TSTP Solution File: SWC183+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC183+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 : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:01:31 EDT 2023

% Result   : Theorem 70.68s 54.57s
% Output   : CNFRefutation 70.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :  112
% Syntax   : Number of formulae    :  607 ( 233 unt;  79 typ;   0 def)
%            Number of atoms       : 1196 ( 434 equ)
%            Maximal formula atoms :   21 (   2 avg)
%            Number of connectives : 1234 ( 566   ~; 561   |;  22   &)
%                                         (   9 <=>;  76  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   3 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    :   60 (  60 usr;  11 con; 0-2 aty)
%            Number of variables   :  252 (; 242   !;  10   ?;   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_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(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_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(f_1040,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 )
                                | ( ~ memberP(Z,Y)
                                  & ~ memberP(X1,Y) ) ) ) )
                    | ( ! [X2] :
                          ( ~ ssItem(X2)
                          | ( cons(X2,nil) != W )
                          | ~ memberP(X,X2)
                          | ? [X3] :
                              ( ssItem(X3)
                              & ( X2 != X3 )
                              & memberP(X,X3)
                              & leq(X2,X3) ) )
                      & ( ( nil != X )
                        | ( nil != W ) ) ) ) ) ) ),
    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_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_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_517,axiom,
    ! [U] :
      ( ssItem(U)
     => ~ memberP(nil,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).

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

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_399,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).

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_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_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_663,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( segmentP(U,V)
              & segmentP(V,U) )
           => ( U = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).

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_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_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_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_120,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( rearsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ( app(W,V) = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).

tff(f_796,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( ( nil != V )
              & ( nil != U )
              & ( hd(V) = hd(U) )
              & ( tl(V) = tl(U) ) )
           => ( V = U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax77) ).

tff(f_371,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssItem(hd(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).

tff(f_612,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( rearsegP(U,V)
              & rearsegP(V,U) )
           => ( U = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax48) ).

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

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_696,axiom,
    ! [U] :
      ( ssItem(U)
     => cyclefreeP(cons(U,nil)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax59) ).

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

tff(c_392,plain,
    ssItem('#skF_52'),
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

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_390,plain,
    ssList('#skF_53'),
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

tff(c_69571,plain,
    ! [U_2773] :
      ( ( tl(U_2773) = '#skF_47'(U_2773) )
      | ( nil = U_2773 )
      | ~ ssList(U_2773) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_69683,plain,
    ( ( tl('#skF_53') = '#skF_47'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_390,c_69571]) ).

tff(c_70631,plain,
    nil = '#skF_53',
    inference(splitLeft,[status(thm)],[c_69683]) ).

tff(c_400,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

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_384,plain,
    ( memberP('#skF_54','#skF_52')
    | memberP('#skF_53','#skF_52') ),
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

tff(c_7197,plain,
    memberP('#skF_53','#skF_52'),
    inference(splitLeft,[status(thm)],[c_384]) ).

tff(c_7744,plain,
    ! [U_1723] :
      ( ( tl(U_1723) = '#skF_47'(U_1723) )
      | ( nil = U_1723 )
      | ~ ssList(U_1723) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_7856,plain,
    ( ( tl('#skF_53') = '#skF_47'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_390,c_7744]) ).

tff(c_7890,plain,
    nil = '#skF_53',
    inference(splitLeft,[status(thm)],[c_7856]) ).

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

tff(c_8138,plain,
    ! [U_1730] :
      ( ~ memberP('#skF_53',U_1730)
      | ~ ssItem(U_1730) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7890,c_228]) ).

tff(c_8141,plain,
    ~ ssItem('#skF_52'),
    inference(resolution,[status(thm)],[c_7197,c_8138]) ).

tff(c_8145,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_8141]) ).

tff(c_8147,plain,
    nil != '#skF_53',
    inference(splitRight,[status(thm)],[c_7856]) ).

tff(c_7278,plain,
    ! [U_1673] :
      ( ( app(nil,U_1673) = U_1673 )
      | ~ ssList(U_1673) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_7297,plain,
    app(nil,'#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_400,c_7278]) ).

tff(c_41989,plain,
    ! [W_2427,U_2428,V_2429] :
      ( ( W_2427 = U_2428 )
      | ( app(W_2427,V_2429) != app(U_2428,V_2429) )
      | ~ ssList(W_2427)
      | ~ ssList(V_2429)
      | ~ ssList(U_2428) ),
    inference(cnfTransformation,[status(thm)],[f_815]) ).

tff(c_42225,plain,
    ! [W_2427] :
      ( ( nil = W_2427 )
      | ( app(W_2427,'#skF_50') != '#skF_50' )
      | ~ ssList(W_2427)
      | ~ ssList('#skF_50')
      | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_7297,c_41989]) ).

tff(c_51771,plain,
    ! [W_2548] :
      ( ( nil = W_2548 )
      | ( app(W_2548,'#skF_50') != '#skF_50' )
      | ~ ssList(W_2548) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_400,c_42225]) ).

tff(c_51909,plain,
    ( ( nil = '#skF_53' )
    | ( app('#skF_53','#skF_50') != '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_390,c_51771]) ).

tff(c_51991,plain,
    app('#skF_53','#skF_50') != '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_8147,c_51909]) ).

tff(c_388,plain,
    ssList('#skF_54'),
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

tff(c_412,plain,
    ( ssItem('#skF_55')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

tff(c_434,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_412]) ).

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_4446,plain,
    ! [U_1539] :
      ( ( tl(U_1539) = '#skF_47'(U_1539) )
      | ( U_1539 = '#skF_50' )
      | ~ ssList(U_1539) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_334]) ).

tff(c_4555,plain,
    ( ( tl('#skF_54') = '#skF_47'('#skF_54') )
    | ( '#skF_54' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_388,c_4446]) ).

tff(c_6033,plain,
    '#skF_54' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_4555]) ).

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_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_839,plain,
    ! [U_1354] :
      ( ( hd(U_1354) = '#skF_46'(U_1354) )
      | ( U_1354 = '#skF_50' )
      | ~ ssList(U_1354) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_330]) ).

tff(c_941,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( '#skF_53' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_390,c_839]) ).

tff(c_945,plain,
    '#skF_53' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_941]) ).

tff(c_488,plain,
    memberP('#skF_53','#skF_52'),
    inference(splitLeft,[status(thm)],[c_384]) ).

tff(c_949,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_945,c_488]) ).

tff(c_467,plain,
    ! [U_948] :
      ( ~ memberP('#skF_50',U_948)
      | ~ ssItem(U_948) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_228]) ).

tff(c_960,plain,
    ~ ssItem('#skF_52'),
    inference(resolution,[status(thm)],[c_949,c_467]) ).

tff(c_964,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_960]) ).

tff(c_966,plain,
    '#skF_53' != '#skF_50',
    inference(splitRight,[status(thm)],[c_941]) ).

tff(c_944,plain,
    ( ( hd('#skF_54') = '#skF_46'('#skF_54') )
    | ( '#skF_54' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_388,c_839]) ).

tff(c_978,plain,
    '#skF_54' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_944]) ).

tff(c_394,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

tff(c_386,plain,
    app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') = '#skF_48',
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

tff(c_425,plain,
    app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_386]) ).

tff(c_625,plain,
    app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_425]) ).

tff(c_979,plain,
    app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_978,c_625]) ).

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_2320,plain,
    ! [U_1419,V_1420] :
      ( ( U_1419 = '#skF_50' )
      | ( app(U_1419,V_1420) != '#skF_50' )
      | ~ ssList(V_1420)
      | ~ ssList(U_1419) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_434,c_352]) ).

tff(c_2322,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_979,c_2320]) ).

tff(c_2331,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_400,c_2322]) ).

tff(c_2363,plain,
    ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
    inference(splitLeft,[status(thm)],[c_2331]) ).

tff(c_2366,plain,
    ( ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_2363]) ).

tff(c_2369,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_2366]) ).

tff(c_2372,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_2369]) ).

tff(c_2376,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_2372]) ).

tff(c_2377,plain,
    app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50',
    inference(splitRight,[status(thm)],[c_2331]) ).

tff(c_2319,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_434,c_434,c_352]) ).

tff(c_2426,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_2377,c_2319]) ).

tff(c_2436,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_2426]) ).

tff(c_2437,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(negUnitSimplification,[status(thm)],[c_966,c_2436]) ).

tff(c_2446,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_2437]) ).

tff(c_2450,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_2446]) ).

tff(c_2452,plain,
    '#skF_54' != '#skF_50',
    inference(splitRight,[status(thm)],[c_944]) ).

