TSTP Solution File: SWC315+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC315+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 : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:02:05 EDT 2023

% Result   : Theorem 22.68s 9.96s
% Output   : CNFRefutation 22.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   98
% Syntax   : Number of formulae    :  394 ( 146 unt;  79 typ;   0 def)
%            Number of atoms       :  626 ( 308 equ)
%            Maximal formula atoms :   19 (   1 avg)
%            Number of connectives :  574 ( 263   ~; 267   |;   7   &)
%                                         (   3 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   60 (  60 usr;  11 con; 0-2 aty)
%            Number of variables   :  107 (; 104   !;   3   ?;   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_1032,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ~ ssList(X)
                    | ( V != X )
                    | ( U != W )
                    | ( ( nil != W )
                      & ( nil = X ) )
                    | ( ! [Y] :
                          ( ssItem(Y)
                         => ! [Z] :
                              ( ~ ssList(Z)
                              | ( app(cons(Y,nil),Z) != V )
                              | ( app(Z,cons(Y,nil)) = U ) ) )
                      & ( ( nil != V )
                        | ( nil = U ) ) )
                    | ( ! [X1] :
                          ( ssItem(X1)
                         => ! [X2] :
                              ( ~ ssList(X2)
                              | ( app(cons(X1,nil),X2) != X )
                              | ( app(X2,cons(X1,nil)) != W ) ) )
                      & neq(X,nil) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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

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_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_311,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> ( U != V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).

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

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_413,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(nil,U) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).

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_779,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssList(V)
            & ( tl(U) = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).

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

tff(f_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_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_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_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_859,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(U,nil) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

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

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

tff(f_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(c_392,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

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

tff(c_384,plain,
    ( ( nil != '#skF_51' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_443,plain,
    nil != '#skF_51',
    inference(splitLeft,[status(thm)],[c_384]) ).

tff(c_388,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_420,plain,
    ( ssItem('#skF_52')
    | ( nil = '#skF_49' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_426,plain,
    ( ssItem('#skF_52')
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_420]) ).

tff(c_2330,plain,
    ssItem('#skF_52'),
    inference(negUnitSimplification,[status(thm)],[c_443,c_426]) ).

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_54090,plain,
    ! [V_2889] :
      ( singletonP(cons(V_2889,nil))
      | ~ ssItem(V_2889)
      | ~ ssList(cons(V_2889,nil)) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_54097,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,nil))
      | ~ ssItem(V_861)
      | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_54090]) ).

tff(c_54100,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,nil))
      | ~ ssItem(V_861) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_54097]) ).

tff(c_390,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_2307,plain,
    ! [U_1340,V_1341] :
      ( neq(U_1340,V_1341)
      | ( V_1341 = U_1340 )
      | ~ ssList(V_1341)
      | ~ ssList(U_1340) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_404,plain,
    ( ssItem('#skF_54')
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_445,plain,
    ~ neq('#skF_51',nil),
    inference(splitLeft,[status(thm)],[c_404]) ).

tff(c_2318,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList(nil)
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_2307,c_445]) ).

tff(c_2325,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_168,c_2318]) ).

tff(c_2327,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_443,c_2325]) ).

tff(c_2328,plain,
    ssItem('#skF_54'),
    inference(splitRight,[status(thm)],[c_404]) ).

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

tff(c_2329,plain,
    neq('#skF_51',nil),
    inference(splitRight,[status(thm)],[c_404]) ).

tff(c_402,plain,
    ( ssList('#skF_55')
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_2334,plain,
    ssList('#skF_55'),
    inference(demodulation,[status(thm),theory(equality)],[c_2329,c_402]) ).

tff(c_2871,plain,
    ! [U_1414] :
      ( ( hd(U_1414) = '#skF_46'(U_1414) )
      | ( nil = U_1414 )
      | ~ ssList(U_1414) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_2983,plain,
    ( ( hd('#skF_55') = '#skF_46'('#skF_55') )
    | ( nil = '#skF_55' ) ),
    inference(resolution,[status(thm)],[c_2334,c_2871]) ).

tff(c_25517,plain,
    nil = '#skF_55',
    inference(splitLeft,[status(thm)],[c_2983]) ).

tff(c_418,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_49' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_422,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_418]) ).

tff(c_2331,plain,
    ssList('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_443,c_422]) ).

tff(c_2984,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_2331,c_2871]) ).

tff(c_3055,plain,
    nil = '#skF_53',
    inference(splitLeft,[status(thm)],[c_2984]) ).

tff(c_2365,plain,
    ! [U_1360] :
      ( ( app(nil,U_1360) = U_1360 )
      | ~ ssList(U_1360) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_2385,plain,
    app(nil,'#skF_51') = '#skF_51',
    inference(resolution,[status(thm)],[c_390,c_2365]) ).

tff(c_3078,plain,
    app('#skF_53','#skF_51') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_2385]) ).

