TSTP Solution File: SWC297+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC297+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 : n002.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 11:02:01 EDT 2023

% Result   : Theorem 134.53s 114.53s
% Output   : CNFRefutation 134.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :  120
% Syntax   : Number of formulae    :  687 ( 251 unt;  80 typ;   0 def)
%            Number of atoms       : 1443 ( 458 equ)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives : 1568 ( 732   ~; 713   |;  18   &)
%                                         (  11 <=>;  94  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   4 avg)
%            Maximal term depth    :    4 (   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    :   61 (  61 usr;  12 con; 0-2 aty)
%            Number of variables   :  353 (; 345   !;   8   ?;   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_52 > #skF_44 > #skF_21 > #skF_16 > #skF_6 > #skF_49 > #skF_18 > #skF_24 > #skF_35 > #skF_19 > #skF_31 > #skF_55 > #skF_22 > #skF_37 > #skF_56 > #skF_54 > #skF_40 > #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_52',type,
    '#skF_52': $i ).

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_55',type,
    '#skF_55': $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('#skF_56',type,
    '#skF_56': $i ).

tff(totalorderP,type,
    totalorderP: $i > $o ).

tff(ssItem,type,
    ssItem: $i > $o ).

tff('#skF_54',type,
    '#skF_54': $i ).

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_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_1035,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ! [Y] :
                          ( ssItem(Y)
                         => ! [Z] :
                              ( ssList(Z)
                             => ! [X1] :
                                  ( ssList(X1)
                                 => ( ( app(app(Z,cons(Y,nil)),X1) != U )
                                    | ! [X2] :
                                        ( ssItem(X2)
                                       => ( ( ~ memberP(Z,X2)
                                            | lt(X2,Y) )
                                          & ( ~ memberP(X1,X2)
                                            | lt(Y,X2) ) ) ) ) ) ) )
                      | ( ( nil != W )
                        & ( nil = X ) )
                      | ( ! [X3] :
                            ( ssItem(X3)
                           => ( ( cons(X3,nil) != W )
                              | ~ memberP(X,X3) ) )
                        & neq(X,nil) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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(f_399,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).

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

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_834,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( cons(V,U) = app(cons(V,nil),U) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).

tff(f_135,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( segmentP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ? [X] :
                    ( ssList(X)
                    & ( app(app(W,V),X) = U ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).

tff(f_844,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( app(app(U,V),W) = app(U,app(V,W)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).

tff(f_87,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( memberP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ? [X] :
                    ( ssList(X)
                    & ( app(W,cons(V,X)) = U ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).

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

tff(f_364,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( nil != cons(V,U) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).

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

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_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_392,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( tl(cons(V,U)) = U ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).

tff(f_378,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( hd(cons(V,U)) = V ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).

tff(f_869,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( nil != U )
           => ( hd(app(U,V)) = hd(U) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).

tff(f_498,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( memberP(app(V,W),U)
              <=> ( memberP(V,U)
                  | memberP(W,U) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).

tff(f_560,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( frontsegP(U,V)
               => frontsegP(app(U,W),V) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).

tff(f_519,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax39) ).

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

tff(f_827,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( ( app(V,W) = app(V,U) )
               => ( W = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).

tff(f_855,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( nil = app(U,V) )
          <=> ( ( nil = V )
              & ( nil = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).

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

tff(f_815,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( ( app(W,V) = app(U,V) )
               => ( W = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).

tff(f_442,axiom,
    ! [U] :
      ( ssItem(U)
     => leq(U,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax31) ).

tff(f_728,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssList(V)
         => ( totalorderedP(cons(U,V))
          <=> ( ( nil = V )
              | ( ( nil != V )
                & totalorderedP(V)
                & leq(U,hd(V)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax67) ).

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

tff(f_950,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ( lt(U,V)
          <=> ( ( U != V )
              & leq(U,V) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).

tff(f_108,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( frontsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ( app(V,W) = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).

tff(f_544,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( frontsegP(U,V)
              & frontsegP(V,U) )
           => ( U = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax41) ).

tff(f_385,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssList(tl(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).

tff(f_803,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ( cons(hd(U),tl(U)) = U ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).

tff(f_577,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( frontsegP(cons(U,W),cons(V,X))
                  <=> ( ( U = V )
                      & frontsegP(W,X) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).

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_371,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssItem(hd(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).

tff(f_344,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssItem(W)
             => ! [X] :
                  ( ssItem(X)
                 => ( ( cons(W,U) = cons(X,V) )
                   => ( ( W = X )
                      & ( V = U ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).

tff(f_758,axiom,
    ! [U] :
      ( ssItem(U)
     => equalelemsP(cons(U,nil)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax73) ).

tff(f_461,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ( lt(U,V)
           => ~ lt(V,U) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax33) ).

tff(c_402,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_394,plain,
    ssItem('#skF_52'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_166,plain,
    ! [V_861,U_859] :
      ( ssList(cons(V_861,U_859))
      | ~ ssItem(V_861)
      | ~ ssList(U_859) ),
    inference(cnfTransformation,[status(thm)],[f_318]) ).

tff(c_392,plain,
    ssList('#skF_53'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_192,plain,
    ! [U_896,V_898] :
      ( ssList(app(U_896,V_898))
      | ~ ssList(V_898)
      | ~ ssList(U_896) ),
    inference(cnfTransformation,[status(thm)],[f_399]) ).

tff(c_386,plain,
    ssItem('#skF_55'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_384,plain,
    ( ( nil != '#skF_51' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_434,plain,
    nil != '#skF_51',
    inference(splitLeft,[status(thm)],[c_384]) ).

tff(c_400,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

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

tff(c_5251,plain,
    ! [U_1590,V_1591] :
      ( neq(U_1590,V_1591)
      | ( V_1591 = U_1590 )
      | ~ ssList(V_1591)
      | ~ ssList(U_1590) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_412,plain,
    ( ssItem('#skF_56')
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_435,plain,
    ~ neq('#skF_51',nil),
    inference(splitLeft,[status(thm)],[c_412]) ).

tff(c_5262,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList(nil)
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_5251,c_435]) ).

tff(c_5269,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_168,c_5262]) ).

tff(c_5271,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_434,c_5269]) ).

tff(c_5272,plain,
    ssItem('#skF_56'),
    inference(splitRight,[status(thm)],[c_412]) ).

tff(c_390,plain,
    ssList('#skF_54'),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_346,plain,
    ! [V_1069,U_1067] :
      ( ( app(cons(V_1069,nil),U_1067) = cons(V_1069,U_1067) )
      | ~ ssItem(V_1069)
      | ~ ssList(U_1067) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_396,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_388,plain,
    app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') = '#skF_48',
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_425,plain,
    app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_388]) ).

tff(c_486118,plain,
    ! [W_8670,V_8671,X_8672] :
      ( segmentP(app(app(W_8670,V_8671),X_8672),V_8671)
      | ~ ssList(X_8672)
      | ~ ssList(W_8670)
      | ~ ssList(V_8671)
      | ~ ssList(app(app(W_8670,V_8671),X_8672)) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_486336,plain,
    ( segmentP('#skF_50',cons('#skF_52',nil))
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_53')
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList(app(app('#skF_53',cons('#skF_52',nil)),'#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_486118]) ).

tff(c_486477,plain,
    ( segmentP('#skF_50',cons('#skF_52',nil))
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_425,c_392,c_390,c_486336]) ).

tff(c_486496,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_486477]) ).

tff(c_486557,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_486496]) ).

tff(c_486561,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_394,c_486557]) ).

tff(c_486563,plain,
    ssList(cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_486477]) ).

tff(c_482413,plain,
    ! [U_8612,V_8613,W_8614] :
      ( ( app(app(U_8612,V_8613),W_8614) = app(U_8612,app(V_8613,W_8614)) )
      | ~ ssList(W_8614)
      | ~ ssList(V_8613)
      | ~ ssList(U_8612) ),
    inference(cnfTransformation,[status(thm)],[f_844]) ).

tff(c_482754,plain,
    ( ( app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_482413]) ).

tff(c_482961,plain,
    ( ( app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_390,c_482754]) ).

tff(c_497845,plain,
    app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_486563,c_482961]) ).

tff(c_497907,plain,
    ( ( app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_346,c_497845]) ).

tff(c_497955,plain,
    app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_394,c_497907]) ).

tff(c_12,plain,
    ! [W_27,V_19,X_29] :
      ( memberP(app(W_27,cons(V_19,X_29)),V_19)
      | ~ ssList(X_29)
      | ~ ssList(W_27)
      | ~ ssItem(V_19)
      | ~ ssList(app(W_27,cons(V_19,X_29))) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_497980,plain,
    ( memberP('#skF_50','#skF_52')
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_53')
    | ~ ssItem('#skF_52')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_54'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_497955,c_12]) ).

tff(c_498048,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_497955,c_394,c_392,c_390,c_497980]) ).

tff(c_5273,plain,
    neq('#skF_51',nil),
    inference(splitRight,[status(thm)],[c_412]) ).

tff(c_410,plain,
    ( ( cons('#skF_56',nil) = '#skF_50' )
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_338784,plain,
    cons('#skF_56',nil) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5273,c_410]) ).

tff(c_483191,plain,
    ! [W_8616,U_8617,V_8618] :
      ( memberP(W_8616,U_8617)
      | ( V_8618 = U_8617 )
      | ~ memberP(cons(V_8618,W_8616),U_8617)
      | ~ ssList(W_8616)
      | ~ ssItem(V_8618)
      | ~ ssItem(U_8617) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_483245,plain,
    ! [U_8617] :
      ( memberP(nil,U_8617)
      | ( U_8617 = '#skF_56' )
      | ~ memberP('#skF_50',U_8617)
      | ~ ssList(nil)
      | ~ ssItem('#skF_56')
      | ~ ssItem(U_8617) ),
    inference(superposition,[status(thm),theory(equality)],[c_338784,c_483191]) ).

tff(c_485839,plain,
    ! [U_8666] :
      ( memberP(nil,U_8666)
      | ( U_8666 = '#skF_56' )
      | ~ memberP('#skF_50',U_8666)
      | ~ ssItem(U_8666) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_483245]) ).

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

tff(c_485843,plain,
    ! [U_8666] :
      ( ( U_8666 = '#skF_56' )
      | ~ memberP('#skF_50',U_8666)
      | ~ ssItem(U_8666) ),
    inference(resolution,[status(thm)],[c_485839,c_228]) ).

tff(c_498093,plain,
    ( ( '#skF_52' = '#skF_56' )
    | ~ ssItem('#skF_52') ),
    inference(resolution,[status(thm)],[c_498048,c_485843]) ).

tff(c_498096,plain,
    '#skF_52' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_498093]) ).

tff(c_154002,plain,
    cons('#skF_56',nil) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5273,c_410]) ).

tff(c_298287,plain,
    ! [V_5888,U_5889] :
      ( ( app(cons(V_5888,nil),U_5889) = cons(V_5888,U_5889) )
      | ~ ssItem(V_5888)
      | ~ ssList(U_5889) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_298312,plain,
    ! [U_5889] :
      ( ( cons('#skF_56',U_5889) = app('#skF_50',U_5889) )
      | ~ ssItem('#skF_56')
      | ~ ssList(U_5889) ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_298287]) ).

tff(c_298321,plain,
    ! [U_5890] :
      ( ( cons('#skF_56',U_5890) = app('#skF_50',U_5890) )
      | ~ ssList(U_5890) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_298312]) ).

tff(c_298474,plain,
    cons('#skF_56','#skF_54') = app('#skF_50','#skF_54'),
    inference(resolution,[status(thm)],[c_390,c_298321]) ).

tff(c_182,plain,
    ! [V_887,U_885] :
      ( ( cons(V_887,U_885) != nil )
      | ~ ssItem(V_887)
      | ~ ssList(U_885) ),
    inference(cnfTransformation,[status(thm)],[f_364]) ).

tff(c_298540,plain,
    ( ( app('#skF_50','#skF_54') != nil )
    | ~ ssItem('#skF_56')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_298474,c_182]) ).

tff(c_298561,plain,
    app('#skF_50','#skF_54') != nil,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_5272,c_298540]) ).