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_3899,plain,
    ! [V_1484,U_1485] :
      ( ( V_1484 = '#skF_50' )
      | ( app(U_1485,V_1484) != '#skF_50' )
      | ~ ssList(V_1484)
      | ~ ssList(U_1485) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_434,c_354]) ).

tff(c_3901,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_625,c_3899]) ).

tff(c_3914,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_3901]) ).

tff(c_3915,plain,
    ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
    inference(negUnitSimplification,[status(thm)],[c_2452,c_3914]) ).

tff(c_3932,plain,
    ( ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_3915]) ).

tff(c_3935,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_3932]) ).

tff(c_3938,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_3935]) ).

tff(c_3942,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_3938]) ).

tff(c_3943,plain,
    memberP('#skF_54','#skF_52'),
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_6039,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_6033,c_3943]) ).

tff(c_6051,plain,
    ~ ssItem('#skF_52'),
    inference(resolution,[status(thm)],[c_6039,c_467]) ).

tff(c_6055,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_6051]) ).

tff(c_6057,plain,
    '#skF_54' != '#skF_50',
    inference(splitRight,[status(thm)],[c_4555]) ).

tff(c_4054,plain,
    app(app('#skF_53',cons('#skF_52','#skF_50')),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_425]) ).

tff(c_6878,plain,
    ! [U_1646,V_1647] :
      ( ( U_1646 = '#skF_50' )
      | ( app(U_1646,V_1647) != '#skF_50' )
      | ~ ssList(V_1647)
      | ~ ssList(U_1646) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_434,c_352]) ).

tff(c_6884,plain,
    ( ( app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_4054,c_6878]) ).

tff(c_6902,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_388,c_6884]) ).

tff(c_7097,plain,
    ~ ssList(app('#skF_53',cons('#skF_52','#skF_50'))),
    inference(splitLeft,[status(thm)],[c_6902]) ).

tff(c_7100,plain,
    ( ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_7097]) ).

tff(c_7103,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_7100]) ).

tff(c_7106,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_7103]) ).

tff(c_7110,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_7106]) ).

tff(c_7111,plain,
    app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50',
    inference(splitRight,[status(thm)],[c_6902]) ).

tff(c_7154,plain,
    app('#skF_50','#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_7111,c_4054]) ).

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

tff(c_3948,plain,
    ! [U_1487] :
      ( ( app('#skF_50',U_1487) = U_1487 )
      | ~ ssList(U_1487) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_196]) ).

tff(c_3960,plain,
    app('#skF_50','#skF_54') = '#skF_54',
    inference(resolution,[status(thm)],[c_388,c_3948]) ).

tff(c_7171,plain,
    '#skF_54' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_7154,c_3960]) ).

tff(c_7173,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6057,c_7171]) ).

tff(c_7175,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_412]) ).

tff(c_410,plain,
    ( ( cons('#skF_55',nil) = '#skF_50' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1040]) ).

tff(c_7188,plain,
    cons('#skF_55',nil) = '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_7175,c_410]) ).

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_58562,plain,
    ! [W_2625,V_2626,X_2627] :
      ( segmentP(app(app(W_2625,V_2626),X_2627),V_2626)
      | ~ ssList(X_2627)
      | ~ ssList(W_2625)
      | ~ ssList(V_2626)
      | ~ ssList(app(app(W_2625,V_2626),X_2627)) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_58789,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_58562]) ).

tff(c_58932,plain,
    ( segmentP('#skF_50',cons('#skF_52',nil))
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_425,c_390,c_388,c_58789]) ).

tff(c_58962,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_58932]) ).

tff(c_58965,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_58962]) ).

tff(c_58969,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_58965]) ).

tff(c_58971,plain,
    ssList(cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_58932]) ).

tff(c_52489,plain,
    ! [U_2557,V_2558,W_2559] :
      ( ( app(app(U_2557,V_2558),W_2559) = app(U_2557,app(V_2558,W_2559)) )
      | ~ ssList(W_2559)
      | ~ ssList(V_2558)
      | ~ ssList(U_2557) ),
    inference(cnfTransformation,[status(thm)],[f_844]) ).

tff(c_52761,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_52489]) ).

tff(c_52926,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_390,c_388,c_52761]) ).

tff(c_67396,plain,
    app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_58971,c_52926]) ).

tff(c_67458,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_67396]) ).

tff(c_67506,plain,
    app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_67458]) ).

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_67534,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_67506,c_12]) ).

tff(c_67601,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_67506,c_392,c_390,c_388,c_67534]) ).

tff(c_7174,plain,
    ssItem('#skF_55'),
    inference(splitRight,[status(thm)],[c_412]) ).

tff(c_53967,plain,
    ! [W_2570,U_2571,V_2572] :
      ( memberP(W_2570,U_2571)
      | ( V_2572 = U_2571 )
      | ~ memberP(cons(V_2572,W_2570),U_2571)
      | ~ ssList(W_2570)
      | ~ ssItem(V_2572)
      | ~ ssItem(U_2571) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_54024,plain,
    ! [U_2571] :
      ( memberP(nil,U_2571)
      | ( U_2571 = '#skF_55' )
      | ~ memberP('#skF_50',U_2571)
      | ~ ssList(nil)
      | ~ ssItem('#skF_55')
      | ~ ssItem(U_2571) ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_53967]) ).

tff(c_59309,plain,
    ! [U_2629] :
      ( memberP(nil,U_2629)
      | ( U_2629 = '#skF_55' )
      | ~ memberP('#skF_50',U_2629)
      | ~ ssItem(U_2629) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7174,c_168,c_54024]) ).

tff(c_59313,plain,
    ! [U_2629] :
      ( ( U_2629 = '#skF_55' )
      | ~ memberP('#skF_50',U_2629)
      | ~ ssItem(U_2629) ),
    inference(resolution,[status(thm)],[c_59309,c_228]) ).

tff(c_67644,plain,
    ( ( '#skF_52' = '#skF_55' )
    | ~ ssItem('#skF_52') ),
    inference(resolution,[status(thm)],[c_67601,c_59313]) ).

tff(c_67647,plain,
    '#skF_52' = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_67644]) ).

tff(c_58970,plain,
    segmentP('#skF_50',cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_58932]) ).

tff(c_67670,plain,
    segmentP('#skF_50',cons('#skF_55',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_67647,c_58970]) ).

tff(c_67699,plain,
    segmentP('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_7188,c_67670]) ).

tff(c_268,plain,
    ! [V_1013,U_1011] :
      ( ( V_1013 = U_1011 )
      | ~ segmentP(V_1013,U_1011)
      | ~ segmentP(U_1011,V_1013)
      | ~ ssList(V_1013)
      | ~ ssList(U_1011) ),
    inference(cnfTransformation,[status(thm)],[f_663]) ).

tff(c_59099,plain,
    ( ( cons('#skF_52',nil) = '#skF_50' )
    | ~ segmentP(cons('#skF_52',nil),'#skF_50')
    | ~ ssList('#skF_50')
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(resolution,[status(thm)],[c_58970,c_268]) ).

tff(c_59105,plain,
    ( ( cons('#skF_52',nil) = '#skF_50' )
    | ~ segmentP(cons('#skF_52',nil),'#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_58971,c_400,c_59099]) ).

tff(c_64178,plain,
    ~ segmentP(cons('#skF_52',nil),'#skF_50'),
    inference(splitLeft,[status(thm)],[c_59105]) ).

tff(c_67657,plain,
    ~ segmentP(cons('#skF_55',nil),'#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_67647,c_64178]) ).

tff(c_67686,plain,
    ~ segmentP('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_7188,c_67657]) ).

tff(c_67721,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_67699,c_67686]) ).

tff(c_67722,plain,
    cons('#skF_52',nil) = '#skF_50',
    inference(splitRight,[status(thm)],[c_59105]) ).

tff(c_8444,plain,
    ! [U_1738] :
      ( ( hd(U_1738) = '#skF_46'(U_1738) )
      | ( nil = U_1738 )
      | ~ ssList(U_1738) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_8534,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_400,c_8444]) ).

tff(c_8575,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_7175,c_8534]) ).

tff(c_33076,plain,
    ! [V_2243,U_2244] :
      ( ( hd(cons(V_2243,U_2244)) = V_2243 )
      | ~ ssItem(V_2243)
      | ~ ssList(U_2244) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_33088,plain,
    ( ( hd('#skF_50') = '#skF_55' )
    | ~ ssItem('#skF_55')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_33076]) ).

tff(c_33092,plain,
    '#skF_46'('#skF_50') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_7174,c_8575,c_33088]) ).

tff(c_33094,plain,
    hd('#skF_50') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_33092,c_8575]) ).

tff(c_38398,plain,
    ! [U_2395,V_2396] :
      ( ( hd(app(U_2395,V_2396)) = hd(U_2395) )
      | ( nil = U_2395 )
      | ~ ssList(V_2396)
      | ~ ssList(U_2395) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_38575,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_38398]) ).

tff(c_38765,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_33094,c_38575]) ).

tff(c_39453,plain,
    ~ ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitLeft,[status(thm)],[c_38765]) ).

tff(c_39462,plain,
    ( ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_39453]) ).

tff(c_39465,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_39462]) ).

tff(c_39468,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_39465]) ).

tff(c_39472,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_39468]) ).

tff(c_39474,plain,
    ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitRight,[status(thm)],[c_38765]) ).

tff(c_67739,plain,
    ssList(app('#skF_53','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_67722,c_39474]) ).

tff(c_40146,plain,
    ! [V_2409,W_2410] :
      ( frontsegP(app(V_2409,W_2410),V_2409)
      | ~ ssList(W_2410)
      | ~ ssList(V_2409)
      | ~ ssList(app(V_2409,W_2410)) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_40319,plain,
    ( frontsegP('#skF_50',app('#skF_53',cons('#skF_52',nil)))
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil)))
    | ~ ssList(app(app('#skF_53',cons('#skF_52',nil)),'#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_40146]) ).

tff(c_40455,plain,
    frontsegP('#skF_50',app('#skF_53',cons('#skF_52',nil))),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_425,c_39474,c_388,c_40319]) ).

tff(c_67738,plain,
    frontsegP('#skF_50',app('#skF_53','#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_67722,c_40455]) ).