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_7758,plain,
    ! [V_1597,U_1598] :
      ( ( app(cons(V_1597,'#skF_53'),U_1598) = cons(V_1597,U_1598) )
      | ~ ssItem(V_1597)
      | ~ ssList(U_1598) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_346]) ).

tff(c_416,plain,
    ( ( app(cons('#skF_52',nil),'#skF_53') = '#skF_49' )
    | ( nil = '#skF_49' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_424,plain,
    ( ( app(cons('#skF_52',nil),'#skF_53') = '#skF_51' )
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_388,c_416]) ).

tff(c_2492,plain,
    app(cons('#skF_52',nil),'#skF_53') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_443,c_424]) ).

tff(c_3069,plain,
    app(cons('#skF_52','#skF_53'),'#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_2492]) ).

tff(c_7768,plain,
    ( ( cons('#skF_52','#skF_53') = '#skF_51' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_7758,c_3069]) ).

tff(c_7792,plain,
    cons('#skF_52','#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2330,c_7768]) ).

tff(c_386,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_414,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) != '#skF_48' )
    | ( nil = '#skF_49' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_423,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) != '#skF_48' )
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_414]) ).

tff(c_432,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) != '#skF_50' )
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_423]) ).

tff(c_2587,plain,
    app('#skF_53',cons('#skF_52',nil)) != '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_443,c_432]) ).

tff(c_3063,plain,
    app('#skF_53',cons('#skF_52','#skF_53')) != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_2587]) ).

tff(c_7802,plain,
    app('#skF_53','#skF_51') != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_7792,c_3063]) ).

tff(c_7804,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_3078,c_7802]) ).

tff(c_2739,plain,
    ! [U_1413] :
      ( ( tl(U_1413) = '#skF_47'(U_1413) )
      | ( nil = U_1413 )
      | ~ ssList(U_1413) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_2851,plain,
    ( ( tl('#skF_55') = '#skF_47'('#skF_55') )
    | ( nil = '#skF_55' ) ),
    inference(resolution,[status(thm)],[c_2334,c_2739]) ).

tff(c_3414,plain,
    ( ( tl('#skF_55') = '#skF_47'('#skF_55') )
    | ( '#skF_55' = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_2851]) ).

tff(c_3415,plain,
    '#skF_55' = '#skF_53',
    inference(splitLeft,[status(thm)],[c_3414]) ).

tff(c_400,plain,
    ( ( app(cons('#skF_54',nil),'#skF_55') = '#skF_51' )
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_2345,plain,
    app(cons('#skF_54',nil),'#skF_55') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_2329,c_400]) ).

tff(c_3090,plain,
    app(cons('#skF_54','#skF_53'),'#skF_55') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_2345]) ).

tff(c_3683,plain,
    app(cons('#skF_54','#skF_53'),'#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_3415,c_3090]) ).

tff(c_7789,plain,
    ( ( cons('#skF_54','#skF_53') = '#skF_51' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_3683,c_7758]) ).

tff(c_7801,plain,
    cons('#skF_54','#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2328,c_7789]) ).

tff(c_398,plain,
    ( ( app('#skF_55',cons('#skF_54',nil)) = '#skF_50' )
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_2360,plain,
    app('#skF_55',cons('#skF_54',nil)) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_2329,c_398]) ).

tff(c_3082,plain,
    app('#skF_55',cons('#skF_54','#skF_53')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_2360]) ).

tff(c_3693,plain,
    app('#skF_53',cons('#skF_54','#skF_53')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_3415,c_3082]) ).

tff(c_7917,plain,
    app('#skF_53','#skF_51') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_7801,c_3693]) ).

tff(c_8078,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_7917,c_3078]) ).

tff(c_8080,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7804,c_8078]) ).

tff(c_8082,plain,
    '#skF_55' != '#skF_53',
    inference(splitRight,[status(thm)],[c_3414]) ).

tff(c_2826,plain,
    ( ( tl('#skF_51') = '#skF_47'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_390,c_2739]) ).

tff(c_2860,plain,
    tl('#skF_51') = '#skF_47'('#skF_51'),
    inference(negUnitSimplification,[status(thm)],[c_443,c_2826]) ).