tff(c_298545,plain,
    ( ssList(app('#skF_50','#skF_54'))
    | ~ ssItem('#skF_56')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_298474,c_166]) ).

tff(c_298565,plain,
    ssList(app('#skF_50','#skF_54')),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_5272,c_298545]) ).

tff(c_196,plain,
    ! [U_906] :
      ( ( app(nil,U_906) = U_906 )
      | ~ ssList(U_906) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_298669,plain,
    app(nil,app('#skF_50','#skF_54')) = app('#skF_50','#skF_54'),
    inference(resolution,[status(thm)],[c_298565,c_196]) ).

tff(c_154694,plain,
    ! [U_3745] :
      ( ( hd(U_3745) = '#skF_46'(U_3745) )
      | ( nil = U_3745 )
      | ~ ssList(U_3745) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_154817,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_402,c_154694]) ).

tff(c_155336,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_154817]) ).

tff(c_155357,plain,
    cons('#skF_56','#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_155336,c_154002]) ).

tff(c_155557,plain,
    ! [V_887,U_885] :
      ( ( cons(V_887,U_885) != '#skF_50' )
      | ~ ssItem(V_887)
      | ~ ssList(U_885) ),
    inference(demodulation,[status(thm),theory(equality)],[c_155336,c_182]) ).

tff(c_155586,plain,
    ( ~ ssItem('#skF_56')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_155357,c_155557]) ).

tff(c_155595,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_5272,c_155586]) ).

tff(c_155597,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_154817]) ).

tff(c_155598,plain,
    ! [U_3761] :
      ( ( tl(U_3761) = '#skF_47'(U_3761) )
      | ( nil = U_3761 )
      | ~ ssList(U_3761) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_155688,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_402,c_155598]) ).

tff(c_155723,plain,
    tl('#skF_50') = '#skF_47'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_155597,c_155688]) ).

tff(c_222715,plain,
    ! [V_4824,U_4825] :
      ( ( tl(cons(V_4824,U_4825)) = U_4825 )
      | ~ ssItem(V_4824)
      | ~ ssList(U_4825) ),
    inference(cnfTransformation,[status(thm)],[f_392]) ).

tff(c_222727,plain,
    ( ( tl('#skF_50') = nil )
    | ~ ssItem('#skF_56')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_222715]) ).

tff(c_222731,plain,
    '#skF_47'('#skF_50') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_5272,c_155723,c_222727]) ).

tff(c_222735,plain,
    tl('#skF_50') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_222731,c_155723]) ).

tff(c_155596,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(splitRight,[status(thm)],[c_154817]) ).

tff(c_222653,plain,
    ! [V_4816,U_4817] :
      ( ( hd(cons(V_4816,U_4817)) = V_4816 )
      | ~ ssItem(V_4816)
      | ~ ssList(U_4817) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_222665,plain,
    ( ( hd('#skF_50') = '#skF_56' )
    | ~ ssItem('#skF_56')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_222653]) ).

tff(c_222669,plain,
    '#skF_46'('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_5272,c_155596,c_222665]) ).

tff(c_222671,plain,
    hd('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_222669,c_155596]) ).

tff(c_299002,plain,
    ! [U_5895,V_5896] :
      ( ( hd(app(U_5895,V_5896)) = hd(U_5895) )
      | ( nil = U_5895 )
      | ~ ssList(V_5896)
      | ~ ssList(U_5895) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_299200,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = hd('#skF_50') )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_299002]) ).

tff(c_299399,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_56' )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_222671,c_299200]) ).

tff(c_299651,plain,
    ~ ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitLeft,[status(thm)],[c_299399]) ).

tff(c_299654,plain,
    ( ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_299651]) ).

tff(c_299657,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_299654]) ).

tff(c_299660,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_299657]) ).

tff(c_299664,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_394,c_299660]) ).

tff(c_299666,plain,
    ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitRight,[status(thm)],[c_299399]) ).

tff(c_313736,plain,
    ! [W_6063,V_6064,X_6065] :
      ( memberP(app(W_6063,cons(V_6064,X_6065)),V_6064)
      | ~ ssList(X_6065)
      | ~ ssList(W_6063)
      | ~ ssItem(V_6064)
      | ~ ssList(app(W_6063,cons(V_6064,X_6065))) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_300592,plain,
    ! [V_5907,U_5908,W_5909] :
      ( ~ memberP(V_5907,U_5908)
      | memberP(app(V_5907,W_5909),U_5908)
      | ~ ssList(W_5909)
      | ~ ssList(V_5907)
      | ~ ssItem(U_5908) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_300772,plain,
    ! [U_5908] :
      ( ~ memberP(app('#skF_53',cons('#skF_52',nil)),U_5908)
      | memberP('#skF_50',U_5908)
      | ~ ssList('#skF_54')
      | ~ ssList(app('#skF_53',cons('#skF_52',nil)))
      | ~ ssItem(U_5908) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_300592]) ).

tff(c_300901,plain,
    ! [U_5908] :
      ( ~ memberP(app('#skF_53',cons('#skF_52',nil)),U_5908)
      | memberP('#skF_50',U_5908)
      | ~ ssItem(U_5908) ),
    inference(demodulation,[status(thm),theory(equality)],[c_299666,c_390,c_300772]) ).

tff(c_313743,plain,
    ( memberP('#skF_50','#skF_52')
    | ~ ssList(nil)
    | ~ ssList('#skF_53')
    | ~ ssItem('#skF_52')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(resolution,[status(thm)],[c_313736,c_300901]) ).

tff(c_313814,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_299666,c_394,c_392,c_168,c_313743]) ).

tff(c_310243,plain,
    ! [W_6020,U_6021,V_6022] :
      ( memberP(W_6020,U_6021)
      | ( V_6022 = U_6021 )
      | ~ memberP(cons(V_6022,W_6020),U_6021)
      | ~ ssList(W_6020)
      | ~ ssItem(V_6022)
      | ~ ssItem(U_6021) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_310294,plain,
    ! [U_6021] :
      ( memberP(nil,U_6021)
      | ( U_6021 = '#skF_56' )
      | ~ memberP('#skF_50',U_6021)
      | ~ ssList(nil)
      | ~ ssItem('#skF_56')
      | ~ ssItem(U_6021) ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_310243]) ).

tff(c_310774,plain,
    ! [U_6028] :
      ( memberP(nil,U_6028)
      | ( U_6028 = '#skF_56' )
      | ~ memberP('#skF_50',U_6028)
      | ~ ssItem(U_6028) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_310294]) ).

tff(c_310778,plain,
    ! [U_6028] :
      ( ( U_6028 = '#skF_56' )
      | ~ memberP('#skF_50',U_6028)
      | ~ ssItem(U_6028) ),
    inference(resolution,[status(thm)],[c_310774,c_228]) ).

tff(c_313841,plain,
    ( ( '#skF_52' = '#skF_56' )
    | ~ ssItem('#skF_52') ),
    inference(resolution,[status(thm)],[c_313814,c_310778]) ).

tff(c_313844,plain,
    '#skF_52' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_313841]) ).

tff(c_313855,plain,
    app(app('#skF_53',cons('#skF_56',nil)),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_313844,c_425]) ).

tff(c_313863,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_154002,c_313855]) ).

tff(c_348,plain,
    ! [U_1070,V_1074,W_1076] :
      ( ( app(app(U_1070,V_1074),W_1076) = app(U_1070,app(V_1074,W_1076)) )
      | ~ ssList(W_1076)
      | ~ ssList(V_1074)
      | ~ ssList(U_1070) ),
    inference(cnfTransformation,[status(thm)],[f_844]) ).

tff(c_314004,plain,
    ( ( app('#skF_53',app('#skF_50','#skF_54')) = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_313863,c_348]) ).

tff(c_314057,plain,
    app('#skF_53',app('#skF_50','#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_402,c_390,c_314004]) ).

tff(c_238,plain,
    ! [U_960,W_966,V_964] :
      ( frontsegP(app(U_960,W_966),V_964)
      | ~ frontsegP(U_960,V_964)
      | ~ ssList(W_966)
      | ~ ssList(V_964)
      | ~ ssList(U_960) ),
    inference(cnfTransformation,[status(thm)],[f_560]) ).

tff(c_5698,plain,
    ! [U_1657] :
      ( ( tl(U_1657) = '#skF_47'(U_1657) )
      | ( nil = U_1657 )
      | ~ ssList(U_1657) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_5806,plain,
    ( ( tl('#skF_53') = '#skF_47'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_392,c_5698]) ).

tff(c_5836,plain,
    nil = '#skF_53',
    inference(splitLeft,[status(thm)],[c_5806]) ).

tff(c_230,plain,
    ~ singletonP(nil),
    inference(cnfTransformation,[status(thm)],[f_519]) ).

tff(c_5879,plain,
    ~ singletonP('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_230]) ).

tff(c_5807,plain,
    ( ( tl('#skF_54') = '#skF_47'('#skF_54') )
    | ( nil = '#skF_54' ) ),
    inference(resolution,[status(thm)],[c_390,c_5698]) ).

tff(c_6089,plain,
    ( ( tl('#skF_54') = '#skF_47'('#skF_54') )
    | ( '#skF_54' = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_5807]) ).

tff(c_6090,plain,
    '#skF_54' = '#skF_53',
    inference(splitLeft,[status(thm)],[c_6089]) ).

tff(c_420,plain,
    ( memberP('#skF_53','#skF_55')
    | memberP('#skF_54','#skF_55') ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_5294,plain,
    memberP('#skF_54','#skF_55'),
    inference(splitLeft,[status(thm)],[c_420]) ).

tff(c_6091,plain,
    memberP('#skF_53','#skF_55'),
    inference(demodulation,[status(thm),theory(equality)],[c_6090,c_5294]) ).

tff(c_6355,plain,
    ! [U_1671] :
      ( ~ memberP('#skF_53',U_1671)
      | ~ ssItem(U_1671) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_228]) ).

tff(c_6358,plain,
    ~ ssItem('#skF_55'),
    inference(resolution,[status(thm)],[c_6091,c_6355]) ).

tff(c_6362,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_6358]) ).

tff(c_6364,plain,
    '#skF_54' != '#skF_53',
    inference(splitRight,[status(thm)],[c_6089]) ).

tff(c_5295,plain,
    ! [U_1608] :
      ( ( app(U_1608,nil) = U_1608 )
      | ~ ssList(U_1608) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_5315,plain,
    app('#skF_50',nil) = '#skF_50',
    inference(resolution,[status(thm)],[c_402,c_5295]) ).

tff(c_5858,plain,
    app('#skF_50','#skF_53') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_5315]) ).

tff(c_83968,plain,
    ! [W_2804,U_2805,V_2806] :
      ( ( W_2804 = U_2805 )
      | ( app(V_2806,W_2804) != app(V_2806,U_2805) )
      | ~ ssList(W_2804)
      | ~ ssList(V_2806)
      | ~ ssList(U_2805) ),
    inference(cnfTransformation,[status(thm)],[f_827]) ).

tff(c_84174,plain,
    ! [U_2805] :
      ( ( U_2805 = '#skF_53' )
      | ( app('#skF_50',U_2805) != '#skF_50' )
      | ~ ssList('#skF_53')
      | ~ ssList('#skF_50')
      | ~ ssList(U_2805) ),
    inference(superposition,[status(thm),theory(equality)],[c_5858,c_83968]) ).

tff(c_84421,plain,
    ! [U_2807] :
      ( ( U_2807 = '#skF_53' )
      | ( app('#skF_50',U_2807) != '#skF_50' )
      | ~ ssList(U_2807) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_392,c_84174]) ).

tff(c_84532,plain,
    ( ( '#skF_54' = '#skF_53' )
    | ( app('#skF_50','#skF_54') != '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_390,c_84421]) ).

tff(c_84586,plain,
    app('#skF_50','#skF_54') != '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_6364,c_84532]) ).

tff(c_5334,plain,
    cons('#skF_56',nil) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5273,c_410]) ).

tff(c_5856,plain,
    cons('#skF_56','#skF_53') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_5334]) ).

tff(c_5847,plain,
    app(app('#skF_53',cons('#skF_52','#skF_53')),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_425]) ).