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_68243,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_67738,c_234]) ).

tff(c_68249,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_50' )
    | ~ frontsegP(app('#skF_53','#skF_50'),'#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_67739,c_400,c_68243]) ).

tff(c_68250,plain,
    ~ frontsegP(app('#skF_53','#skF_50'),'#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_51991,c_68249]) ).

tff(c_68254,plain,
    ( ~ frontsegP('#skF_53','#skF_50')
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_238,c_68250]) ).

tff(c_68257,plain,
    ~ frontsegP('#skF_53','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_400,c_68254]) ).

tff(c_8146,plain,
    tl('#skF_53') = '#skF_47'('#skF_53'),
    inference(splitRight,[status(thm)],[c_7856]) ).

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

tff(c_8151,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_8146,c_188]) ).

tff(c_8155,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_8151]) ).

tff(c_8156,plain,
    ssList('#skF_47'('#skF_53')),
    inference(negUnitSimplification,[status(thm)],[c_8147,c_8155]) ).

tff(c_8416,plain,
    app(nil,'#skF_47'('#skF_53')) = '#skF_47'('#skF_53'),
    inference(resolution,[status(thm)],[c_8156,c_196]) ).

tff(c_40310,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_8416,c_40146]) ).

tff(c_40449,plain,
    frontsegP('#skF_47'('#skF_53'),nil),
    inference(demodulation,[status(thm),theory(equality)],[c_8156,c_8416,c_168,c_8156,c_40310]) ).

tff(c_38066,plain,
    ! [V_2392,U_2393] :
      ( ( app(cons(V_2392,nil),U_2393) = cons(V_2392,U_2393) )
      | ~ ssItem(V_2392)
      | ~ ssList(U_2393) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_38085,plain,
    ! [U_2393] :
      ( ( cons('#skF_55',U_2393) = app('#skF_50',U_2393) )
      | ~ ssItem('#skF_55')
      | ~ ssList(U_2393) ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_38066]) ).

tff(c_38096,plain,
    ! [U_2394] :
      ( ( cons('#skF_55',U_2394) = app('#skF_50',U_2394) )
      | ~ ssList(U_2394) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7174,c_38085]) ).

tff(c_38268,plain,
    cons('#skF_55','#skF_54') = app('#skF_50','#skF_54'),
    inference(resolution,[status(thm)],[c_388,c_38096]) ).

tff(c_39032,plain,
    ( ssList(app('#skF_50','#skF_54'))
    | ~ ssItem('#skF_55')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_38268,c_166]) ).

tff(c_39049,plain,
    ssList(app('#skF_50','#skF_54')),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_7174,c_39032]) ).

tff(c_8528,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_390,c_8444]) ).

tff(c_8570,plain,
    hd('#skF_53') = '#skF_46'('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_8147,c_8528]) ).

tff(c_67740,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_67722,c_425]) ).

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_68382,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_67740,c_348]) ).

tff(c_68439,plain,
    app('#skF_53',app('#skF_50','#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_400,c_388,c_68382]) ).

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_68527,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_68439,c_358]) ).

tff(c_68568,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_55' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_39049,c_8570,c_33094,c_68527]) ).

tff(c_68569,plain,
    '#skF_46'('#skF_53') = '#skF_55',
    inference(negUnitSimplification,[status(thm)],[c_8147,c_68568]) ).

tff(c_35599,plain,
    ! [U_2322] :
      ( ( cons(hd(U_2322),tl(U_2322)) = U_2322 )
      | ( nil = U_2322 )
      | ~ ssList(U_2322) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_35669,plain,
    ( ( cons(hd('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_8146,c_35599]) ).

tff(c_35714,plain,
    ( ( cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_8570,c_35669]) ).

tff(c_35715,plain,
    cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53',
    inference(negUnitSimplification,[status(thm)],[c_8147,c_35714]) ).

tff(c_68591,plain,
    cons('#skF_55','#skF_47'('#skF_53')) = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_68569,c_35715]) ).

tff(c_54214,plain,
    ! [V_2576,W_2577,X_2578] :
      ( frontsegP(cons(V_2576,W_2577),cons(V_2576,X_2578))
      | ~ frontsegP(W_2577,X_2578)
      | ~ ssList(X_2578)
      | ~ ssList(W_2577)
      | ~ ssItem(V_2576) ),
    inference(cnfTransformation,[status(thm)],[f_577]) ).

tff(c_54320,plain,
    ! [W_2577] :
      ( frontsegP(cons('#skF_55',W_2577),'#skF_50')
      | ~ frontsegP(W_2577,nil)
      | ~ ssList(nil)
      | ~ ssList(W_2577)
      | ~ ssItem('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_54214]) ).

tff(c_54378,plain,
    ! [W_2577] :
      ( frontsegP(cons('#skF_55',W_2577),'#skF_50')
      | ~ frontsegP(W_2577,nil)
      | ~ ssList(W_2577) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7174,c_168,c_54320]) ).

tff(c_68757,plain,
    ( frontsegP('#skF_53','#skF_50')
    | ~ frontsegP('#skF_47'('#skF_53'),nil)
    | ~ ssList('#skF_47'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_68591,c_54378]) ).

tff(c_68851,plain,
    frontsegP('#skF_53','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_8156,c_40449,c_68757]) ).

tff(c_68853,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_68257,c_68851]) ).

tff(c_68854,plain,
    memberP('#skF_54','#skF_52'),
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_69689,plain,
    ( ( tl('#skF_54') = '#skF_47'('#skF_54') )
    | ( nil = '#skF_54' ) ),
    inference(resolution,[status(thm)],[c_388,c_69571]) ).

tff(c_70273,plain,
    nil = '#skF_54',
    inference(splitLeft,[status(thm)],[c_69689]) ).

tff(c_70591,plain,
    ! [U_2800] :
      ( ~ memberP('#skF_54',U_2800)
      | ~ ssItem(U_2800) ),
    inference(demodulation,[status(thm),theory(equality)],[c_70273,c_228]) ).

tff(c_70594,plain,
    ~ ssItem('#skF_52'),
    inference(resolution,[status(thm)],[c_68854,c_70591]) ).

tff(c_70598,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_70594]) ).

tff(c_70600,plain,
    nil != '#skF_54',
    inference(splitRight,[status(thm)],[c_69689]) ).

tff(c_70769,plain,
    '#skF_54' != '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_70631,c_70600]) ).

tff(c_69652,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_400,c_69571]) ).

tff(c_69688,plain,
    tl('#skF_50') = '#skF_47'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_7175,c_69652]) ).

tff(c_70801,plain,
    cons('#skF_55','#skF_53') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_70631,c_7188]) ).

tff(c_70924,plain,
    ! [V_2805,U_2806] :
      ( ( tl(cons(V_2805,U_2806)) = U_2806 )
      | ~ ssItem(V_2805)
      | ~ ssList(U_2806) ),
    inference(cnfTransformation,[status(thm)],[f_392]) ).

tff(c_70933,plain,
    ( ( tl('#skF_50') = '#skF_53' )
    | ~ ssItem('#skF_55')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_70801,c_70924]) ).

tff(c_70937,plain,
    '#skF_47'('#skF_50') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_7174,c_69688,c_70933]) ).

tff(c_70939,plain,
    tl('#skF_50') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_70937,c_69688]) ).

tff(c_70782,plain,
    app(app('#skF_53',cons('#skF_52','#skF_53')),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_70631,c_425]) ).

tff(c_160527,plain,
    ! [W_4011,V_4012,X_4013] :
      ( segmentP(app(app(W_4011,V_4012),X_4013),V_4012)
      | ~ ssList(X_4013)
      | ~ ssList(W_4011)
      | ~ ssList(V_4012)
      | ~ ssList(app(app(W_4011,V_4012),X_4013)) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_160784,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_70782,c_160527]) ).

tff(c_160949,plain,
    ( segmentP('#skF_50',cons('#skF_52','#skF_53'))
    | ~ ssList(cons('#skF_52','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_70782,c_390,c_388,c_160784]) ).

tff(c_161246,plain,
    ~ ssList(cons('#skF_52','#skF_53')),
    inference(splitLeft,[status(thm)],[c_160949]) ).