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

tff(c_3012,plain,
    ( ssList('#skF_47'('#skF_51'))
    | ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_2860,c_188]) ).

tff(c_3016,plain,
    ( ssList('#skF_47'('#skF_51'))
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_3012]) ).

tff(c_3017,plain,
    ssList('#skF_47'('#skF_51')),
    inference(negUnitSimplification,[status(thm)],[c_443,c_3016]) ).

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_3031,plain,
    ( ( hd('#skF_47'('#skF_51')) = '#skF_46'('#skF_47'('#skF_51')) )
    | ( '#skF_47'('#skF_51') = nil ) ),
    inference(resolution,[status(thm)],[c_3017,c_330]) ).

tff(c_8612,plain,
    ( ( hd('#skF_47'('#skF_51')) = '#skF_46'('#skF_47'('#skF_51')) )
    | ( '#skF_47'('#skF_51') = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_3031]) ).

tff(c_8613,plain,
    '#skF_47'('#skF_51') = '#skF_53',
    inference(splitLeft,[status(thm)],[c_8612]) ).

tff(c_8618,plain,
    tl('#skF_51') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_8613,c_2860]) ).

tff(c_3103,plain,
    ~ singletonP('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_230]) ).

tff(c_410,plain,
    ( ssList('#skF_53')
    | ( nil != '#skF_48' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_430,plain,
    ( ssList('#skF_53')
    | ( nil != '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_410]) ).

tff(c_444,plain,
    nil != '#skF_50',
    inference(splitLeft,[status(thm)],[c_430]) ).

tff(c_2955,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_392,c_2871]) ).

tff(c_2989,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_444,c_2955]) ).

tff(c_8100,plain,
    ( ( hd('#skF_55') = '#skF_46'('#skF_55') )
    | ( '#skF_55' = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_2983]) ).

tff(c_8101,plain,
    hd('#skF_55') = '#skF_46'('#skF_55'),
    inference(negUnitSimplification,[status(thm)],[c_8082,c_8100]) ).

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_14194,plain,
    ! [U_1796,V_1797] :
      ( ( hd(app(U_1796,V_1797)) = hd(U_1796) )
      | ( U_1796 = '#skF_53' )
      | ~ ssList(V_1797)
      | ~ ssList(U_1796) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_358]) ).

tff(c_14371,plain,
    ( ( hd('#skF_55') = hd('#skF_50') )
    | ( '#skF_55' = '#skF_53' )
    | ~ ssList(cons('#skF_54','#skF_53'))
    | ~ ssList('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_3082,c_14194]) ).

tff(c_14564,plain,
    ( ( '#skF_46'('#skF_55') = '#skF_46'('#skF_50') )
    | ( '#skF_55' = '#skF_53' )
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2989,c_8101,c_14371]) ).

tff(c_14565,plain,
    ( ( '#skF_46'('#skF_55') = '#skF_46'('#skF_50') )
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(negUnitSimplification,[status(thm)],[c_8082,c_14564]) ).

tff(c_14591,plain,
    ~ ssList(cons('#skF_54','#skF_53')),
    inference(splitLeft,[status(thm)],[c_14565]) ).

tff(c_14594,plain,
    ( ~ ssItem('#skF_54')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_14591]) ).

tff(c_14598,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2328,c_14594]) ).

tff(c_14600,plain,
    ssList(cons('#skF_54','#skF_53')),
    inference(splitRight,[status(thm)],[c_14565]) ).

tff(c_2958,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_390,c_2871]) ).

tff(c_2992,plain,
    hd('#skF_51') = '#skF_46'('#skF_51'),
    inference(negUnitSimplification,[status(thm)],[c_443,c_2958]) ).

tff(c_14377,plain,
    ( ( hd(cons('#skF_54','#skF_53')) = hd('#skF_51') )
    | ( cons('#skF_54','#skF_53') = '#skF_53' )
    | ~ ssList('#skF_55')
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3090,c_14194]) ).

tff(c_14569,plain,
    ( ( hd(cons('#skF_54','#skF_53')) = '#skF_46'('#skF_51') )
    | ( cons('#skF_54','#skF_53') = '#skF_53' )
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2992,c_14377]) ).

tff(c_14642,plain,
    ( ( hd(cons('#skF_54','#skF_53')) = '#skF_46'('#skF_51') )
    | ( cons('#skF_54','#skF_53') = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14600,c_14569]) ).

tff(c_14643,plain,
    cons('#skF_54','#skF_53') = '#skF_53',
    inference(splitLeft,[status(thm)],[c_14642]) ).