tff(c_96978,plain,
    ! [W_2975,V_2976,X_2977] :
      ( segmentP(app(app(W_2975,V_2976),X_2977),V_2976)
      | ~ ssList(X_2977)
      | ~ ssList(W_2975)
      | ~ ssList(V_2976)
      | ~ ssList(app(app(W_2975,V_2976),X_2977)) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_97238,plain,
    ( segmentP('#skF_50',cons('#skF_52','#skF_53'))
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_53')
    | ~ ssList(cons('#skF_52','#skF_53'))
    | ~ ssList(app(app('#skF_53',cons('#skF_52','#skF_53')),'#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_5847,c_96978]) ).

tff(c_97393,plain,
    ( segmentP('#skF_50',cons('#skF_52','#skF_53'))
    | ~ ssList(cons('#skF_52','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_5847,c_392,c_390,c_97238]) ).

tff(c_97551,plain,
    ~ ssList(cons('#skF_52','#skF_53')),
    inference(splitLeft,[status(thm)],[c_97393]) ).

tff(c_97554,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_97551]) ).

tff(c_97558,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_394,c_97554]) ).

tff(c_97560,plain,
    ssList(cons('#skF_52','#skF_53')),
    inference(splitRight,[status(thm)],[c_97393]) ).

tff(c_5853,plain,
    ! [U_906] :
      ( ( app('#skF_53',U_906) = U_906 )
      | ~ ssList(U_906) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_196]) ).

tff(c_97672,plain,
    app('#skF_53',cons('#skF_52','#skF_53')) = cons('#skF_52','#skF_53'),
    inference(resolution,[status(thm)],[c_97560,c_5853]) ).

tff(c_5813,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_402,c_5698]) ).

tff(c_5990,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( '#skF_53' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_5813]) ).

tff(c_5991,plain,
    '#skF_53' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_5990]) ).

tff(c_6075,plain,
    cons('#skF_56','#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5991,c_5856]) ).

tff(c_6002,plain,
    nil = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5991,c_5836]) ).

tff(c_6035,plain,
    ! [V_887,U_885] :
      ( ( cons(V_887,U_885) != '#skF_50' )
      | ~ ssItem(V_887)
      | ~ ssList(U_885) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6002,c_182]) ).

tff(c_6078,plain,
    ( ~ ssItem('#skF_56')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_6075,c_6035]) ).

tff(c_6086,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_5272,c_6078]) ).

tff(c_6088,plain,
    '#skF_53' != '#skF_50',
    inference(splitRight,[status(thm)],[c_5990]) ).

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_5888,plain,
    ! [U_1658] :
      ( ( hd(U_1658) = '#skF_46'(U_1658) )
      | ( U_1658 = '#skF_53' )
      | ~ ssList(U_1658) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_330]) ).

tff(c_5989,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( '#skF_53' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_402,c_5888]) ).

tff(c_6370,plain,
    '#skF_53' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_5989]) ).

tff(c_6376,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6088,c_6370]) ).

tff(c_6377,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(splitRight,[status(thm)],[c_5989]) ).

tff(c_7221,plain,
    ! [V_1707,U_1708] :
      ( ( hd(cons(V_1707,U_1708)) = V_1707 )
      | ~ ssItem(V_1707)
      | ~ ssList(U_1708) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_7233,plain,
    ( ( hd('#skF_50') = '#skF_56' )
    | ~ ssItem('#skF_56')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_5856,c_7221]) ).

tff(c_7237,plain,
    '#skF_46'('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_5272,c_6377,c_7233]) ).

tff(c_7239,plain,
    hd('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_7237,c_6377]) ).

tff(c_358,plain,
    ! [U_1081,V_1083] :
      ( ( hd(app(U_1081,V_1083)) = hd(U_1081) )
      | ( nil = U_1081 )
      | ~ ssList(V_1083)
      | ~ ssList(U_1081) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_79066,plain,
    ! [U_2753,V_2754] :
      ( ( hd(app(U_2753,V_2754)) = hd(U_2753) )
      | ( U_2753 = '#skF_53' )
      | ~ ssList(V_2754)
      | ~ ssList(U_2753) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_358]) ).

tff(c_79219,plain,
    ( ( hd(app('#skF_53',cons('#skF_52','#skF_53'))) = hd('#skF_50') )
    | ( app('#skF_53',cons('#skF_52','#skF_53')) = '#skF_53' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_53'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_5847,c_79066]) ).

tff(c_79382,plain,
    ( ( hd(app('#skF_53',cons('#skF_52','#skF_53'))) = '#skF_56' )
    | ( app('#skF_53',cons('#skF_52','#skF_53')) = '#skF_53' )
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_53'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_7239,c_79219]) ).

tff(c_79404,plain,
    ~ ssList(app('#skF_53',cons('#skF_52','#skF_53'))),
    inference(splitLeft,[status(thm)],[c_79382]) ).

tff(c_79407,plain,
    ( ~ ssList(cons('#skF_52','#skF_53'))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_79404]) ).

tff(c_79410,plain,
    ~ ssList(cons('#skF_52','#skF_53')),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_79407]) ).

tff(c_79413,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_79410]) ).

tff(c_79417,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_394,c_79413]) ).

tff(c_79418,plain,
    ( ( app('#skF_53',cons('#skF_52','#skF_53')) = '#skF_53' )
    | ( hd(app('#skF_53',cons('#skF_52','#skF_53'))) = '#skF_56' ) ),
    inference(splitRight,[status(thm)],[c_79382]) ).

tff(c_79470,plain,
    hd(app('#skF_53',cons('#skF_52','#skF_53'))) = '#skF_56',
    inference(splitLeft,[status(thm)],[c_79418]) ).

tff(c_97765,plain,
    hd(cons('#skF_52','#skF_53')) = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_97672,c_79470]) ).

tff(c_186,plain,
    ! [V_891,U_889] :
      ( ( hd(cons(V_891,U_889)) = V_891 )
      | ~ ssItem(V_891)
      | ~ ssList(U_889) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_97898,plain,
    ( ( '#skF_52' = '#skF_56' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_97765,c_186]) ).

tff(c_97918,plain,
    '#skF_52' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_394,c_97898]) ).

tff(c_97767,plain,
    app(cons('#skF_52','#skF_53'),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_97672,c_5847]) ).

tff(c_98367,plain,
    app('#skF_50','#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5856,c_97918,c_97767]) ).

tff(c_98368,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_84586,c_98367]) ).

tff(c_98369,plain,
    app('#skF_53',cons('#skF_52','#skF_53')) = '#skF_53',
    inference(splitRight,[status(thm)],[c_79418]) ).

tff(c_354,plain,
    ! [V_1079,U_1077] :
      ( ( nil = V_1079 )
      | ( app(U_1077,V_1079) != nil )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(cnfTransformation,[status(thm)],[f_855]) ).

tff(c_77164,plain,
    ! [V_1079,U_1077] :
      ( ( V_1079 = '#skF_53' )
      | ( app(U_1077,V_1079) != '#skF_53' )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_5836,c_354]) ).

tff(c_98419,plain,
    ( ( cons('#skF_52','#skF_53') = '#skF_53' )
    | ~ ssList(cons('#skF_52','#skF_53'))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_98369,c_77164]) ).

tff(c_98434,plain,
    ( ( cons('#skF_52','#skF_53') = '#skF_53' )
    | ~ ssList(cons('#skF_52','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_98419]) ).

tff(c_99338,plain,
    ~ ssList(cons('#skF_52','#skF_53')),
    inference(splitLeft,[status(thm)],[c_98434]) ).

tff(c_99371,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_99338]) ).

tff(c_99375,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_394,c_99371]) ).

tff(c_99376,plain,
    cons('#skF_52','#skF_53') = '#skF_53',
    inference(splitRight,[status(thm)],[c_98434]) ).

tff(c_20,plain,
    ! [V_33] :
      ( singletonP(cons(V_33,nil))
      | ~ ssItem(V_33)
      | ~ ssList(cons(V_33,nil)) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_76545,plain,
    ! [V_2640] :
      ( singletonP(cons(V_2640,'#skF_53'))
      | ~ ssItem(V_2640)
      | ~ ssList(cons(V_2640,'#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5836,c_5836,c_20]) ).

tff(c_76555,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_53'))
      | ~ ssItem(V_861)
      | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_76545]) ).

tff(c_76560,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_53'))
      | ~ ssItem(V_861) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_76555]) ).

tff(c_99439,plain,
    ( singletonP('#skF_53')
    | ~ ssItem('#skF_52') ),
    inference(superposition,[status(thm),theory(equality)],[c_99376,c_76560]) ).

tff(c_99488,plain,
    singletonP('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_99439]) ).

tff(c_99490,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5879,c_99488]) ).

tff(c_99492,plain,
    nil != '#skF_53',
    inference(splitRight,[status(thm)],[c_5806]) ).

tff(c_5374,plain,
    ! [U_1611] :
      ( ( app(nil,U_1611) = U_1611 )
      | ~ ssList(U_1611) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_5395,plain,
    app(nil,'#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_402,c_5374]) ).

tff(c_137024,plain,
    ! [W_3501,U_3502,V_3503] :
      ( ( W_3501 = U_3502 )
      | ( app(W_3501,V_3503) != app(U_3502,V_3503) )
      | ~ ssList(W_3501)
      | ~ ssList(V_3503)
      | ~ ssList(U_3502) ),
    inference(cnfTransformation,[status(thm)],[f_815]) ).

tff(c_137248,plain,
    ! [W_3501] :
      ( ( nil = W_3501 )
      | ( app(W_3501,'#skF_50') != '#skF_50' )
      | ~ ssList(W_3501)
      | ~ ssList('#skF_50')
      | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_5395,c_137024]) ).

tff(c_142419,plain,
    ! [W_3555] :
      ( ( nil = W_3555 )
      | ( app(W_3555,'#skF_50') != '#skF_50' )
      | ~ ssList(W_3555) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_402,c_137248]) ).

tff(c_142563,plain,
    ( ( nil = '#skF_53' )
    | ( app('#skF_53','#skF_50') != '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_392,c_142419]) ).

tff(c_142647,plain,
    app('#skF_53','#skF_50') != '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_99492,c_142563]) ).

tff(c_202,plain,
    ! [U_917] :
      ( leq(U_917,U_917)
      | ~ ssItem(U_917) ),
    inference(cnfTransformation,[status(thm)],[f_442]) ).

tff(c_105924,plain,
    ! [V_3166,U_3167] :
      ( ( app(cons(V_3166,nil),U_3167) = cons(V_3166,U_3167) )
      | ~ ssItem(V_3166)
      | ~ ssList(U_3167) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_105943,plain,
    ! [U_3167] :
      ( ( cons('#skF_56',U_3167) = app('#skF_50',U_3167) )
      | ~ ssItem('#skF_56')
      | ~ ssList(U_3167) ),
    inference(superposition,[status(thm),theory(equality)],[c_5334,c_105924]) ).

tff(c_105954,plain,
    ! [U_3168] :
      ( ( cons('#skF_56',U_3168) = app('#skF_50',U_3168) )
      | ~ ssList(U_3168) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_105943]) ).

tff(c_106131,plain,
    cons('#skF_56','#skF_50') = app('#skF_50','#skF_50'),
    inference(resolution,[status(thm)],[c_402,c_105954]) ).

tff(c_100121,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_5813]) ).

tff(c_100143,plain,
    cons('#skF_56','#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_100121,c_5334]) ).

tff(c_100509,plain,
    ! [V_3022,U_3023] :
      ( ( cons(V_3022,U_3023) != '#skF_50' )
      | ~ ssItem(V_3022)
      | ~ ssList(U_3023) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100121,c_182]) ).

tff(c_100511,plain,
    ( ~ ssItem('#skF_56')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_100143,c_100509]) ).

tff(c_100515,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_5272,c_100511]) ).

tff(c_100517,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_5813]) ).

tff(c_100964,plain,
    ! [U_3030] :
      ( ( hd(U_3030) = '#skF_46'(U_3030) )
      | ( nil = U_3030 )
      | ~ ssList(U_3030) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_101066,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_402,c_100964]) ).

tff(c_101109,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_100517,c_101066]) ).