tff(c_161249,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_161246]) ).

tff(c_161253,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_392,c_161249]) ).

tff(c_161255,plain,
    ssList(cons('#skF_52','#skF_53')),
    inference(splitRight,[status(thm)],[c_160949]) ).

tff(c_70789,plain,
    ! [U_906] :
      ( ( app('#skF_53',U_906) = U_906 )
      | ~ ssList(U_906) ),
    inference(demodulation,[status(thm),theory(equality)],[c_70631,c_196]) ).

tff(c_161357,plain,
    app('#skF_53',cons('#skF_52','#skF_53')) = cons('#skF_52','#skF_53'),
    inference(resolution,[status(thm)],[c_161255,c_70789]) ).

tff(c_161378,plain,
    app(cons('#skF_52','#skF_53'),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_161357,c_70782]) ).

tff(c_139955,plain,
    ! [V_1069,U_1067] :
      ( ( app(cons(V_1069,'#skF_53'),U_1067) = cons(V_1069,U_1067) )
      | ~ ssItem(V_1069)
      | ~ ssList(U_1067) ),
    inference(demodulation,[status(thm),theory(equality)],[c_70631,c_346]) ).

tff(c_161627,plain,
    ( ( cons('#skF_52','#skF_54') = '#skF_50' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_161378,c_139955]) ).

tff(c_161674,plain,
    cons('#skF_52','#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_161627]) ).

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_161743,plain,
    ( ( tl('#skF_50') = '#skF_54' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_161674,c_190]) ).

tff(c_161795,plain,
    '#skF_54' = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_70939,c_161743]) ).

tff(c_161797,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_70769,c_161795]) ).

tff(c_161799,plain,
    nil != '#skF_53',
    inference(splitRight,[status(thm)],[c_69683]) ).

tff(c_161929,plain,
    ! [U_4024] :
      ( ( hd(U_4024) = '#skF_46'(U_4024) )
      | ( nil = U_4024 )
      | ~ ssList(U_4024) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_162019,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_390,c_161929]) ).

tff(c_162063,plain,
    hd('#skF_53') = '#skF_46'('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_161799,c_162019]) ).

tff(c_162025,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_400,c_161929]) ).

tff(c_162068,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_7175,c_162025]) ).

tff(c_162116,plain,
    ! [V_4026,U_4027] :
      ( ( hd(cons(V_4026,U_4027)) = V_4026 )
      | ~ ssItem(V_4026)
      | ~ ssList(U_4027) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_162128,plain,
    ( ( hd('#skF_50') = '#skF_55' )
    | ~ ssItem('#skF_55')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_162116]) ).

tff(c_162132,plain,
    '#skF_46'('#skF_50') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_7174,c_162068,c_162128]) ).

tff(c_162134,plain,
    hd('#skF_50') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_162132,c_162068]) ).

tff(c_253946,plain,
    ! [U_5410,V_5411] :
      ( ( hd(app(U_5410,V_5411)) = hd(U_5410) )
      | ( nil = U_5410 )
      | ~ ssList(V_5411)
      | ~ ssList(U_5410) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_254117,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_253946]) ).

tff(c_254304,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_162134,c_254117]) ).

tff(c_254335,plain,
    ~ ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitLeft,[status(thm)],[c_254304]) ).

tff(c_254338,plain,
    ( ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_254335]) ).

tff(c_254341,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_254338]) ).

tff(c_254344,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_254341]) ).

tff(c_254348,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_254344]) ).

tff(c_254349,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' ) ),
    inference(splitRight,[status(thm)],[c_254304]) ).

tff(c_254410,plain,
    hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55',
    inference(splitLeft,[status(thm)],[c_254349]) ).

tff(c_254414,plain,
    ( ( hd('#skF_53') = '#skF_55' )
    | ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_254410,c_358]) ).

tff(c_254427,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_55' )
    | ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_162063,c_254414]) ).

tff(c_254428,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_55' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(negUnitSimplification,[status(thm)],[c_161799,c_254427]) ).

tff(c_254437,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_254428]) ).

tff(c_254440,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_254437]) ).

tff(c_254444,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_254440]) ).

tff(c_254445,plain,
    '#skF_46'('#skF_53') = '#skF_55',
    inference(splitRight,[status(thm)],[c_254428]) ).

tff(c_161798,plain,
    tl('#skF_53') = '#skF_47'('#skF_53'),
    inference(splitRight,[status(thm)],[c_69683]) ).

tff(c_161804,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_161798,c_188]) ).

tff(c_161808,plain,
    ( ssList('#skF_47'('#skF_53'))
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_161804]) ).

tff(c_161809,plain,
    ssList('#skF_47'('#skF_53')),
    inference(negUnitSimplification,[status(thm)],[c_161799,c_161808]) ).

tff(c_162033,plain,
    ( ( hd('#skF_47'('#skF_53')) = '#skF_46'('#skF_47'('#skF_53')) )
    | ( '#skF_47'('#skF_53') = nil ) ),
    inference(resolution,[status(thm)],[c_161809,c_161929]) ).

tff(c_251168,plain,
    '#skF_47'('#skF_53') = nil,
    inference(splitLeft,[status(thm)],[c_162033]) ).

tff(c_251175,plain,
    tl('#skF_53') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_251168,c_161798]) ).

tff(c_340,plain,
    ! [U_1052] :
      ( ( cons(hd(U_1052),tl(U_1052)) = U_1052 )
      | ( nil = U_1052 )
      | ~ ssList(U_1052) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_251192,plain,
    ( ( cons(hd('#skF_53'),nil) = '#skF_53' )
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_251175,c_340]) ).

tff(c_251199,plain,
    ( ( cons('#skF_46'('#skF_53'),nil) = '#skF_53' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_162063,c_251192]) ).

tff(c_251200,plain,
    cons('#skF_46'('#skF_53'),nil) = '#skF_53',
    inference(negUnitSimplification,[status(thm)],[c_161799,c_251199]) ).

tff(c_254447,plain,
    cons('#skF_55',nil) = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_254445,c_251200]) ).

tff(c_254451,plain,
    '#skF_53' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_7188,c_254447]) ).

tff(c_68855,plain,
    ~ memberP('#skF_53','#skF_52'),
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_254481,plain,
    ~ memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_254451,c_68855]) ).

tff(c_254350,plain,
    ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitRight,[status(thm)],[c_254304]) ).

tff(c_254465,plain,
    ssList(app('#skF_50',cons('#skF_52',nil))),
    inference(demodulation,[status(thm),theory(equality)],[c_254451,c_254350]) ).

tff(c_254478,plain,
    app(app('#skF_50',cons('#skF_52',nil)),'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_254451,c_425]) ).

tff(c_263501,plain,
    ! [W_5523,U_5524,V_5525] :
      ( ~ memberP(W_5523,U_5524)
      | memberP(app(V_5525,W_5523),U_5524)
      | ~ ssList(W_5523)
      | ~ ssList(V_5525)
      | ~ ssItem(U_5524) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_263531,plain,
    ! [U_5524] :
      ( ~ memberP('#skF_54',U_5524)
      | memberP('#skF_50',U_5524)
      | ~ ssList('#skF_54')
      | ~ ssList(app('#skF_50',cons('#skF_52',nil)))
      | ~ ssItem(U_5524) ),
    inference(superposition,[status(thm),theory(equality)],[c_254478,c_263501]) ).

tff(c_268902,plain,
    ! [U_5587] :
      ( ~ memberP('#skF_54',U_5587)
      | memberP('#skF_50',U_5587)
      | ~ ssItem(U_5587) ),
    inference(demodulation,[status(thm),theory(equality)],[c_254465,c_388,c_263531]) ).

tff(c_268908,plain,
    ( memberP('#skF_50','#skF_52')
    | ~ ssItem('#skF_52') ),
    inference(resolution,[status(thm)],[c_68854,c_268902]) ).

tff(c_268914,plain,
    memberP('#skF_50','#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_268908]) ).

tff(c_268916,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_254481,c_268914]) ).

tff(c_268917,plain,
    app('#skF_53',cons('#skF_52',nil)) = nil,
    inference(splitRight,[status(thm)],[c_254349]) ).

tff(c_268929,plain,
    ( ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_268917,c_352]) ).

tff(c_268943,plain,
    ( ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_268929]) ).

tff(c_268944,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(negUnitSimplification,[status(thm)],[c_161799,c_268943]) ).

tff(c_269026,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_268944]) ).

tff(c_269030,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_269026]) ).

tff(c_269032,plain,
    '#skF_47'('#skF_53') != nil,
    inference(splitRight,[status(thm)],[c_162033]) ).

tff(c_68936,plain,
    ! [U_2720] :
      ( ( app(nil,U_2720) = U_2720 )
      | ~ ssList(U_2720) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_68952,plain,
    app(nil,'#skF_53') = '#skF_53',
    inference(resolution,[status(thm)],[c_390,c_68936]) ).