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_11947,plain,
    ! [V_1719] :
      ( singletonP(cons(V_1719,'#skF_53'))
      | ~ ssItem(V_1719)
      | ~ ssList(cons(V_1719,'#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_3055,c_20]) ).

tff(c_11957,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_53'))
      | ~ ssItem(V_861)
      | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_11947]) ).

tff(c_11962,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_53'))
      | ~ ssItem(V_861) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_11957]) ).

tff(c_14651,plain,
    ( singletonP('#skF_53')
    | ~ ssItem('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_14643,c_11962]) ).

tff(c_14692,plain,
    singletonP('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_2328,c_14651]) ).

tff(c_14694,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3103,c_14692]) ).

tff(c_14695,plain,
    hd(cons('#skF_54','#skF_53')) = '#skF_46'('#skF_51'),
    inference(splitRight,[status(thm)],[c_14642]) ).

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

tff(c_14747,plain,
    ( ( '#skF_46'('#skF_51') = '#skF_54' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_14695,c_186]) ).

tff(c_14760,plain,
    '#skF_46'('#skF_51') = '#skF_54',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2328,c_14747]) ).

tff(c_3096,plain,
    '#skF_53' != '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_443]) ).

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_11753,plain,
    ! [U_1718] :
      ( ( cons(hd(U_1718),tl(U_1718)) = U_1718 )
      | ( U_1718 = '#skF_53' )
      | ~ ssList(U_1718) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_340]) ).

tff(c_11805,plain,
    ( ( cons('#skF_46'('#skF_51'),tl('#skF_51')) = '#skF_51' )
    | ( '#skF_53' = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_2992,c_11753]) ).

tff(c_11838,plain,
    ( ( cons('#skF_46'('#skF_51'),'#skF_53') = '#skF_51' )
    | ( '#skF_53' = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_8618,c_11805]) ).

tff(c_11839,plain,
    cons('#skF_46'('#skF_51'),'#skF_53') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_3096,c_11838]) ).

tff(c_14766,plain,
    cons('#skF_54','#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_14760,c_11839]) ).

tff(c_14800,plain,
    app('#skF_51','#skF_55') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_14766,c_3090]) ).

tff(c_15152,plain,
    ! [V_1804,U_1805] :
      ( ( app(cons(V_1804,'#skF_53'),U_1805) = cons(V_1804,U_1805) )
      | ~ ssItem(V_1804)
      | ~ ssList(U_1805) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_346]) ).

tff(c_15171,plain,
    ! [U_1805] :
      ( ( cons('#skF_54',U_1805) = app('#skF_51',U_1805) )
      | ~ ssItem('#skF_54')
      | ~ ssList(U_1805) ),
    inference(superposition,[status(thm),theory(equality)],[c_14766,c_15152]) ).

tff(c_15184,plain,
    ! [U_1806] :
      ( ( cons('#skF_54',U_1806) = app('#skF_51',U_1806) )
      | ~ ssList(U_1806) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2328,c_15171]) ).

tff(c_15298,plain,
    cons('#skF_54','#skF_55') = app('#skF_51','#skF_55'),
    inference(resolution,[status(thm)],[c_2334,c_15184]) ).

tff(c_15346,plain,
    cons('#skF_54','#skF_55') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_14800,c_15298]) ).

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_15354,plain,
    ( ( tl('#skF_51') = '#skF_55' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_15346,c_190]) ).

tff(c_15371,plain,
    '#skF_55' = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2328,c_8618,c_15354]) ).

tff(c_15373,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8082,c_15371]) ).

tff(c_15375,plain,
    '#skF_47'('#skF_51') != '#skF_53',
    inference(splitRight,[status(thm)],[c_8612]) ).

tff(c_24424,plain,
    ! [U_2070,V_2071] :
      ( ( hd(app(U_2070,V_2071)) = hd(U_2070) )
      | ( U_2070 = '#skF_53' )
      | ~ ssList(V_2071)
      | ~ ssList(U_2070) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_358]) ).

tff(c_24613,plain,
    ( ( hd('#skF_55') = hd('#skF_50') )
    | ( '#skF_55' = '#skF_53' )
    | ~ ssList(cons('#skF_54','#skF_53'))
    | ~ ssList('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_3082,c_24424]) ).