tff(c_101214,plain,
    ! [V_3039,U_3040] :
      ( ( hd(cons(V_3039,U_3040)) = V_3039 )
      | ~ ssItem(V_3039)
      | ~ ssList(U_3040) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_101229,plain,
    ( ( hd('#skF_50') = '#skF_56' )
    | ~ ssItem('#skF_56')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_5334,c_101214]) ).

tff(c_101235,plain,
    '#skF_46'('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_5272,c_101109,c_101229]) ).

tff(c_101237,plain,
    hd('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_101235,c_101109]) ).

tff(c_112603,plain,
    ! [U_3227,V_3228] :
      ( leq(U_3227,hd(V_3228))
      | ( nil = V_3228 )
      | ~ totalorderedP(cons(U_3227,V_3228))
      | ~ ssList(V_3228)
      | ~ ssItem(U_3227) ),
    inference(cnfTransformation,[status(thm)],[f_728]) ).

tff(c_112650,plain,
    ! [U_3227] :
      ( leq(U_3227,'#skF_56')
      | ( nil = '#skF_50' )
      | ~ totalorderedP(cons(U_3227,'#skF_50'))
      | ~ ssList('#skF_50')
      | ~ ssItem(U_3227) ),
    inference(superposition,[status(thm),theory(equality)],[c_101237,c_112603]) ).

tff(c_112702,plain,
    ! [U_3227] :
      ( leq(U_3227,'#skF_56')
      | ( nil = '#skF_50' )
      | ~ totalorderedP(cons(U_3227,'#skF_50'))
      | ~ ssItem(U_3227) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_112650]) ).

tff(c_121719,plain,
    ! [U_3334] :
      ( leq(U_3334,'#skF_56')
      | ~ totalorderedP(cons(U_3334,'#skF_50'))
      | ~ ssItem(U_3334) ),
    inference(negUnitSimplification,[status(thm)],[c_100517,c_112702]) ).

tff(c_121722,plain,
    ( leq('#skF_56','#skF_56')
    | ~ totalorderedP(app('#skF_50','#skF_50'))
    | ~ ssItem('#skF_56') ),
    inference(superposition,[status(thm),theory(equality)],[c_106131,c_121719]) ).

tff(c_121727,plain,
    ( leq('#skF_56','#skF_56')
    | ~ totalorderedP(app('#skF_50','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_121722]) ).

tff(c_121729,plain,
    ~ totalorderedP(app('#skF_50','#skF_50')),
    inference(splitLeft,[status(thm)],[c_121727]) ).

tff(c_5364,plain,
    ! [U_1610] :
      ( totalorderedP(cons(U_1610,nil))
      | ~ ssItem(U_1610) ),
    inference(cnfTransformation,[status(thm)],[f_711]) ).

tff(c_5367,plain,
    ( totalorderedP('#skF_50')
    | ~ ssItem('#skF_56') ),
    inference(superposition,[status(thm),theory(equality)],[c_5334,c_5364]) ).

tff(c_5369,plain,
    totalorderedP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_5367]) ).

tff(c_117114,plain,
    ! [U_3285,V_3286] :
      ( ~ leq(U_3285,hd(V_3286))
      | ~ totalorderedP(V_3286)
      | ( nil = V_3286 )
      | totalorderedP(cons(U_3285,V_3286))
      | ~ ssList(V_3286)
      | ~ ssItem(U_3285) ),
    inference(cnfTransformation,[status(thm)],[f_728]) ).

tff(c_117163,plain,
    ! [U_3285] :
      ( ~ leq(U_3285,'#skF_56')
      | ~ totalorderedP('#skF_50')
      | ( nil = '#skF_50' )
      | totalorderedP(cons(U_3285,'#skF_50'))
      | ~ ssList('#skF_50')
      | ~ ssItem(U_3285) ),
    inference(superposition,[status(thm),theory(equality)],[c_101237,c_117114]) ).

tff(c_117219,plain,
    ! [U_3285] :
      ( ~ leq(U_3285,'#skF_56')
      | ( nil = '#skF_50' )
      | totalorderedP(cons(U_3285,'#skF_50'))
      | ~ ssItem(U_3285) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_5369,c_117163]) ).

tff(c_121962,plain,
    ! [U_3336] :
      ( ~ leq(U_3336,'#skF_56')
      | totalorderedP(cons(U_3336,'#skF_50'))
      | ~ ssItem(U_3336) ),
    inference(negUnitSimplification,[status(thm)],[c_100517,c_117219]) ).

tff(c_121971,plain,
    ( ~ leq('#skF_56','#skF_56')
    | totalorderedP(app('#skF_50','#skF_50'))
    | ~ ssItem('#skF_56') ),
    inference(superposition,[status(thm),theory(equality)],[c_106131,c_121962]) ).

tff(c_121978,plain,
    ( ~ leq('#skF_56','#skF_56')
    | totalorderedP(app('#skF_50','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_121971]) ).

tff(c_121979,plain,
    ~ leq('#skF_56','#skF_56'),
    inference(negUnitSimplification,[status(thm)],[c_121729,c_121978]) ).

tff(c_121985,plain,
    ~ ssItem('#skF_56'),
    inference(resolution,[status(thm)],[c_202,c_121979]) ).

tff(c_121992,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_121985]) ).

tff(c_121993,plain,
    leq('#skF_56','#skF_56'),
    inference(splitRight,[status(thm)],[c_121727]) ).

tff(c_106418,plain,
    ! [U_3171,V_3172] :
      ( ( hd(app(U_3171,V_3172)) = hd(U_3171) )
      | ( nil = U_3171 )
      | ~ ssList(V_3172)
      | ~ ssList(U_3171) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_106583,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = hd('#skF_50') )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_106418]) ).

tff(c_106761,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_56' )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_101237,c_106583]) ).

tff(c_107209,plain,
    ~ ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitLeft,[status(thm)],[c_106761]) ).

tff(c_107218,plain,
    ( ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_107209]) ).

tff(c_107221,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_107218]) ).

tff(c_107224,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_107221]) ).

tff(c_107228,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_394,c_107224]) ).

tff(c_107230,plain,
    ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitRight,[status(thm)],[c_106761]) ).

tff(c_109882,plain,
    ! [V_3204,U_3205,W_3206] :
      ( ~ memberP(V_3204,U_3205)
      | memberP(app(V_3204,W_3206),U_3205)
      | ~ ssList(W_3206)
      | ~ ssList(V_3204)
      | ~ ssItem(U_3205) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_110047,plain,
    ! [U_3205] :
      ( ~ memberP(app('#skF_53',cons('#skF_52',nil)),U_3205)
      | memberP('#skF_50',U_3205)
      | ~ ssList('#skF_54')
      | ~ ssList(app('#skF_53',cons('#skF_52',nil)))
      | ~ ssItem(U_3205) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_109882]) ).

tff(c_135984,plain,
    ! [U_3492] :
      ( ~ memberP(app('#skF_53',cons('#skF_52',nil)),U_3492)
      | memberP('#skF_50',U_3492)
      | ~ ssItem(U_3492) ),
    inference(demodulation,[status(thm),theory(equality)],[c_107230,c_390,c_110047]) ).

tff(c_135992,plain,
    ( memberP('#skF_50','#skF_52')
    | ~ ssList(nil)
    | ~ ssList('#skF_53')
    | ~ ssItem('#skF_52')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(resolution,[status(thm)],[c_12,c_135984]) ).

tff(c_136006,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_107230,c_394,c_392,c_168,c_135992]) ).

tff(c_117289,plain,
    ! [W_3288,U_3289,V_3290] :
      ( memberP(W_3288,U_3289)
      | ( V_3290 = U_3289 )
      | ~ memberP(cons(V_3290,W_3288),U_3289)
      | ~ ssList(W_3288)
      | ~ ssItem(V_3290)
      | ~ ssItem(U_3289) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_117346,plain,
    ! [U_3289] :
      ( memberP(nil,U_3289)
      | ( U_3289 = '#skF_56' )
      | ~ memberP('#skF_50',U_3289)
      | ~ ssList(nil)
      | ~ ssItem('#skF_56')
      | ~ ssItem(U_3289) ),
    inference(superposition,[status(thm),theory(equality)],[c_5334,c_117289]) ).

tff(c_122600,plain,
    ! [U_3342] :
      ( memberP(nil,U_3342)
      | ( U_3342 = '#skF_56' )
      | ~ memberP('#skF_50',U_3342)
      | ~ ssItem(U_3342) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_117346]) ).

tff(c_122604,plain,
    ! [U_3342] :
      ( ( U_3342 = '#skF_56' )
      | ~ memberP('#skF_50',U_3342)
      | ~ ssItem(U_3342) ),
    inference(resolution,[status(thm)],[c_122600,c_228]) ).

tff(c_136015,plain,
    ( ( '#skF_52' = '#skF_56' )
    | ~ ssItem('#skF_52') ),
    inference(resolution,[status(thm)],[c_136006,c_122604]) ).

tff(c_136018,plain,
    '#skF_52' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_136015]) ).

tff(c_109540,plain,
    ! [W_3200,U_3201,V_3202] :
      ( ~ memberP(W_3200,U_3201)
      | memberP(app(V_3202,W_3200),U_3201)
      | ~ ssList(W_3200)
      | ~ ssList(V_3202)
      | ~ ssItem(U_3201) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_109705,plain,
    ! [U_3201] :
      ( ~ memberP('#skF_54',U_3201)
      | memberP('#skF_50',U_3201)
      | ~ ssList('#skF_54')
      | ~ ssList(app('#skF_53',cons('#skF_52',nil)))
      | ~ ssItem(U_3201) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_109540]) ).

tff(c_109869,plain,
    ! [U_3203] :
      ( ~ memberP('#skF_54',U_3203)
      | memberP('#skF_50',U_3203)
      | ~ ssItem(U_3203) ),
    inference(demodulation,[status(thm),theory(equality)],[c_107230,c_390,c_109705]) ).

tff(c_109875,plain,
    ( memberP('#skF_50','#skF_55')
    | ~ ssItem('#skF_55') ),
    inference(resolution,[status(thm)],[c_5294,c_109869]) ).

tff(c_109881,plain,
    memberP('#skF_50','#skF_55'),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_109875]) ).

tff(c_122605,plain,
    ! [U_3343] :
      ( ( U_3343 = '#skF_56' )
      | ~ memberP('#skF_50',U_3343)
      | ~ ssItem(U_3343) ),
    inference(resolution,[status(thm)],[c_122600,c_228]) ).

tff(c_122611,plain,
    ( ( '#skF_55' = '#skF_56' )
    | ~ ssItem('#skF_55') ),
    inference(resolution,[status(thm)],[c_109881,c_122605]) ).

tff(c_122620,plain,
    '#skF_55' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_122611]) ).

tff(c_107554,plain,
    ! [U_3181,V_3182] :
      ( lt(U_3181,V_3182)
      | ~ leq(U_3181,V_3182)
      | ( V_3182 = U_3181 )
      | ~ ssItem(V_3182)
      | ~ ssItem(U_3181) ),
    inference(cnfTransformation,[status(thm)],[f_950]) ).

tff(c_418,plain,
    ( ~ lt('#skF_55','#skF_52')
    | memberP('#skF_54','#skF_55') ),
    inference(cnfTransformation,[status(thm)],[f_1035]) ).

tff(c_5289,plain,
    ~ lt('#skF_55','#skF_52'),
    inference(splitLeft,[status(thm)],[c_418]) ).

tff(c_107577,plain,
    ( ~ leq('#skF_55','#skF_52')
    | ( '#skF_52' = '#skF_55' )
    | ~ ssItem('#skF_52')
    | ~ ssItem('#skF_55') ),
    inference(resolution,[status(thm)],[c_107554,c_5289]) ).

tff(c_107594,plain,
    ( ~ leq('#skF_55','#skF_52')
    | ( '#skF_52' = '#skF_55' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_394,c_107577]) ).

tff(c_107600,plain,
    ~ leq('#skF_55','#skF_52'),
    inference(splitLeft,[status(thm)],[c_107594]) ).

tff(c_122629,plain,
    ~ leq('#skF_56','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_122620,c_107600]) ).