tff(c_201421,plain,
    ! [V_4613,W_4614] :
      ( frontsegP(app(V_4613,W_4614),V_4613)
      | ~ ssList(W_4614)
      | ~ ssList(V_4613)
      | ~ ssList(app(V_4613,W_4614)) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_201573,plain,
    ( frontsegP('#skF_53',nil)
    | ~ ssList('#skF_53')
    | ~ ssList(nil)
    | ~ ssList(app(nil,'#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_68952,c_201421]) ).

tff(c_201685,plain,
    frontsegP('#skF_53',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_68952,c_168,c_390,c_201573]) ).

tff(c_201715,plain,
    ( ( nil = '#skF_53' )
    | ~ frontsegP(nil,'#skF_53')
    | ~ ssList('#skF_53')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_201685,c_234]) ).

tff(c_201718,plain,
    ( ( nil = '#skF_53' )
    | ~ frontsegP(nil,'#skF_53') ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_390,c_201715]) ).

tff(c_201719,plain,
    ~ frontsegP(nil,'#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_161799,c_201718]) ).

tff(c_68955,plain,
    app(nil,'#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_400,c_68936]) ).

tff(c_201751,plain,
    ! [W_4615,V_4616] :
      ( rearsegP(app(W_4615,V_4616),V_4616)
      | ~ ssList(W_4615)
      | ~ ssList(V_4616)
      | ~ ssList(app(W_4615,V_4616)) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_201900,plain,
    ( rearsegP('#skF_50','#skF_50')
    | ~ ssList(nil)
    | ~ ssList('#skF_50')
    | ~ ssList(app(nil,'#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_68955,c_201751]) ).

tff(c_202013,plain,
    rearsegP('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_68955,c_400,c_168,c_201900]) ).

tff(c_200161,plain,
    ! [U_4599,V_4600] :
      ( ( hd(app(U_4599,V_4600)) = hd(U_4599) )
      | ( nil = U_4599 )
      | ~ ssList(V_4600)
      | ~ ssList(U_4599) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_200314,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_200161]) ).

tff(c_200480,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_162134,c_200314]) ).

tff(c_200778,plain,
    ~ ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitLeft,[status(thm)],[c_200480]) ).

tff(c_200787,plain,
    ( ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_200778]) ).

tff(c_200790,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_200787]) ).

tff(c_200793,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_200790]) ).

tff(c_200797,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_200793]) ).

tff(c_200799,plain,
    ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitRight,[status(thm)],[c_200480]) ).

tff(c_68956,plain,
    app(nil,'#skF_54') = '#skF_54',
    inference(resolution,[status(thm)],[c_388,c_68936]) ).

tff(c_208803,plain,
    ! [W_4715,U_4716,V_4717] :
      ( ( W_4715 = U_4716 )
      | ( app(W_4715,V_4717) != app(U_4716,V_4717) )
      | ~ ssList(W_4715)
      | ~ ssList(V_4717)
      | ~ ssList(U_4716) ),
    inference(cnfTransformation,[status(thm)],[f_815]) ).

tff(c_208997,plain,
    ! [U_4716] :
      ( ( nil = U_4716 )
      | ( app(U_4716,'#skF_54') != '#skF_54' )
      | ~ ssList(nil)
      | ~ ssList('#skF_54')
      | ~ ssList(U_4716) ),
    inference(superposition,[status(thm),theory(equality)],[c_68956,c_208803]) ).

tff(c_210755,plain,
    ! [U_4736] :
      ( ( nil = U_4736 )
      | ( app(U_4736,'#skF_54') != '#skF_54' )
      | ~ ssList(U_4736) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_168,c_208997]) ).

tff(c_210764,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ( app(app('#skF_53',cons('#skF_52',nil)),'#skF_54') != '#skF_54' ) ),
    inference(resolution,[status(thm)],[c_200799,c_210755]) ).

tff(c_210910,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ( '#skF_54' != '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_425,c_210764]) ).

tff(c_216100,plain,
    '#skF_54' != '#skF_50',
    inference(splitLeft,[status(thm)],[c_210910]) ).

tff(c_162028,plain,
    ( ( hd('#skF_54') = '#skF_46'('#skF_54') )
    | ( nil = '#skF_54' ) ),
    inference(resolution,[status(thm)],[c_388,c_161929]) ).

tff(c_162071,plain,
    hd('#skF_54') = '#skF_46'('#skF_54'),
    inference(negUnitSimplification,[status(thm)],[c_70600,c_162028]) ).

tff(c_70599,plain,
    tl('#skF_54') = '#skF_47'('#skF_54'),
    inference(splitRight,[status(thm)],[c_69689]) ).

tff(c_70604,plain,
    ( ssList('#skF_47'('#skF_54'))
    | ( nil = '#skF_54' )
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_70599,c_188]) ).

tff(c_70608,plain,
    ( ssList('#skF_47'('#skF_54'))
    | ( nil = '#skF_54' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_70604]) ).

tff(c_70609,plain,
    ssList('#skF_47'('#skF_54')),
    inference(negUnitSimplification,[status(thm)],[c_70600,c_70608]) ).

tff(c_70626,plain,
    ( ( tl('#skF_47'('#skF_54')) = '#skF_47'('#skF_47'('#skF_54')) )
    | ( '#skF_47'('#skF_54') = nil ) ),
    inference(resolution,[status(thm)],[c_70609,c_334]) ).

tff(c_197467,plain,
    '#skF_47'('#skF_54') = nil,
    inference(splitLeft,[status(thm)],[c_70626]) ).

tff(c_197476,plain,
    tl('#skF_54') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_197467,c_70599]) ).

tff(c_162169,plain,
    ! [V_4030,U_4031] :
      ( ( tl(cons(V_4030,U_4031)) = U_4031 )
      | ~ ssItem(V_4030)
      | ~ ssList(U_4031) ),
    inference(cnfTransformation,[status(thm)],[f_392]) ).

tff(c_162181,plain,
    ( ( tl('#skF_50') = nil )
    | ~ ssItem('#skF_55')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_162169]) ).

tff(c_162185,plain,
    '#skF_47'('#skF_50') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_7174,c_69688,c_162181]) ).

tff(c_162189,plain,
    tl('#skF_50') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_162185,c_69688]) ).

tff(c_217377,plain,
    ! [V_4818,U_4819] :
      ( ( V_4818 = U_4819 )
      | ( tl(V_4818) != tl(U_4819) )
      | ( hd(V_4818) != hd(U_4819) )
      | ( nil = U_4819 )
      | ( nil = V_4818 )
      | ~ ssList(V_4818)
      | ~ ssList(U_4819) ),
    inference(cnfTransformation,[status(thm)],[f_796]) ).

tff(c_217431,plain,
    ! [U_4819] :
      ( ( U_4819 = '#skF_50' )
      | ( tl(U_4819) != nil )
      | ( hd(U_4819) != hd('#skF_50') )
      | ( nil = U_4819 )
      | ( nil = '#skF_50' )
      | ~ ssList('#skF_50')
      | ~ ssList(U_4819) ),
    inference(superposition,[status(thm),theory(equality)],[c_162189,c_217377]) ).

tff(c_217513,plain,
    ! [U_4819] :
      ( ( U_4819 = '#skF_50' )
      | ( tl(U_4819) != nil )
      | ( hd(U_4819) != '#skF_55' )
      | ( nil = U_4819 )
      | ( nil = '#skF_50' )
      | ~ ssList(U_4819) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_162134,c_217431]) ).

tff(c_217552,plain,
    ! [U_4820] :
      ( ( U_4820 = '#skF_50' )
      | ( tl(U_4820) != nil )
      | ( hd(U_4820) != '#skF_55' )
      | ( nil = U_4820 )
      | ~ ssList(U_4820) ),
    inference(negUnitSimplification,[status(thm)],[c_7175,c_217513]) ).

tff(c_217696,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ( tl('#skF_54') != nil )
    | ( hd('#skF_54') != '#skF_55' )
    | ( nil = '#skF_54' ) ),
    inference(resolution,[status(thm)],[c_388,c_217552]) ).

tff(c_217784,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ( '#skF_46'('#skF_54') != '#skF_55' )
    | ( nil = '#skF_54' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_162071,c_197476,c_217696]) ).

tff(c_217785,plain,
    '#skF_46'('#skF_54') != '#skF_55',
    inference(negUnitSimplification,[status(thm)],[c_70600,c_216100,c_217784]) ).

