app(nil,cons(Y_2036,nil)),X1_2035) != '#skF_50' )
      | ~ ssList(X1_2035)
      | ~ ssItem(Y_2036)
      | ( nil = '#skF_50' )
      | ~ ssList(cons(Y_2036,nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_168,c_1665,c_1665,c_17312]) ).

tff(c_17385,plain,
    ! [X1_2049,Y_2050] :
      ( memberP(X1_2049,'#skF_52'(Y_2050,nil,X1_2049))
      | ( app(app(nil,cons(Y_2050,nil)),X1_2049) != '#skF_50' )
      | ~ ssList(X1_2049)
      | ~ ssItem(Y_2050)
      | ~ ssList(cons(Y_2050,nil)) ),
    inference(negUnitSimplification,[status(thm)],[c_432,c_17339]) ).

tff(c_17392,plain,
    ! [X1_2049] :
      ( memberP(X1_2049,'#skF_52'('#skF_53',nil,X1_2049))
      | ( app(app(nil,'#skF_50'),X1_2049) != '#skF_50' )
      | ~ ssList(X1_2049)
      | ~ ssItem('#skF_53')
      | ~ ssList(cons('#skF_53',nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_433,c_17385]) ).

tff(c_38522,plain,
    ! [X1_2475] :
      ( memberP(X1_2475,'#skF_52'('#skF_53',nil,X1_2475))
      | ( app('#skF_50',X1_2475) != '#skF_50' )
      | ~ ssList(X1_2475) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_433,c_436,c_484,c_17392]) ).

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

tff(c_38550,plain,
    ( ~ ssItem('#skF_52'('#skF_53',nil,nil))
    | ( app('#skF_50',nil) != '#skF_50' )
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_38522,c_228]) ).

tff(c_38571,plain,
    ~ ssItem('#skF_52'('#skF_53',nil,nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_502,c_38550]) ).

tff(c_38577,plain,
    ( ( app('#skF_50',nil) != '#skF_50' )
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_17218,c_38571]) ).

tff(c_38584,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_502,c_38577]) ).

tff(c_38586,plain,
    '#skF_47'('#skF_50') != nil,
    inference(splitRight,[status(thm)],[c_1605]) ).

tff(c_38797,plain,
    ! [V_2480,U_2481] :
      ( ( tl(cons(V_2480,U_2481)) = U_2481 )
      | ~ ssItem(V_2480)
      | ~ ssList(U_2481) ),
    inference(cnfTransformation,[status(thm)],[f_392]) ).

tff(c_38809,plain,
    ( ( tl('#skF_50') = nil )
    | ~ ssItem('#skF_53')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_433,c_38797]) ).

tff(c_38813,plain,
    '#skF_47'('#skF_50') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_436,c_1547,c_38809]) ).

tff(c_38815,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_38586,c_38813]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC239+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
% 0.19/0.36  % Computer : n025.cluster.edu
% 0.19/0.36  % Model    : x86_64 x86_64
% 0.19/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36  % Memory   : 8042.1875MB
% 0.19/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36  % CPULimit : 300
% 0.19/0.36  % WCLimit  : 300
% 0.19/0.36  % DateTime : Thu Aug  3 21:34:19 EDT 2023
% 0.19/0.36  % CPUTime  : 
% 24.07/11.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.07/11.81  
% 24.07/11.81  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.33/11.84  
% 24.33/11.84  Inference rules
% 24.33/11.84  ----------------------
% 24.33/11.84  #Ref     : 7
% 24.33/11.84  #Sup     : 8408
% 24.33/11.84  #Fact    : 0
% 24.33/11.84  #Define  : 0
% 24.33/11.84  #Split   : 36
% 24.33/11.84  #Chain   : 0
% 24.33/11.84  #Close   : 0
% 24.33/11.84  
% 24.33/11.84  Ordering : KBO
% 24.33/11.84  
% 24.33/11.84  Simplification rules
% 24.33/11.84  ----------------------
% 24.33/11.84  #Subsume      : 1144
% 24.33/11.84  #Demod        : 7548
% 24.33/11.84  #Tautology    : 1833
% 24.33/11.84  #SimpNegUnit  : 873
% 24.33/11.84  #BackRed      : 80
% 24.33/11.84  
% 24.33/11.84  #Partial instantiations: 0
% 24.33/11.84  #Strategies tried      : 1
% 24.33/11.84  
% 24.33/11.84  Timing (in seconds)
% 24.33/11.84  ----------------------
% 24.33/11.85  Preprocessing        : 0.88
% 24.33/11.85  Parsing              : 0.40
% 24.33/11.85  CNF conversion       : 0.11
% 24.33/11.85  Main loop            : 9.90
% 24.33/11.85  Inferencing          : 2.24
% 24.33/11.85  Reduction            : 4.19
% 24.33/11.85  Demodulation         : 2.98
% 24.33/11.85  BG Simplification    : 0.14
% 24.33/11.85  Subsumption          : 2.66
% 24.33/11.85  Abstraction          : 0.16
% 24.33/11.85  MUC search           : 0.00
% 24.33/11.85  Cooper               : 0.00
% 24.33/11.85  Total                : 10.84
% 24.33/11.85  Index Insertion      : 0.00
% 24.33/11.85  Index Deletion       : 0.00
% 24.33/11.85  Index Matching       : 0.00
% 24.33/11.85  BG Taut test         : 0.00
%------------------------------------------------------------------------------