tff(c_136040,plain,
    ~ leq('#skF_56','#skF_56'),
    inference(demodulation,[status(thm),theory(equality)],[c_136018,c_122629]) ).

tff(c_136087,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_121993,c_136040]) ).

tff(c_136088,plain,
    '#skF_52' = '#skF_55',
    inference(splitRight,[status(thm)],[c_107594]) ).

tff(c_136090,plain,
    ssList(app('#skF_53',cons('#skF_55',nil))),
    inference(demodulation,[status(thm),theory(equality)],[c_136088,c_107230]) ).

tff(c_136093,plain,
    app(app('#skF_53',cons('#skF_55',nil)),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_136088,c_425]) ).

tff(c_140623,plain,
    ! [W_3530,U_3531,V_3532] :
      ( ~ memberP(W_3530,U_3531)
      | memberP(app(V_3532,W_3530),U_3531)
      | ~ ssList(W_3530)
      | ~ ssList(V_3532)
      | ~ ssItem(U_3531) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_140629,plain,
    ! [U_3531] :
      ( ~ memberP('#skF_54',U_3531)
      | memberP('#skF_50',U_3531)
      | ~ ssList('#skF_54')
      | ~ ssList(app('#skF_53',cons('#skF_55',nil)))
      | ~ ssItem(U_3531) ),
    inference(superposition,[status(thm),theory(equality)],[c_136093,c_140623]) ).

tff(c_147159,plain,
    ! [U_3617] :
      ( ~ memberP('#skF_54',U_3617)
      | memberP('#skF_50',U_3617)
      | ~ ssItem(U_3617) ),
    inference(demodulation,[status(thm),theory(equality)],[c_136090,c_390,c_140629]) ).

tff(c_147165,plain,
    ( memberP('#skF_50','#skF_55')
    | ~ ssItem('#skF_55') ),
    inference(resolution,[status(thm)],[c_5294,c_147159]) ).

tff(c_147171,plain,
    memberP('#skF_50','#skF_55'),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_147165]) ).

tff(c_146421,plain,
    ! [W_3603,U_3604,V_3605] :
      ( memberP(W_3603,U_3604)
      | ( V_3605 = U_3604 )
      | ~ memberP(cons(V_3605,W_3603),U_3604)
      | ~ ssList(W_3603)
      | ~ ssItem(V_3605)
      | ~ ssItem(U_3604) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_146478,plain,
    ! [U_3604] :
      ( memberP(nil,U_3604)
      | ( U_3604 = '#skF_56' )
      | ~ memberP('#skF_50',U_3604)
      | ~ ssList(nil)
      | ~ ssItem('#skF_56')
      | ~ ssItem(U_3604) ),
    inference(superposition,[status(thm),theory(equality)],[c_5334,c_146421]) ).

tff(c_152011,plain,
    ! [U_3669] :
      ( memberP(nil,U_3669)
      | ( U_3669 = '#skF_56' )
      | ~ memberP('#skF_50',U_3669)
      | ~ ssItem(U_3669) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_146478]) ).

tff(c_152272,plain,
    ! [U_3674] :
      ( ( U_3674 = '#skF_56' )
      | ~ memberP('#skF_50',U_3674)
      | ~ ssItem(U_3674) ),
    inference(resolution,[status(thm)],[c_152011,c_228]) ).

tff(c_152278,plain,
    ( ( '#skF_55' = '#skF_56' )
    | ~ ssItem('#skF_55') ),
    inference(resolution,[status(thm)],[c_147171,c_152272]) ).

tff(c_152287,plain,
    '#skF_55' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_152278]) ).

tff(c_152295,plain,
    ssList(app('#skF_53',cons('#skF_56',nil))),
    inference(demodulation,[status(thm),theory(equality)],[c_152287,c_136090]) ).

tff(c_152306,plain,
    ssList(app('#skF_53','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_5334,c_152295]) ).

tff(c_136616,plain,
    ! [V_3497,W_3498] :
      ( frontsegP(app(V_3497,W_3498),V_3497)
      | ~ ssList(W_3498)
      | ~ ssList(V_3497)
      | ~ ssList(app(V_3497,W_3498)) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_136621,plain,
    ( frontsegP('#skF_50',app('#skF_53',cons('#skF_55',nil)))
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_55',nil)))
    | ~ ssList(app(app('#skF_53',cons('#skF_55',nil)),'#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_136093,c_136616]) ).

tff(c_136804,plain,
    frontsegP('#skF_50',app('#skF_53',cons('#skF_55',nil))),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_136093,c_136090,c_390,c_136621]) ).

tff(c_152293,plain,
    frontsegP('#skF_50',app('#skF_53',cons('#skF_56',nil))),
    inference(demodulation,[status(thm),theory(equality)],[c_152287,c_136804]) ).

tff(c_152304,plain,
    frontsegP('#skF_50',app('#skF_53','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_5334,c_152293]) ).

tff(c_234,plain,
    ! [V_958,U_956] :
      ( ( V_958 = U_956 )
      | ~ frontsegP(V_958,U_956)
      | ~ frontsegP(U_956,V_958)
      | ~ ssList(V_958)
      | ~ ssList(U_956) ),
    inference(cnfTransformation,[status(thm)],[f_544]) ).

tff(c_152513,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_50' )
    | ~ frontsegP(app('#skF_53','#skF_50'),'#skF_50')
    | ~ ssList('#skF_50')
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(resolution,[status(thm)],[c_152304,c_234]) ).

tff(c_152519,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_50' )
    | ~ frontsegP(app('#skF_53','#skF_50'),'#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_152306,c_402,c_152513]) ).

tff(c_152520,plain,
    ~ frontsegP(app('#skF_53','#skF_50'),'#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_142647,c_152519]) ).

tff(c_152915,plain,
    ( ~ frontsegP('#skF_53','#skF_50')
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_238,c_152520]) ).

tff(c_152918,plain,
    ~ frontsegP('#skF_53','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_402,c_152915]) ).

tff(c_99491,plain,
    tl('#skF_53') = '#skF_47'('#skF_53'),
    inference(splitRight,[status(thm)],[c_5806]) ).

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

tff(c_100102,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_99491,c_188]) ).

tff(c_100106,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_100102]) ).

tff(c_100107,plain,
    ssList('#skF_47'('#skF_53')),
    inference(negUnitSimplification,[status(thm)],[c_99492,c_100106]) ).

tff(c_100119,plain,
    app(nil,'#skF_47'('#skF_53')) = '#skF_47'('#skF_53'),
    inference(resolution,[status(thm)],[c_100107,c_196]) ).

tff(c_136759,plain,
    ( frontsegP('#skF_47'('#skF_53'),nil)
    | ~ ssList('#skF_47'('#skF_53'))
    | ~ ssList(nil)
    | ~ ssList(app(nil,'#skF_47'('#skF_53'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_100119,c_136616]) ).

tff(c_136892,plain,
    frontsegP('#skF_47'('#skF_53'),nil),
    inference(demodulation,[status(thm),theory(equality)],[c_100107,c_100119,c_168,c_100107,c_136759]) ).

tff(c_106127,plain,
    cons('#skF_56','#skF_54') = app('#skF_50','#skF_54'),
    inference(resolution,[status(thm)],[c_390,c_105954]) ).

tff(c_106345,plain,
    ( ssList(app('#skF_50','#skF_54'))
    | ~ ssItem('#skF_56')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_106127,c_166]) ).

tff(c_106362,plain,
    ssList(app('#skF_50','#skF_54')),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_5272,c_106345]) ).

tff(c_101054,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_392,c_100964]) ).

tff(c_101098,plain,
    hd('#skF_53') = '#skF_46'('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_99492,c_101054]) ).

tff(c_152294,plain,
    app(app('#skF_53',cons('#skF_56',nil)),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_152287,c_136093]) ).

tff(c_152305,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5334,c_152294]) ).

tff(c_153337,plain,
    ( ( app('#skF_53',app('#skF_50','#skF_54')) = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_152305,c_348]) ).

tff(c_153395,plain,
    app('#skF_53',app('#skF_50','#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_402,c_390,c_153337]) ).

tff(c_153727,plain,
    ( ( hd('#skF_53') = hd('#skF_50') )
    | ( nil = '#skF_53' )
    | ~ ssList(app('#skF_50','#skF_54'))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_153395,c_358]) ).

tff(c_153768,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_56' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_106362,c_101098,c_101237,c_153727]) ).

tff(c_153769,plain,
    '#skF_46'('#skF_53') = '#skF_56',
    inference(negUnitSimplification,[status(thm)],[c_99492,c_153768]) ).

tff(c_101479,plain,
    ! [U_3054] :
      ( ( cons(hd(U_3054),tl(U_3054)) = U_3054 )
      | ( nil = U_3054 )
      | ~ ssList(U_3054) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_101525,plain,
    ( ( cons(hd('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_99491,c_101479]) ).

tff(c_101552,plain,
    ( ( cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_101098,c_101525]) ).

tff(c_101553,plain,
    cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53',
    inference(negUnitSimplification,[status(thm)],[c_99492,c_101552]) ).

tff(c_153791,plain,
    cons('#skF_56','#skF_47'('#skF_53')) = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_153769,c_101553]) ).

tff(c_146235,plain,
    ! [V_3599,W_3600,X_3601] :
      ( frontsegP(cons(V_3599,W_3600),cons(V_3599,X_3601))
      | ~ frontsegP(W_3600,X_3601)
      | ~ ssList(X_3601)
      | ~ ssList(W_3600)
      | ~ ssItem(V_3599) ),
    inference(cnfTransformation,[status(thm)],[f_577]) ).

tff(c_146341,plain,
    ! [W_3600] :
      ( frontsegP(cons('#skF_56',W_3600),'#skF_50')
      | ~ frontsegP(W_3600,nil)
      | ~ ssList(nil)
      | ~ ssList(W_3600)
      | ~ ssItem('#skF_56') ),
    inference(superposition,[status(thm),theory(equality)],[c_5334,c_146235]) ).

tff(c_146399,plain,
    ! [W_3600] :
      ( frontsegP(cons('#skF_56',W_3600),'#skF_50')
      | ~ frontsegP(W_3600,nil)
      | ~ ssList(W_3600) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_146341]) ).

tff(c_153876,plain,
    ( frontsegP('#skF_53','#skF_50')
    | ~ frontsegP('#skF_47'('#skF_53'),nil)
    | ~ ssList('#skF_47'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_153791,c_146399]) ).

tff(c_153962,plain,
    frontsegP('#skF_53','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_100107,c_136892,c_153876]) ).

tff(c_153964,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_152918,c_153962]) ).

tff(c_153965,plain,
    memberP('#skF_53','#skF_55'),
    inference(splitRight,[status(thm)],[c_420]) ).

tff(c_154810,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_392,c_154694]) ).

tff(c_154829,plain,
    nil = '#skF_53',
    inference(splitLeft,[status(thm)],[c_154810]) ).

tff(c_155326,plain,
    ! [U_3757] :
      ( ~ memberP('#skF_53',U_3757)
      | ~ ssItem(U_3757) ),
    inference(demodulation,[status(thm),theory(equality)],[c_154829,c_228]) ).

tff(c_155329,plain,
    ~ ssItem('#skF_55'),
    inference(resolution,[status(thm)],[c_153965,c_155326]) ).

tff(c_155333,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_155329]) ).

tff(c_155335,plain,
    nil != '#skF_53',
    inference(splitRight,[status(thm)],[c_154810]) ).

tff(c_155714,plain,
    ( ( tl('#skF_53') = '#skF_47'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_392,c_155598]) ).

tff(c_222525,plain,
    tl('#skF_53') = '#skF_47'('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_155335,c_155714]) ).

tff(c_222529,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_222525,c_188]) ).

tff(c_222533,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_222529]) ).

tff(c_222534,plain,
    ssList('#skF_47'('#skF_53')),
    inference(negUnitSimplification,[status(thm)],[c_155335,c_222533]) ).

tff(c_222555,plain,
    ( ( hd('#skF_47'('#skF_53')) = '#skF_46'('#skF_47'('#skF_53')) )
    | ( '#skF_47'('#skF_53') = nil ) ),
    inference(resolution,[status(thm)],[c_222534,c_330]) ).