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

tff(c_162109,plain,
    ( ssItem('#skF_46'('#skF_54'))
    | ( nil = '#skF_54' )
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_162071,c_184]) ).

tff(c_162113,plain,
    ( ssItem('#skF_46'('#skF_54'))
    | ( nil = '#skF_54' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_162109]) ).

tff(c_162114,plain,
    ssItem('#skF_46'('#skF_54')),
    inference(negUnitSimplification,[status(thm)],[c_70600,c_162113]) ).

tff(c_196196,plain,
    ! [U_4503] :
      ( ( cons(hd(U_4503),tl(U_4503)) = U_4503 )
      | ( nil = U_4503 )
      | ~ ssList(U_4503) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_196233,plain,
    ( ( cons('#skF_46'('#skF_54'),tl('#skF_54')) = '#skF_54' )
    | ( nil = '#skF_54' )
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_162071,c_196196]) ).

tff(c_196260,plain,
    ( ( cons('#skF_46'('#skF_54'),'#skF_47'('#skF_54')) = '#skF_54' )
    | ( nil = '#skF_54' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_70599,c_196233]) ).

tff(c_196261,plain,
    cons('#skF_46'('#skF_54'),'#skF_47'('#skF_54')) = '#skF_54',
    inference(negUnitSimplification,[status(thm)],[c_70600,c_196260]) ).

tff(c_226,plain,
    ! [V_945,W_947] :
      ( memberP(cons(V_945,W_947),V_945)
      | ~ ssList(W_947)
      | ~ ssItem(V_945) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_196280,plain,
    ( memberP('#skF_54','#skF_46'('#skF_54'))
    | ~ ssList('#skF_47'('#skF_54'))
    | ~ ssItem('#skF_46'('#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_196261,c_226]) ).

tff(c_196297,plain,
    memberP('#skF_54','#skF_46'('#skF_54')),
    inference(demodulation,[status(thm),theory(equality)],[c_162114,c_70609,c_196280]) ).

tff(c_202255,plain,
    ! [W_4622,U_4623,V_4624] :
      ( ~ memberP(W_4622,U_4623)
      | memberP(app(V_4624,W_4622),U_4623)
      | ~ ssList(W_4622)
      | ~ ssList(V_4624)
      | ~ ssItem(U_4623) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_202396,plain,
    ! [U_4623] :
      ( ~ memberP('#skF_54',U_4623)
      | memberP('#skF_50',U_4623)
      | ~ ssList('#skF_54')
      | ~ ssList(app('#skF_53',cons('#skF_52',nil)))
      | ~ ssItem(U_4623) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_202255]) ).

tff(c_208001,plain,
    ! [U_4699] :
      ( ~ memberP('#skF_54',U_4699)
      | memberP('#skF_50',U_4699)
      | ~ ssItem(U_4699) ),
    inference(demodulation,[status(thm),theory(equality)],[c_200799,c_388,c_202396]) ).

tff(c_208004,plain,
    ( memberP('#skF_50','#skF_46'('#skF_54'))
    | ~ ssItem('#skF_46'('#skF_54')) ),
    inference(resolution,[status(thm)],[c_196297,c_208001]) ).

tff(c_208010,plain,
    memberP('#skF_50','#skF_46'('#skF_54')),
    inference(demodulation,[status(thm),theory(equality)],[c_162114,c_208004]) ).

tff(c_213795,plain,
    ! [W_4774,U_4775,V_4776] :
      ( memberP(W_4774,U_4775)
      | ( V_4776 = U_4775 )
      | ~ memberP(cons(V_4776,W_4774),U_4775)
      | ~ ssList(W_4774)
      | ~ ssItem(V_4776)
      | ~ ssItem(U_4775) ),
    inference(cnfTransformation,[status(thm)],[f_512]) ).

tff(c_213846,plain,
    ! [U_4775] :
      ( memberP(nil,U_4775)
      | ( U_4775 = '#skF_55' )
      | ~ memberP('#skF_50',U_4775)
      | ~ ssList(nil)
      | ~ ssItem('#skF_55')
      | ~ ssItem(U_4775) ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_213795]) ).

tff(c_219708,plain,
    ! [U_4837] :
      ( memberP(nil,U_4837)
      | ( U_4837 = '#skF_55' )
      | ~ memberP('#skF_50',U_4837)
      | ~ ssItem(U_4837) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7174,c_168,c_213846]) ).

tff(c_219723,plain,
    ! [U_4838] :
      ( ( U_4838 = '#skF_55' )
      | ~ memberP('#skF_50',U_4838)
      | ~ ssItem(U_4838) ),
    inference(resolution,[status(thm)],[c_219708,c_228]) ).

tff(c_219726,plain,
    ( ( '#skF_46'('#skF_54') = '#skF_55' )
    | ~ ssItem('#skF_46'('#skF_54')) ),
    inference(resolution,[status(thm)],[c_208010,c_219723]) ).

tff(c_219735,plain,
    '#skF_46'('#skF_54') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_162114,c_219726]) ).

tff(c_219737,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_217785,c_219735]) ).

tff(c_219739,plain,
    '#skF_54' = '#skF_50',
    inference(splitRight,[status(thm)],[c_210910]) ).

tff(c_201891,plain,
    ( rearsegP('#skF_50','#skF_54')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil)))
    | ~ ssList('#skF_54')
    | ~ ssList(app(app('#skF_53',cons('#skF_52',nil)),'#skF_54')) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_201751]) ).

tff(c_202007,plain,
    rearsegP('#skF_50','#skF_54'),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_425,c_388,c_200799,c_201891]) ).

tff(c_254,plain,
    ! [V_993,U_991] :
      ( ( V_993 = U_991 )
      | ~ rearsegP(V_993,U_991)
      | ~ rearsegP(U_991,V_993)
      | ~ ssList(V_993)
      | ~ ssList(U_991) ),
    inference(cnfTransformation,[status(thm)],[f_612]) ).

tff(c_202027,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ rearsegP('#skF_54','#skF_50')
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_54') ),
    inference(resolution,[status(thm)],[c_202007,c_254]) ).

tff(c_202030,plain,
    ( ( '#skF_54' = '#skF_50' )
    | ~ rearsegP('#skF_54','#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_400,c_202027]) ).

tff(c_202530,plain,
    ~ rearsegP('#skF_54','#skF_50'),
    inference(splitLeft,[status(thm)],[c_202030]) ).

tff(c_219804,plain,
    ~ rearsegP('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_219739,c_202530]) ).

tff(c_219845,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_202013,c_219804]) ).

tff(c_219846,plain,
    '#skF_54' = '#skF_50',
    inference(splitRight,[status(thm)],[c_202030]) ).

tff(c_219878,plain,
    app(app('#skF_53',cons('#skF_52',nil)),'#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_219846,c_425]) ).

tff(c_221789,plain,
    ! [W_4859,U_4860,V_4861] :
      ( ( W_4859 = U_4860 )
      | ( app(W_4859,V_4861) != app(U_4860,V_4861) )
      | ~ ssList(W_4859)
      | ~ ssList(V_4861)
      | ~ ssList(U_4860) ),
    inference(cnfTransformation,[status(thm)],[f_815]) ).

tff(c_221989,plain,
    ! [W_4859] :
      ( ( nil = W_4859 )
      | ( app(W_4859,'#skF_50') != '#skF_50' )
      | ~ ssList(W_4859)
      | ~ ssList('#skF_50')
      | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_68955,c_221789]) ).

tff(c_224969,plain,
    ! [W_4900] :
      ( ( nil = W_4900 )
      | ( app(W_4900,'#skF_50') != '#skF_50' )
      | ~ ssList(W_4900) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_400,c_221989]) ).

tff(c_224978,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ( app(app('#skF_53',cons('#skF_52',nil)),'#skF_50') != '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_200799,c_224969]) ).

tff(c_225119,plain,
    app('#skF_53',cons('#skF_52',nil)) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_219878,c_224978]) ).

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_225422,plain,
    ( frontsegP(nil,'#skF_53')
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53')
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(superposition,[status(thm),theory(equality)],[c_225119,c_26]) ).

tff(c_225454,plain,
    ( frontsegP(nil,'#skF_53')
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_225119,c_390,c_225422]) ).

tff(c_225455,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(negUnitSimplification,[status(thm)],[c_201719,c_225454]) ).

tff(c_225471,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_225455]) ).

tff(c_225475,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_225471]) ).

tff(c_225477,plain,
    '#skF_47'('#skF_54') != nil,
    inference(splitRight,[status(thm)],[c_70626]) ).

tff(c_68883,plain,
    ! [U_2717] :
      ( ( app(U_2717,nil) = U_2717 )
      | ~ ssList(U_2717) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_68900,plain,
    app(nil,nil) = nil,
    inference(resolution,[status(thm)],[c_168,c_68883]) ).

tff(c_168808,plain,
    ! [W_4185,V_4186] :
      ( rearsegP(app(W_4185,V_4186),V_4186)
      | ~ ssList(W_4185)
      | ~ ssList(V_4186)
      | ~ ssList(app(W_4185,V_4186)) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_169026,plain,
    ( rearsegP(nil,nil)
    | ~ ssList(nil)
    | ~ ssList(nil)
    | ~ ssList(app(nil,nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_68900,c_168808]) ).

tff(c_169172,plain,
    rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_68900,c_168,c_168,c_169026]) ).

tff(c_166382,plain,
    ! [U_4155,V_4156] :
      ( ( hd(app(U_4155,V_4156)) = hd(U_4155) )
      | ( nil = U_4155 )
      | ~ ssList(V_4156)
      | ~ ssList(U_4155) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_166550,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_166382]) ).