tff(c_280322,plain,
    '#skF_47'('#skF_53') = nil,
    inference(splitLeft,[status(thm)],[c_222555]) ).

tff(c_280327,plain,
    tl('#skF_53') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_280322,c_222525]) ).

tff(c_302747,plain,
    ! [U_5923,V_5924] :
      ( ( app(tl(U_5923),V_5924) = tl(app(U_5923,V_5924)) )
      | ( nil = U_5923 )
      | ~ ssList(V_5924)
      | ~ ssList(U_5923) ),
    inference(cnfTransformation,[status(thm)],[f_879]) ).

tff(c_302819,plain,
    ! [V_5924] :
      ( ( tl(app('#skF_53',V_5924)) = app(nil,V_5924) )
      | ( nil = '#skF_53' )
      | ~ ssList(V_5924)
      | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_280327,c_302747]) ).

tff(c_302860,plain,
    ! [V_5924] :
      ( ( tl(app('#skF_53',V_5924)) = app(nil,V_5924) )
      | ( nil = '#skF_53' )
      | ~ ssList(V_5924) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_302819]) ).

tff(c_302861,plain,
    ! [V_5924] :
      ( ( tl(app('#skF_53',V_5924)) = app(nil,V_5924) )
      | ~ ssList(V_5924) ),
    inference(negUnitSimplification,[status(thm)],[c_155335,c_302860]) ).

tff(c_314324,plain,
    ( ( app(nil,app('#skF_50','#skF_54')) = tl('#skF_50') )
    | ~ ssList(app('#skF_50','#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_314057,c_302861]) ).

tff(c_314374,plain,
    app('#skF_50','#skF_54') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_298565,c_298669,c_222735,c_314324]) ).

tff(c_314376,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_298561,c_314374]) ).

tff(c_314378,plain,
    '#skF_47'('#skF_53') != nil,
    inference(splitRight,[status(thm)],[c_222555]) ).

tff(c_154050,plain,
    ! [U_3693] :
      ( ( app(nil,U_3693) = U_3693 )
      | ~ ssList(U_3693) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_154071,plain,
    app(nil,'#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_402,c_154050]) ).

tff(c_153967,plain,
    ! [U_3690] :
      ( ( app(U_3690,nil) = U_3690 )
      | ~ ssList(U_3690) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_153987,plain,
    app('#skF_50',nil) = '#skF_50',
    inference(resolution,[status(thm)],[c_402,c_153967]) ).

tff(c_155334,plain,
    hd('#skF_53') = '#skF_46'('#skF_53'),
    inference(splitRight,[status(thm)],[c_154810]) ).

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

tff(c_222518,plain,
    ( ssItem('#skF_46'('#skF_53'))
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_155334,c_184]) ).

tff(c_222522,plain,
    ( ssItem('#skF_46'('#skF_53'))
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_222518]) ).

tff(c_222523,plain,
    ssItem('#skF_46'('#skF_53')),
    inference(negUnitSimplification,[status(thm)],[c_155335,c_222522]) ).

tff(c_225047,plain,
    ! [U_4909] :
      ( ( cons(hd(U_4909),tl(U_4909)) = U_4909 )
      | ( nil = U_4909 )
      | ~ ssList(U_4909) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_225099,plain,
    ( ( cons(hd('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_222525,c_225047]) ).

tff(c_225138,plain,
    ( ( cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_155334,c_225099]) ).

tff(c_225139,plain,
    cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53',
    inference(negUnitSimplification,[status(thm)],[c_155335,c_225138]) ).

tff(c_262037,plain,
    ! [X_5337,W_5338,V_5339,U_5340] :
      ( ( X_5337 = W_5338 )
      | ( cons(X_5337,V_5339) != cons(W_5338,U_5340) )
      | ~ ssItem(X_5337)
      | ~ ssItem(W_5338)
      | ~ ssList(V_5339)
      | ~ ssList(U_5340) ),
    inference(cnfTransformation,[status(thm)],[f_344]) ).

tff(c_262095,plain,
    ! [W_5338,U_5340] :
      ( ( W_5338 = '#skF_56' )
      | ( cons(W_5338,U_5340) != '#skF_50' )
      | ~ ssItem('#skF_56')
      | ~ ssItem(W_5338)
      | ~ ssList(nil)
      | ~ ssList(U_5340) ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_262037]) ).

tff(c_267806,plain,
    ! [W_5411,U_5412] :
      ( ( W_5411 = '#skF_56' )
      | ( cons(W_5411,U_5412) != '#skF_50' )
      | ~ ssItem(W_5411)
      | ~ ssList(U_5412) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_5272,c_262095]) ).

tff(c_267828,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_56' )
    | ( '#skF_53' != '#skF_50' )
    | ~ ssItem('#skF_46'('#skF_53'))
    | ~ ssList('#skF_47'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_225139,c_267806]) ).

tff(c_267858,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_56' )
    | ( '#skF_53' != '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_222534,c_222523,c_267828]) ).

tff(c_267868,plain,
    '#skF_53' != '#skF_50',
    inference(splitLeft,[status(thm)],[c_267858]) ).

tff(c_227244,plain,
    ! [V_4966,U_4967] :
      ( ( app(cons(V_4966,nil),U_4967) = cons(V_4966,U_4967) )
      | ~ ssItem(V_4966)
      | ~ ssList(U_4967) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_227266,plain,
    ! [U_4967] :
      ( ( cons('#skF_56',U_4967) = app('#skF_50',U_4967) )
      | ~ ssItem('#skF_56')
      | ~ ssList(U_4967) ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_227244]) ).

tff(c_227273,plain,
    ! [U_4968] :
      ( ( cons('#skF_56',U_4968) = app('#skF_50',U_4968) )
      | ~ ssList(U_4968) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_227266]) ).

tff(c_227438,plain,
    cons('#skF_56','#skF_54') = app('#skF_50','#skF_54'),
    inference(resolution,[status(thm)],[c_390,c_227273]) ).

tff(c_227854,plain,
    ( ssList(app('#skF_50','#skF_54'))
    | ~ ssItem('#skF_56')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_227438,c_166]) ).

tff(c_227868,plain,
    ssList(app('#skF_50','#skF_54')),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_5272,c_227854]) ).

tff(c_269486,plain,
    ! [W_5430,V_5431,X_5432] :
      ( segmentP(app(app(W_5430,V_5431),X_5432),V_5431)
      | ~ ssList(X_5432)
      | ~ ssList(W_5430)
      | ~ ssList(V_5431)
      | ~ ssList(app(app(W_5430,V_5431),X_5432)) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_269728,plain,
    ( segmentP('#skF_50',cons('#skF_52',nil))
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_53')
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList(app(app('#skF_53',cons('#skF_52',nil)),'#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_269486]) ).

tff(c_269865,plain,
    ( segmentP('#skF_50',cons('#skF_52',nil))
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_425,c_392,c_390,c_269728]) ).

tff(c_269909,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_269865]) ).

tff(c_269912,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_269909]) ).

tff(c_269916,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_394,c_269912]) ).

tff(c_269918,plain,
    ssList(cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_269865]) ).

tff(c_262564,plain,
    ! [U_5347,V_5348,W_5349] :
      ( ( app(app(U_5347,V_5348),W_5349) = app(U_5347,app(V_5348,W_5349)) )
      | ~ ssList(W_5349)
      | ~ ssList(V_5348)
      | ~ ssList(U_5347) ),
    inference(cnfTransformation,[status(thm)],[f_844]) ).

tff(c_262697,plain,
    ( ( app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_262564,c_425]) ).

tff(c_262940,plain,
    ( ( app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_390,c_262697]) ).

tff(c_278341,plain,
    app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_269918,c_262940]) ).

tff(c_278397,plain,
    ( ( app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_346,c_278341]) ).

tff(c_278442,plain,
    app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_394,c_278397]) ).

tff(c_278467,plain,
    ( memberP('#skF_50','#skF_52')
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_53')
    | ~ ssItem('#skF_52')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_54'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_278442,c_12]) ).

tff(c_278533,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_278442,c_394,c_392,c_390,c_278467]) ).

tff(c_263268,plain,
    ! [W_5355,U_5356,V_5357] :
      ( memberP(W_5355,U_5356)
      | ( V_5357 = U_5356 )
      | ~ memberP(cons(V_5357,W_5355),U_5356)
      | ~ ssList(W_5355)
      | ~ ssItem(V_5357)
      | ~ ssItem(U_5356) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_263319,plain,
    ! [U_5356] :
      ( memberP(nil,U_5356)
      | ( U_5356 = '#skF_56' )
      | ~ memberP('#skF_50',U_5356)
      | ~ ssList(nil)
      | ~ ssItem('#skF_56')
      | ~ ssItem(U_5356) ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_263268]) ).

tff(c_268770,plain,
    ! [U_5423] :
      ( memberP(nil,U_5423)
      | ( U_5423 = '#skF_56' )
      | ~ memberP('#skF_50',U_5423)
      | ~ ssItem(U_5423) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_263319]) ).

tff(c_268774,plain,
    ! [U_5423] :
      ( ( U_5423 = '#skF_56' )
      | ~ memberP('#skF_50',U_5423)
      | ~ ssItem(U_5423) ),
    inference(resolution,[status(thm)],[c_268770,c_228]) ).

tff(c_278576,plain,
    ( ( '#skF_52' = '#skF_56' )
    | ~ ssItem('#skF_52') ),
    inference(resolution,[status(thm)],[c_278533,c_268774]) ).

tff(c_278579,plain,
    '#skF_52' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_278576]) ).

tff(c_266213,plain,
    ! [V_5393,U_5394,W_5395,X_5396] :
      ( ( V_5393 = U_5394 )
      | ~ frontsegP(cons(U_5394,W_5395),cons(V_5393,X_5396))
      | ~ ssList(X_5396)
      | ~ ssList(W_5395)
      | ~ ssItem(V_5393)
      | ~ ssItem(U_5394) ),
    inference(cnfTransformation,[status(thm)],[f_577]) ).

tff(c_266309,plain,
    ! [V_5393,X_5396] :
      ( ( V_5393 = '#skF_56' )
      | ~ frontsegP('#skF_50',cons(V_5393,X_5396))
      | ~ ssList(X_5396)
      | ~ ssList(nil)
      | ~ ssItem(V_5393)
      | ~ ssItem('#skF_56') ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_266213]) ).

tff(c_277738,plain,
    ! [V_5503,X_5504] :
      ( ( V_5503 = '#skF_56' )
      | ~ frontsegP('#skF_50',cons(V_5503,X_5504))
      | ~ ssList(X_5504)
      | ~ ssItem(V_5503) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_266309]) ).

tff(c_277780,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_56' )
    | ~ frontsegP('#skF_50','#skF_53')
    | ~ ssList('#skF_47'('#skF_53'))
    | ~ ssItem('#skF_46'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_225139,c_277738]) ).

tff(c_277826,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_56' )
    | ~ frontsegP('#skF_50','#skF_53') ),
    inference(demodulation,[status(thm),theory(equality)],[c_222523,c_222534,c_277780]) ).

tff(c_278128,plain,
    ~ frontsegP('#skF_50','#skF_53'),
    inference(splitLeft,[status(thm)],[c_277826]) ).

tff(c_26,plain,
    ! [V_40,W_43] :
      ( frontsegP(app(V_40,W_43),V_40)
      | ~ ssList(W_43)
      | ~ ssList(V_40)
      | ~ ssList(app(V_40,W_43)) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_278502,plain,
    ( frontsegP('#skF_50','#skF_53')
    | ~ ssList(cons('#skF_52','#skF_54'))
    | ~ ssList('#skF_53')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_54'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_278442,c_26]) ).

tff(c_278559,plain,
    ( frontsegP('#skF_50','#skF_53')
    | ~ ssList(cons('#skF_52','#skF_54')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_278442,c_392,c_278502]) ).

tff(c_278560,plain,
    ~ ssList(cons('#skF_52','#skF_54')),
    inference(negUnitSimplification,[status(thm)],[c_278128,c_278559]) ).

tff(c_278950,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_227868,c_227438,c_278579,c_278560]) ).

tff(c_278952,plain,
    frontsegP('#skF_50','#skF_53'),
    inference(splitRight,[status(thm)],[c_277826]) ).