tff(c_166734,plain,
    ( ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' )
    | ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ~ ssList(app('#skF_53',cons('#skF_52',nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_162134,c_166550]) ).

tff(c_166910,plain,
    ~ ssList(app('#skF_53',cons('#skF_52',nil))),
    inference(splitLeft,[status(thm)],[c_166734]) ).

tff(c_166913,plain,
    ( ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_166910]) ).

tff(c_166916,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_166913]) ).

tff(c_166919,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_166916]) ).

tff(c_166923,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_166919]) ).

tff(c_166924,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) = nil )
    | ( hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55' ) ),
    inference(splitRight,[status(thm)],[c_166734]) ).

tff(c_167098,plain,
    hd(app('#skF_53',cons('#skF_52',nil))) = '#skF_55',
    inference(splitLeft,[status(thm)],[c_166924]) ).

tff(c_167115,plain,
    ( ( hd('#skF_53') = '#skF_55' )
    | ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_167098,c_358]) ).

tff(c_167128,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_55' )
    | ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_162063,c_167115]) ).

tff(c_167129,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_55' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(negUnitSimplification,[status(thm)],[c_161799,c_167128]) ).

tff(c_167138,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_167129]) ).

tff(c_167158,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_167138]) ).

tff(c_167162,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_392,c_167158]) ).

tff(c_167163,plain,
    '#skF_46'('#skF_53') = '#skF_55',
    inference(splitRight,[status(thm)],[c_167129]) ).

tff(c_167168,plain,
    hd('#skF_53') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_167163,c_162063]) ).

tff(c_167183,plain,
    ( ( cons('#skF_55',tl('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_167168,c_340]) ).

tff(c_167190,plain,
    ( ( cons('#skF_55','#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_161798,c_167183]) ).

tff(c_167191,plain,
    cons('#skF_55','#skF_47'('#skF_53')) = '#skF_53',
    inference(negUnitSimplification,[status(thm)],[c_161799,c_167190]) ).

tff(c_167868,plain,
    ! [V_4176,U_4177] :
      ( ( app(cons(V_4176,nil),U_4177) = cons(V_4176,U_4177) )
      | ~ ssItem(V_4176)
      | ~ ssList(U_4177) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_167899,plain,
    ! [U_4177] :
      ( ( cons('#skF_55',U_4177) = app('#skF_50',U_4177) )
      | ~ ssItem('#skF_55')
      | ~ ssList(U_4177) ),
    inference(superposition,[status(thm),theory(equality)],[c_7188,c_167868]) ).

tff(c_167915,plain,
    ! [U_4178] :
      ( ( cons('#skF_55',U_4178) = app('#skF_50',U_4178) )
      | ~ ssList(U_4178) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7174,c_167899]) ).

tff(c_167960,plain,
    cons('#skF_55','#skF_47'('#skF_53')) = app('#skF_50','#skF_47'('#skF_53')),
    inference(resolution,[status(thm)],[c_161809,c_167915]) ).

tff(c_168069,plain,
    app('#skF_50','#skF_47'('#skF_53')) = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_167191,c_167960]) ).

tff(c_169295,plain,
    ! [V_4189,W_4190] :
      ( frontsegP(app(V_4189,W_4190),V_4189)
      | ~ ssList(W_4190)
      | ~ ssList(V_4189)
      | ~ ssList(app(V_4189,W_4190)) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_169303,plain,
    ( frontsegP('#skF_53','#skF_50')
    | ~ ssList('#skF_47'('#skF_53'))
    | ~ ssList('#skF_50')
    | ~ ssList(app('#skF_50','#skF_47'('#skF_53'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_168069,c_169295]) ).

tff(c_169522,plain,
    frontsegP('#skF_53','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_168069,c_400,c_161809,c_169303]) ).

tff(c_169752,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ frontsegP('#skF_50','#skF_53')
    | ~ ssList('#skF_53')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_169522,c_234]) ).

tff(c_169755,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ frontsegP('#skF_50','#skF_53') ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_390,c_169752]) ).

tff(c_183332,plain,
    ~ frontsegP('#skF_50','#skF_53'),
    inference(splitLeft,[status(thm)],[c_169755]) ).

tff(c_167164,plain,
    ssList(cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_167129]) ).

tff(c_194742,plain,
    ! [U_4495,V_4496,W_4497] :
      ( ( app(app(U_4495,V_4496),W_4497) = app(U_4495,app(V_4496,W_4497)) )
      | ~ ssList(W_4497)
      | ~ ssList(V_4496)
      | ~ ssList(U_4495) ),
    inference(cnfTransformation,[status(thm)],[f_844]) ).

tff(c_195047,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_194742]) ).

tff(c_195234,plain,
    app('#skF_53',app(cons('#skF_52',nil),'#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_167164,c_388,c_195047]) ).

tff(c_195737,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_195234]) ).

tff(c_195776,plain,
    app('#skF_53',cons('#skF_52','#skF_54')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_195737]) ).

tff(c_195806,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_195776,c_26]) ).

tff(c_195843,plain,
    ( frontsegP('#skF_50','#skF_53')
    | ~ ssList(cons('#skF_52','#skF_54')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_195776,c_390,c_195806]) ).

tff(c_195844,plain,
    ~ ssList(cons('#skF_52','#skF_54')),
    inference(negUnitSimplification,[status(thm)],[c_183332,c_195843]) ).

tff(c_195860,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_54') ),
    inference(resolution,[status(thm)],[c_166,c_195844]) ).

tff(c_195864,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_392,c_195860]) ).

tff(c_195865,plain,
    '#skF_53' = '#skF_50',
    inference(splitRight,[status(thm)],[c_169755]) ).

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_162238,plain,
    ! [U_4041] :
      ( ( cons('#skF_5'(U_4041),nil) = U_4041 )
      | ~ singletonP(U_4041)
      | ~ ssList(U_4041) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_280,plain,
    ! [U_1032] :
      ( cyclefreeP(cons(U_1032,nil))
      | ~ ssItem(U_1032) ),
    inference(cnfTransformation,[status(thm)],[f_696]) ).

tff(c_162299,plain,
    ! [U_4044] :
      ( cyclefreeP(U_4044)
      | ~ ssItem('#skF_5'(U_4044))
      | ~ singletonP(U_4044)
      | ~ ssList(U_4044) ),
    inference(superposition,[status(thm),theory(equality)],[c_162238,c_280]) ).

tff(c_162304,plain,
    ! [U_4045] :
      ( cyclefreeP(U_4045)
      | ~ singletonP(U_4045)
      | ~ ssList(U_4045) ),
    inference(resolution,[status(thm)],[c_24,c_162299]) ).

tff(c_162432,plain,
    ( cyclefreeP('#skF_53')
    | ~ singletonP('#skF_53') ),
    inference(resolution,[status(thm)],[c_390,c_162304]) ).

tff(c_162439,plain,
    ~ singletonP('#skF_53'),
    inference(splitLeft,[status(thm)],[c_162432]) ).

tff(c_162078,plain,
    ( ssItem('#skF_46'('#skF_53'))
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_162063,c_184]) ).

tff(c_162082,plain,
    ( ssItem('#skF_46'('#skF_53'))
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_162078]) ).

tff(c_162083,plain,
    ssItem('#skF_46'('#skF_53')),
    inference(negUnitSimplification,[status(thm)],[c_161799,c_162082]) ).

tff(c_164115,plain,
    '#skF_47'('#skF_53') = nil,
    inference(splitLeft,[status(thm)],[c_162033]) ).

tff(c_162446,plain,
    ! [U_4048] :
      ( ( cons(hd(U_4048),tl(U_4048)) = U_4048 )
      | ( nil = U_4048 )
      | ~ ssList(U_4048) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_162492,plain,
    ( ( cons(hd('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_161798,c_162446]) ).

tff(c_162519,plain,
    ( ( cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53' )
    | ( nil = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_162063,c_162492]) ).

tff(c_162520,plain,
    cons('#skF_46'('#skF_53'),'#skF_47'('#skF_53')) = '#skF_53',
    inference(negUnitSimplification,[status(thm)],[c_161799,c_162519]) ).

tff(c_164119,plain,
    cons('#skF_46'('#skF_53'),nil) = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_164115,c_162520]) ).

tff(c_163948,plain,
    ! [V_4084] :
      ( singletonP(cons(V_4084,nil))
      | ~ ssItem(V_4084)
      | ~ ssList(cons(V_4084,nil)) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_163955,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,nil))
      | ~ ssItem(V_861)
      | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_163948]) ).

tff(c_163961,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,nil))
      | ~ ssItem(V_861) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_163955]) ).

tff(c_164158,plain,
    ( singletonP('#skF_53')
    | ~ ssItem('#skF_46'('#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_164119,c_163961]) ).

tff(c_164199,plain,
    singletonP('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_162083,c_164158]) ).

tff(c_164201,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_162439,c_164199]) ).

tff(c_164203,plain,
    '#skF_47'('#skF_53') != nil,
    inference(splitRight,[status(thm)],[c_162033]) ).

tff(c_356,plain,
    ! [U_1080] :
      ( ( app(U_1080,nil) = U_1080 )
      | ~ ssList(U_1080) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_161830,plain,
    app('#skF_47'('#skF_53'),nil) = '#skF_47'('#skF_53'),
    inference(resolution,[status(thm)],[c_161809,c_356]) ).

tff(c_168993,plain,
    ( rearsegP('#skF_47'('#skF_53'),nil)
    | ~ ssList('#skF_47'('#skF_53'))
    | ~ ssList(nil)
    | ~ ssList(app('#skF_47'('#skF_53'),nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_161830,c_168808]) ).

tff(c_169150,plain,
    rearsegP('#skF_47'('#skF_53'),nil),
    inference(demodulation,[status(thm),theory(equality)],[c_161809,c_161830,c_168,c_161809,c_168993]) ).

tff(c_169278,plain,
    ( ( '#skF_47'('#skF_53') = nil )
    | ~ rearsegP(nil,'#skF_47'('#skF_53'))
    | ~ ssList('#skF_47'('#skF_53'))
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_169150,c_254]) ).

tff(c_169281,plain,
    ( ( '#skF_47'('#skF_53') = nil )
    | ~ rearsegP(nil,'#skF_47'('#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_161809,c_169278]) ).

tff(c_169282,plain,
    ~ rearsegP(nil,'#skF_47'('#skF_53')),
    inference(negUnitSimplification,[status(thm)],[c_164203,c_169281]) ).

tff(c_195872,plain,
    ~ rearsegP(nil,'#skF_47'('#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_195865,c_169282]) ).

tff(c_195945,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_169172,c_162185,c_195872]) ).

tff(c_195946,plain,
    app('#skF_53',cons('#skF_52',nil)) = nil,
    inference(splitRight,[status(thm)],[c_166924]) ).

tff(c_196077,plain,
    app(nil,'#skF_54') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_195946,c_425]) ).

tff(c_196105,plain,
    '#skF_54' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_196077,c_68956]) ).

tff(c_162437,plain,
    ( cyclefreeP('#skF_54')
    | ~ singletonP('#skF_54') ),
    inference(resolution,[status(thm)],[c_388,c_162304]) ).

tff(c_162442,plain,
    ~ singletonP('#skF_54'),
    inference(splitLeft,[status(thm)],[c_162437]) ).

tff(c_162034,plain,
    ( ( hd('#skF_47'('#skF_54')) = '#skF_46'('#skF_47'('#skF_54')) )
    | ( '#skF_47'('#skF_54') = nil ) ),
    inference(resolution,[status(thm)],[c_70609,c_161929]) ).

tff(c_163194,plain,
    '#skF_47'('#skF_54') = nil,
    inference(splitLeft,[status(thm)],[c_162034]) ).

tff(c_162483,plain,
    ( ( cons('#skF_46'('#skF_54'),tl('#skF_54')) = '#skF_54' )
    | ( nil = '#skF_54' )
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_162071,c_162446]) ).

tff(c_162510,plain,
    ( ( cons('#skF_46'('#skF_54'),'#skF_47'('#skF_54')) = '#skF_54' )
    | ( nil = '#skF_54' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_70599,c_162483]) ).

tff(c_162511,plain,
    cons('#skF_46'('#skF_54'),'#skF_47'('#skF_54')) = '#skF_54',
    inference(negUnitSimplification,[status(thm)],[c_70600,c_162510]) ).

tff(c_163196,plain,
    cons('#skF_46'('#skF_54'),nil) = '#skF_54',
    inference(demodulation,[status(thm),theory(equality)],[c_163194,c_162511]) ).

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_163250,plain,
    ( singletonP(cons('#skF_46'('#skF_54'),nil))
    | ~ ssItem('#skF_46'('#skF_54'))
    | ~ ssList('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_163196,c_20]) ).

tff(c_163291,plain,
    singletonP('#skF_54'),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_162114,c_163196,c_163250]) ).

tff(c_163293,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_162442,c_163291]) ).

tff(c_163295,plain,
    '#skF_47'('#skF_54') != nil,
    inference(splitRight,[status(thm)],[c_162034]) ).

tff(c_196151,plain,
    '#skF_47'('#skF_50') != nil,
    inference(demodulation,[status(thm),theory(equality)],[c_196105,c_163295]) ).

tff(c_196192,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_162185,c_196151]) ).

tff(c_196194,plain,
    singletonP('#skF_54'),
    inference(splitRight,[status(thm)],[c_162437]) ).

tff(c_162247,plain,
    ! [U_4041] :
      ( ( tl(U_4041) = nil )
      | ~ ssItem('#skF_5'(U_4041))
      | ~ ssList(nil)
      | ~ singletonP(U_4041)
      | ~ ssList(U_4041) ),
    inference(superposition,[status(thm),theory(equality)],[c_162238,c_190]) ).

tff(c_225876,plain,
    ! [U_4911] :
      ( ( tl(U_4911) = nil )
      | ~ ssItem('#skF_5'(U_4911))
      | ~ singletonP(U_4911)
      | ~ ssList(U_4911) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_162247]) ).

tff(c_225882,plain,
    ! [U_4912] :
      ( ( tl(U_4912) = nil )
      | ~ singletonP(U_4912)
      | ~ ssList(U_4912) ),
    inference(resolution,[status(thm)],[c_24,c_225876]) ).

tff(c_225996,plain,
    ( ( tl('#skF_54') = nil )
    | ~ singletonP('#skF_54') ),
    inference(resolution,[status(thm)],[c_388,c_225882]) ).

tff(c_226046,plain,
    '#skF_47'('#skF_54') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_196194,c_70599,c_225996]) ).

tff(c_226048,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_225477,c_226046]) ).

tff(c_226050,plain,
    singletonP('#skF_53'),
    inference(splitRight,[status(thm)],[c_162432]) ).

tff(c_271707,plain,
    ! [U_5675] :
      ( ( tl(U_5675) = nil )
      | ~ ssItem('#skF_5'(U_5675))
      | ~ singletonP(U_5675)
      | ~ ssList(U_5675) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_162247]) ).

tff(c_271717,plain,
    ! [U_5678] :
      ( ( tl(U_5678) = nil )
      | ~ singletonP(U_5678)
      | ~ ssList(U_5678) ),
    inference(resolution,[status(thm)],[c_24,c_271707]) ).

tff(c_271831,plain,
    ( ( tl('#skF_53') = nil )
    | ~ singletonP('#skF_53') ),
    inference(resolution,[status(thm)],[c_390,c_271717]) ).

tff(c_271889,plain,
    '#skF_47'('#skF_53') = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_226050,c_161798,c_271831]) ).

tff(c_271891,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_269032,c_271889]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SWC183+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.15  % 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
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 21:39:36 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 70.68/54.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 70.68/54.63  
% 70.68/54.63  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 70.68/54.70  
% 70.68/54.70  Inference rules
% 70.68/54.70  ----------------------
% 70.68/54.70  #Ref     : 64
% 70.68/54.70  #Sup     : 59036
% 70.68/54.70  #Fact    : 0
% 70.68/54.70  #Define  : 0
% 70.68/54.70  #Split   : 581
% 70.68/54.70  #Chain   : 0
% 70.68/54.70  #Close   : 0
% 70.68/54.70  
% 70.68/54.70  Ordering : KBO
% 70.68/54.70  
% 70.68/54.70  Simplification rules
% 70.68/54.70  ----------------------
% 70.68/54.70  #Subsume      : 7943
% 70.68/54.70  #Demod        : 55846
% 70.68/54.70  #Tautology    : 15080
% 70.68/54.70  #SimpNegUnit  : 6911
% 70.68/54.70  #BackRed      : 2082
% 70.68/54.70  
% 70.68/54.70  #Partial instantiations: 0
% 70.68/54.70  #Strategies tried      : 1
% 70.68/54.70  
% 70.68/54.70  Timing (in seconds)
% 70.68/54.70  ----------------------
% 70.68/54.71  Preprocessing        : 0.88
% 70.68/54.71  Parsing              : 0.41
% 70.68/54.71  CNF conversion       : 0.11
% 70.68/54.71  Main loop            : 52.63
% 70.68/54.71  Inferencing          : 9.41
% 70.68/54.71  Reduction            : 26.49
% 70.68/54.71  Demodulation         : 20.07
% 70.68/54.71  BG Simplification    : 0.36
% 70.68/54.71  Subsumption          : 13.16
% 70.68/54.71  Abstraction          : 0.60
% 70.68/54.71  MUC search           : 0.00
% 70.68/54.71  Cooper               : 0.00
% 70.68/54.71  Total                : 53.66
% 70.68/54.71  Index Insertion      : 0.00
% 70.68/54.71  Index Deletion       : 0.00
% 70.68/54.71  Index Matching       : 0.00
% 70.68/54.71  BG Taut test         : 0.00
%------------------------------------------------------------------------------