tff(c_279066,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ frontsegP('#skF_53','#skF_50')
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_278952,c_234]) ).

tff(c_279072,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ frontsegP('#skF_53','#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_402,c_279066]) ).

tff(c_279073,plain,
    ~ frontsegP('#skF_53','#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_267868,c_279072]) ).

tff(c_222558,plain,
    app(nil,'#skF_47'('#skF_53')) = '#skF_47'('#skF_53'),
    inference(resolution,[status(thm)],[c_222534,c_196]) ).

tff(c_255264,plain,
    ! [V_5256,W_5257] :
      ( frontsegP(app(V_5256,W_5257),V_5256)
      | ~ ssList(W_5257)
      | ~ ssList(V_5256)
      | ~ ssList(app(V_5256,W_5257)) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_255401,plain,
    ( frontsegP('#skF_47'('#skF_53'),nil)
    | ~ ssList('#skF_47'('#skF_53'))
    | ~ ssList(nil)
    | ~ ssList(app(nil,'#skF_47'('#skF_53'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_222558,c_255264]) ).

tff(c_255519,plain,
    frontsegP('#skF_47'('#skF_53'),nil),
    inference(demodulation,[status(thm),theory(equality)],[c_222534,c_222558,c_168,c_222534,c_255401]) ).

tff(c_278951,plain,
    '#skF_46'('#skF_53') = '#skF_56',
    inference(splitRight,[status(thm)],[c_277826]) ).

tff(c_279075,plain,
    cons('#skF_56','#skF_47'('#skF_53')) = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_278951,c_225139]) ).

tff(c_263119,plain,
    ! [V_5352,W_5353,X_5354] :
      ( frontsegP(cons(V_5352,W_5353),cons(V_5352,X_5354))
      | ~ frontsegP(W_5353,X_5354)
      | ~ ssList(X_5354)
      | ~ ssList(W_5353)
      | ~ ssItem(V_5352) ),
    inference(cnfTransformation,[status(thm)],[f_577]) ).

tff(c_263213,plain,
    ! [W_5353] :
      ( frontsegP(cons('#skF_56',W_5353),'#skF_50')
      | ~ frontsegP(W_5353,nil)
      | ~ ssList(nil)
      | ~ ssList(W_5353)
      | ~ ssItem('#skF_56') ),
    inference(superposition,[status(thm),theory(equality)],[c_154002,c_263119]) ).

tff(c_263267,plain,
    ! [W_5353] :
      ( frontsegP(cons('#skF_56',W_5353),'#skF_50')
      | ~ frontsegP(W_5353,nil)
      | ~ ssList(W_5353) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_168,c_263213]) ).

tff(c_279181,plain,
    ( frontsegP('#skF_53','#skF_50')
    | ~ frontsegP('#skF_47'('#skF_53'),nil)
    | ~ ssList('#skF_47'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_279075,c_263267]) ).

tff(c_279281,plain,
    frontsegP('#skF_53','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_222534,c_255519,c_279181]) ).

tff(c_279283,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_279073,c_279281]) ).

tff(c_279285,plain,
    '#skF_53' = '#skF_50',
    inference(splitRight,[status(thm)],[c_267858]) ).

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_222794,plain,
    ! [U_4830] :
      ( ( cons('#skF_5'(U_4830),nil) = U_4830 )
      | ~ singletonP(U_4830)
      | ~ ssList(U_4830) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_326,plain,
    ! [U_1044] :
      ( equalelemsP(cons(U_1044,nil))
      | ~ ssItem(U_1044) ),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_223156,plain,
    ! [U_4836] :
      ( equalelemsP(U_4836)
      | ~ ssItem('#skF_5'(U_4836))
      | ~ singletonP(U_4836)
      | ~ ssList(U_4836) ),
    inference(superposition,[status(thm),theory(equality)],[c_222794,c_326]) ).

tff(c_223162,plain,
    ! [U_4837] :
      ( equalelemsP(U_4837)
      | ~ singletonP(U_4837)
      | ~ ssList(U_4837) ),
    inference(resolution,[status(thm)],[c_24,c_223156]) ).

tff(c_223286,plain,
    ( equalelemsP('#skF_53')
    | ~ singletonP('#skF_53') ),
    inference(resolution,[status(thm)],[c_392,c_223162]) ).

tff(c_223293,plain,
    ~ singletonP('#skF_53'),
    inference(splitLeft,[status(thm)],[c_223286]) ).

tff(c_334,plain,
    ! [U_1047] :
      ( ( tl(U_1047) = '#skF_47'(U_1047) )
      | ( nil = U_1047 )
      | ~ ssList(U_1047) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_222554,plain,
    ( ( tl('#skF_47'('#skF_53')) = '#skF_47'('#skF_47'('#skF_53')) )
    | ( '#skF_47'('#skF_53') = nil ) ),
    inference(resolution,[status(thm)],[c_222534,c_334]) ).

tff(c_224096,plain,
    '#skF_47'('#skF_53') = nil,
    inference(splitLeft,[status(thm)],[c_222554]) ).

tff(c_224102,plain,
    tl('#skF_53') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_224096,c_222525]) ).

tff(c_224166,plain,
    ! [U_4881] :
      ( ( cons(hd(U_4881),tl(U_4881)) = U_4881 )
      | ( nil = U_4881 )
      | ~ ssList(U_4881) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_224212,plain,
    ( ( cons('#skF_46'('#skF_53'),tl('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_155334,c_224166]) ).

tff(c_224239,plain,
    ( ( cons('#skF_46'('#skF_53'),nil) = '#skF_53' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_224102,c_224212]) ).

tff(c_224240,plain,
    cons('#skF_46'('#skF_53'),nil) = '#skF_53',
    inference(negUnitSimplification,[status(thm)],[c_155335,c_224239]) ).

tff(c_223295,plain,
    ! [V_4838] :
      ( singletonP(cons(V_4838,nil))
      | ~ ssItem(V_4838)
      | ~ ssList(cons(V_4838,nil)) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_223302,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,nil))
      | ~ ssItem(V_861)
      | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_223295]) ).

tff(c_223308,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,nil))
      | ~ ssItem(V_861) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_223302]) ).

tff(c_224340,plain,
    ( singletonP('#skF_53')
    | ~ ssItem('#skF_46'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_224240,c_223308]) ).

tff(c_224381,plain,
    singletonP('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_222523,c_224340]) ).

tff(c_224383,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_223293,c_224381]) ).

tff(c_224385,plain,
    '#skF_47'('#skF_53') != nil,
    inference(splitRight,[status(thm)],[c_222554]) ).

tff(c_259306,plain,
    ! [W_5294,U_5295,V_5296] :
      ( ( W_5294 = U_5295 )
      | ( app(V_5296,W_5294) != app(V_5296,U_5295) )
      | ~ ssList(W_5294)
      | ~ ssList(V_5296)
      | ~ ssList(U_5295) ),
    inference(cnfTransformation,[status(thm)],[f_827]) ).

tff(c_259530,plain,
    ! [W_5294] :
      ( ( nil = W_5294 )
      | ( app('#skF_50',W_5294) != '#skF_50' )
      | ~ ssList(W_5294)
      | ~ ssList('#skF_50')
      | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_153987,c_259306]) ).

tff(c_260357,plain,
    ! [W_5309] :
      ( ( nil = W_5309 )
      | ( app('#skF_50',W_5309) != '#skF_50' )
      | ~ ssList(W_5309) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_402,c_259530]) ).

tff(c_260411,plain,
    ( ( '#skF_47'('#skF_53') = nil )
    | ( app('#skF_50','#skF_47'('#skF_53')) != '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_222534,c_260357]) ).

tff(c_260540,plain,
    app('#skF_50','#skF_47'('#skF_53')) != '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_224385,c_260411]) ).

tff(c_227410,plain,
    cons('#skF_56','#skF_47'('#skF_53')) = app('#skF_50','#skF_47'('#skF_53')),
    inference(resolution,[status(thm)],[c_222534,c_227273]) ).

tff(c_254578,plain,
    ( ssList(app('#skF_50','#skF_47'('#skF_53')))
    | ~ ssItem('#skF_56')
    | ~ ssList('#skF_47'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_227410,c_166]) ).

tff(c_254598,plain,
    ssList(app('#skF_50','#skF_47'('#skF_53'))),
    inference(demodulation,[status(thm),theory(equality)],[c_222534,c_5272,c_254578]) ).

tff(c_259496,plain,
    ! [U_5295] :
      ( ( U_5295 = '#skF_50' )
      | ( app(nil,U_5295) != '#skF_50' )
      | ~ ssList('#skF_50')
      | ~ ssList(nil)
      | ~ ssList(U_5295) ),
    inference(superposition,[status(thm),theory(equality)],[c_154071,c_259306]) ).

tff(c_262150,plain,
    ! [U_5341] :
      ( ( U_5341 = '#skF_50' )
      | ( app(nil,U_5341) != '#skF_50' )
      | ~ ssList(U_5341) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_402,c_259496]) ).

tff(c_262153,plain,
    ( ( app('#skF_50','#skF_47'('#skF_53')) = '#skF_50' )
    | ( app(nil,app('#skF_50','#skF_47'('#skF_53'))) != '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_254598,c_262150]) ).

tff(c_262300,plain,
    app(nil,app('#skF_50','#skF_47'('#skF_53'))) != '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_260540,c_262153]) ).

tff(c_279310,plain,
    app(nil,app('#skF_50','#skF_47'('#skF_50'))) != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_279285,c_262300]) ).

tff(c_279469,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_154071,c_153987,c_222731,c_279310]) ).

tff(c_279471,plain,
    singletonP('#skF_53'),
    inference(splitRight,[status(thm)],[c_223286]) ).

tff(c_190,plain,
    ! [V_895,U_893] :
      ( ( tl(cons(V_895,U_893)) = U_893 )
      | ~ ssItem(V_895)
      | ~ ssList(U_893) ),
    inference(cnfTransformation,[status(thm)],[f_392]) ).

tff(c_222800,plain,
    ! [U_4830] :
      ( ( tl(U_4830) = nil )
      | ~ ssItem('#skF_5'(U_4830))
      | ~ ssList(nil)
      | ~ singletonP(U_4830)
      | ~ ssList(U_4830) ),
    inference(superposition,[status(thm),theory(equality)],[c_222794,c_190]) ).

tff(c_338288,plain,
    ! [U_6387] :
      ( ( tl(U_6387) = nil )
      | ~ ssItem('#skF_5'(U_6387))
      | ~ singletonP(U_6387)
      | ~ ssList(U_6387) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_222800]) ).

tff(c_338484,plain,
    ! [U_6391] :
      ( ( tl(U_6391) = nil )
      | ~ singletonP(U_6391)
      | ~ ssList(U_6391) ),
    inference(resolution,[status(thm)],[c_24,c_338288]) ).

tff(c_338625,plain,
    ( ( tl('#skF_53') = nil )
    | ~ singletonP('#skF_53') ),
    inference(resolution,[status(thm)],[c_392,c_338484]) ).

tff(c_338706,plain,
    '#skF_47'('#skF_53') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_279471,c_222525,c_338625]) ).

tff(c_338708,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_314378,c_338706]) ).

tff(c_338709,plain,
    memberP('#skF_54','#skF_55'),
    inference(splitRight,[status(thm)],[c_418]) ).

tff(c_339377,plain,
    ! [V_6449,U_6450] :
      ( ( cons(V_6449,U_6450) != nil )
      | ~ ssItem(V_6449)
      | ~ ssList(U_6450) ),
    inference(cnfTransformation,[status(thm)],[f_364]) ).

tff(c_339379,plain,
    ( ( nil != '#skF_50' )
    | ~ ssItem('#skF_56')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_338784,c_339377]) ).

tff(c_339381,plain,
    nil != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_5272,c_339379]) ).

tff(c_339454,plain,
    ! [U_6455] :
      ( ( hd(U_6455) = '#skF_46'(U_6455) )
      | ( nil = U_6455 )
      | ~ ssList(U_6455) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_339544,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_402,c_339454]) ).

tff(c_339579,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_339381,c_339544]) ).

tff(c_466333,plain,
    ! [V_8318,U_8319] :
      ( ( hd(cons(V_8318,U_8319)) = V_8318 )
      | ~ ssItem(V_8318)
      | ~ ssList(U_8319) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_466345,plain,
    ( ( hd('#skF_50') = '#skF_56' )
    | ~ ssItem('#skF_56')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_338784,c_466333]) ).

tff(c_466349,plain,
    '#skF_46'('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_5272,c_339579,c_466345]) ).

tff(c_466351,plain,
    hd('#skF_50') = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_466349,c_339579]) ).

tff(c_472623,plain,
    ! [U_8497,V_8498] :
      ( ( hd(app(U_8497,V_8498)) = hd(U_8497) )
      | ( nil = U_8497 )
      | ~ ssList(V_8498)
      | ~ ssList(U_8497) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_472803,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = hd('#skF_50') )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_472623]) ).

tff(c_472996,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_56' )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_466351,c_472803]) ).

tff(c_473065,plain,
    ~ ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitLeft,[status(thm)],[c_472996]) ).

tff(c_473068,plain,
    ( ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_473065]) ).

tff(c_473071,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_473068]) ).

tff(c_473074,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_473071]) ).

tff(c_473078,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_394,c_473074]) ).

tff(c_473080,plain,
    ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitRight,[status(thm)],[c_472996]) ).

tff(c_475625,plain,
    ! [W_8519,U_8520,V_8521] :
      ( ~ memberP(W_8519,U_8520)
      | memberP(app(V_8521,W_8519),U_8520)
      | ~ ssList(W_8519)
      | ~ ssList(V_8521)
      | ~ ssItem(U_8520) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_475784,plain,
    ! [U_8520] :
      ( ~ memberP('#skF_54',U_8520)
      | memberP('#skF_50',U_8520)
      | ~ ssList('#skF_54')
      | ~ ssList(app('#skF_53',cons('#skF_52',nil)))
      | ~ ssItem(U_8520) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_475625]) ).

tff(c_475942,plain,
    ! [U_8522] :
      ( ~ memberP('#skF_54',U_8522)
      | memberP('#skF_50',U_8522)
      | ~ ssItem(U_8522) ),
    inference(demodulation,[status(thm),theory(equality)],[c_473080,c_390,c_475784]) ).

tff(c_475948,plain,
    ( memberP('#skF_50','#skF_55')
    | ~ ssItem('#skF_55') ),
    inference(resolution,[status(thm)],[c_338709,c_475942]) ).

tff(c_475954,plain,
    memberP('#skF_50','#skF_55'),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_475948]) ).

tff(c_485844,plain,
    ! [U_8667] :
      ( ( U_8667 = '#skF_56' )
      | ~ memberP('#skF_50',U_8667)
      | ~ ssItem(U_8667) ),
    inference(resolution,[status(thm)],[c_485839,c_228]) ).

tff(c_485850,plain,
    ( ( '#skF_55' = '#skF_56' )
    | ~ ssItem('#skF_55') ),
    inference(resolution,[status(thm)],[c_475954,c_485844]) ).

tff(c_485859,plain,
    '#skF_55' = '#skF_56',
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_485850]) ).

tff(c_338710,plain,
    lt('#skF_55','#skF_52'),
    inference(splitRight,[status(thm)],[c_418]) ).

tff(c_485891,plain,
    lt('#skF_56','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_485859,c_338710]) ).

tff(c_498149,plain,
    lt('#skF_56','#skF_56'),
    inference(demodulation,[status(thm),theory(equality)],[c_498096,c_485891]) ).

tff(c_208,plain,
    ! [V_923,U_921] :
      ( ~ lt(V_923,U_921)
      | ~ lt(U_921,V_923)
      | ~ ssItem(V_923)
      | ~ ssItem(U_921) ),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_498210,plain,
    ( ~ lt('#skF_56','#skF_56')
    | ~ ssItem('#skF_56') ),
    inference(resolution,[status(thm)],[c_498149,c_208]) ).

tff(c_498232,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5272,c_498149,c_498210]) ).

tff(c_498233,plain,
    nil = '#skF_50',
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_502326,plain,
    ! [U_9012] :
      ( ( tl(U_9012) = '#skF_47'(U_9012) )
      | ( U_9012 = '#skF_50' )
      | ~ ssList(U_9012) ),
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_334]) ).

tff(c_502428,plain,
    ( ( tl('#skF_53') = '#skF_47'('#skF_53') )
    | ( '#skF_53' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_392,c_502326]) ).

tff(c_502432,plain,
    '#skF_53' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_502428]) ).

tff(c_498921,plain,
    ! [U_8857] :
      ( ( tl(U_8857) = '#skF_47'(U_8857) )
      | ( U_8857 = '#skF_50' )
      | ~ ssList(U_8857) ),
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_334]) ).

tff(c_499032,plain,
    ( ( tl('#skF_54') = '#skF_47'('#skF_54') )
    | ( '#skF_54' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_390,c_498921]) ).

tff(c_500303,plain,
    '#skF_54' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_499032]) ).

tff(c_498282,plain,
    memberP('#skF_54','#skF_55'),
    inference(splitLeft,[status(thm)],[c_420]) ).

tff(c_500309,plain,
    memberP('#skF_50','#skF_55'),
    inference(demodulation,[status(thm),theory(equality)],[c_500303,c_498282]) ).

tff(c_498272,plain,
    ! [U_948] :
      ( ~ memberP('#skF_50',U_948)
      | ~ ssItem(U_948) ),
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_228]) ).

tff(c_500321,plain,
    ~ ssItem('#skF_55'),
    inference(resolution,[status(thm)],[c_500309,c_498272]) ).

tff(c_500325,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_500321]) ).

tff(c_500327,plain,
    '#skF_54' != '#skF_50',
    inference(splitRight,[status(thm)],[c_499032]) ).

tff(c_498397,plain,
    app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_425]) ).

tff(c_501907,plain,
    ! [V_8958,U_8959] :
      ( ( V_8958 = '#skF_50' )
      | ( app(U_8959,V_8958) != '#skF_50' )
      | ~ ssList(V_8958)
      | ~ ssList(U_8959) ),
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_498233,c_354]) ).

tff(c_501917,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_498397,c_501907]) ).

tff(c_501940,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_501917]) ).

tff(c_501941,plain,
    ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
    inference(negUnitSimplification,[status(thm)],[c_500327,c_501940]) ).

tff(c_501958,plain,
    ( ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_501941]) ).

tff(c_501961,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_501958]) ).

tff(c_501964,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_501961]) ).

tff(c_501968,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_394,c_501964]) ).

tff(c_501969,plain,
    memberP('#skF_53','#skF_55'),
    inference(splitRight,[status(thm)],[c_420]) ).

tff(c_502436,plain,
    memberP('#skF_50','#skF_55'),
    inference(demodulation,[status(thm),theory(equality)],[c_502432,c_501969]) ).

tff(c_502449,plain,
    ~ ssItem('#skF_55'),
    inference(resolution,[status(thm)],[c_502436,c_498272]) ).

tff(c_502453,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_502449]) ).

tff(c_502455,plain,
    '#skF_53' != '#skF_50',
    inference(splitRight,[status(thm)],[c_502428]) ).

tff(c_502429,plain,
    ( ( tl('#skF_54') = '#skF_47'('#skF_54') )
    | ( '#skF_54' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_390,c_502326]) ).

tff(c_502466,plain,
    '#skF_54' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_502429]) ).

tff(c_502111,plain,
    app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_425]) ).

tff(c_502467,plain,
    app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_502466,c_502111]) ).

tff(c_352,plain,
    ! [U_1077,V_1079] :
      ( ( nil = U_1077 )
      | ( app(U_1077,V_1079) != nil )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(cnfTransformation,[status(thm)],[f_855]) ).

tff(c_503836,plain,
    ! [U_9085,V_9086] :
      ( ( U_9085 = '#skF_50' )
      | ( app(U_9085,V_9086) != '#skF_50' )
      | ~ ssList(V_9086)
      | ~ ssList(U_9085) ),
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_498233,c_352]) ).

tff(c_503838,plain,
    ( ( app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50' )
    | ~ ssList('#skF_50')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_502467,c_503836]) ).

tff(c_503851,plain,
    ( ( app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50' )
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_503838]) ).

tff(c_503914,plain,
    ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
    inference(splitLeft,[status(thm)],[c_503851]) ).

tff(c_503917,plain,
    ( ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_503914]) ).

tff(c_503920,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_503917]) ).

tff(c_503923,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_503920]) ).

tff(c_503927,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_394,c_503923]) ).

tff(c_503928,plain,
    app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50',
    inference(splitRight,[status(thm)],[c_503851]) ).

tff(c_503835,plain,
    ! [U_1077,V_1079] :
      ( ( U_1077 = '#skF_50' )
      | ( app(U_1077,V_1079) != '#skF_50' )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_498233,c_352]) ).

tff(c_503990,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_503928,c_503835]) ).

tff(c_503998,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_503990]) ).

tff(c_503999,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(negUnitSimplification,[status(thm)],[c_502455,c_503998]) ).

tff(c_504005,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_503999]) ).

tff(c_504009,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_394,c_504005]) ).

tff(c_504011,plain,
    '#skF_54' != '#skF_50',
    inference(splitRight,[status(thm)],[c_502429]) ).

tff(c_505987,plain,
    ! [V_9159,U_9160] :
      ( ( V_9159 = '#skF_50' )
      | ( app(U_9160,V_9159) != '#skF_50' )
      | ~ ssList(V_9159)
      | ~ ssList(U_9160) ),
    inference(demodulation,[status(thm),theory(equality)],[c_498233,c_498233,c_354]) ).

tff(c_506005,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_502111,c_505987]) ).

tff(c_506038,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_506005]) ).

tff(c_506039,plain,
    ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
    inference(negUnitSimplification,[status(thm)],[c_504011,c_506038]) ).

tff(c_506056,plain,
    ( ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_506039]) ).

tff(c_506059,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_506056]) ).

tff(c_506062,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_506059]) ).

tff(c_506066,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_402,c_394,c_506062]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC297+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
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 21:47:46 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 134.53/114.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 134.53/114.60  
% 134.53/114.60  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 134.97/114.68  
% 134.97/114.68  Inference rules
% 134.97/114.68  ----------------------
% 134.97/114.68  #Ref     : 119
% 134.97/114.68  #Sup     : 110594
% 134.97/114.68  #Fact    : 0
% 134.97/114.68  #Define  : 0
% 134.97/114.68  #Split   : 857
% 134.97/114.68  #Chain   : 0
% 134.97/114.68  #Close   : 0
% 134.97/114.68  
% 134.97/114.68  Ordering : KBO
% 134.97/114.68  
% 134.97/114.68  Simplification rules
% 134.97/114.68  ----------------------
% 134.97/114.68  #Subsume      : 13599
% 134.97/114.68  #Demod        : 114313
% 134.97/114.68  #Tautology    : 28071
% 134.97/114.68  #SimpNegUnit  : 11841
% 134.97/114.68  #BackRed      : 3013
% 134.97/114.68  
% 134.97/114.68  #Partial instantiations: 0
% 134.97/114.68  #Strategies tried      : 1
% 134.97/114.68  
% 134.97/114.68  Timing (in seconds)
% 134.97/114.68  ----------------------
% 134.97/114.68  Preprocessing        : 0.89
% 134.97/114.68  Parsing              : 0.41
% 134.97/114.68  CNF conversion       : 0.12
% 134.97/114.68  Main loop            : 112.60
% 134.97/114.68  Inferencing          : 18.62
% 134.97/114.68  Reduction            : 58.96
% 134.97/114.68  Demodulation         : 45.53
% 134.97/114.68  BG Simplification    : 0.66
% 134.97/114.68  Subsumption          : 27.51
% 134.97/114.68  Abstraction          : 1.16
% 134.97/114.68  MUC search           : 0.00
% 134.97/114.68  Cooper               : 0.00
% 134.97/114.68  Total                : 113.66
% 134.97/114.68  Index Insertion      : 0.00
% 134.97/114.68  Index Deletion       : 0.00
% 134.97/114.68  Index Matching       : 0.00
% 134.97/114.68  BG Taut test         : 0.00
%------------------------------------------------------------------------------