tff(c_24818,plain,
    ( ( '#skF_46'('#skF_55') = '#skF_46'('#skF_50') )
    | ( '#skF_55' = '#skF_53' )
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2989,c_8101,c_24613]) ).

tff(c_24819,plain,
    ( ( '#skF_46'('#skF_55') = '#skF_46'('#skF_50') )
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(negUnitSimplification,[status(thm)],[c_8082,c_24818]) ).

tff(c_24845,plain,
    ~ ssList(cons('#skF_54','#skF_53')),
    inference(splitLeft,[status(thm)],[c_24819]) ).

tff(c_24848,plain,
    ( ~ ssItem('#skF_54')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_24845]) ).

tff(c_24852,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2328,c_24848]) ).

tff(c_24854,plain,
    ssList(cons('#skF_54','#skF_53')),
    inference(splitRight,[status(thm)],[c_24819]) ).

tff(c_24619,plain,
    ( ( hd(cons('#skF_54','#skF_53')) = hd('#skF_51') )
    | ( cons('#skF_54','#skF_53') = '#skF_53' )
    | ~ ssList('#skF_55')
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3090,c_24424]) ).

tff(c_24823,plain,
    ( ( hd(cons('#skF_54','#skF_53')) = '#skF_46'('#skF_51') )
    | ( cons('#skF_54','#skF_53') = '#skF_53' )
    | ~ ssList(cons('#skF_54','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2992,c_24619]) ).

tff(c_24896,plain,
    ( ( hd(cons('#skF_54','#skF_53')) = '#skF_46'('#skF_51') )
    | ( cons('#skF_54','#skF_53') = '#skF_53' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24854,c_24823]) ).

tff(c_24897,plain,
    cons('#skF_54','#skF_53') = '#skF_53',
    inference(splitLeft,[status(thm)],[c_24896]) ).

tff(c_22051,plain,
    ! [V_1991] :
      ( singletonP(cons(V_1991,'#skF_53'))
      | ~ ssItem(V_1991)
      | ~ ssList(cons(V_1991,'#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_3055,c_20]) ).

tff(c_22058,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_53'))
      | ~ ssItem(V_861)
      | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_22051]) ).

tff(c_22061,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_53'))
      | ~ ssItem(V_861) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_22058]) ).

tff(c_24905,plain,
    ( singletonP('#skF_53')
    | ~ ssItem('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_24897,c_22061]) ).

tff(c_24946,plain,
    singletonP('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_2328,c_24905]) ).

tff(c_24948,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3103,c_24946]) ).

tff(c_24949,plain,
    hd(cons('#skF_54','#skF_53')) = '#skF_46'('#skF_51'),
    inference(splitRight,[status(thm)],[c_24896]) ).

tff(c_25001,plain,
    ( ( '#skF_46'('#skF_51') = '#skF_54' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_24949,c_186]) ).

tff(c_25014,plain,
    '#skF_46'('#skF_51') = '#skF_54',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2328,c_25001]) ).

tff(c_24616,plain,
    ( ( hd(cons('#skF_52','#skF_53')) = hd('#skF_51') )
    | ( cons('#skF_52','#skF_53') = '#skF_53' )
    | ~ ssList('#skF_53')
    | ~ ssList(cons('#skF_52','#skF_53')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3069,c_24424]) ).

tff(c_24821,plain,
    ( ( hd(cons('#skF_52','#skF_53')) = '#skF_46'('#skF_51') )
    | ( cons('#skF_52','#skF_53') = '#skF_53' )
    | ~ ssList(cons('#skF_52','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2992,c_24616]) ).

tff(c_25297,plain,
    ( ( hd(cons('#skF_52','#skF_53')) = '#skF_54' )
    | ( cons('#skF_52','#skF_53') = '#skF_53' )
    | ~ ssList(cons('#skF_52','#skF_53')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_25014,c_24821]) ).

tff(c_25298,plain,
    ~ ssList(cons('#skF_52','#skF_53')),
    inference(splitLeft,[status(thm)],[c_25297]) ).

tff(c_25307,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_166,c_25298]) ).

tff(c_25311,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2330,c_25307]) ).

tff(c_25313,plain,
    ssList(cons('#skF_52','#skF_53')),
    inference(splitRight,[status(thm)],[c_25297]) ).

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

tff(c_3074,plain,
    ! [U_1080] :
      ( ( app(U_1080,'#skF_53') = U_1080 )
      | ~ ssList(U_1080) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3055,c_356]) ).

tff(c_25340,plain,
    app(cons('#skF_52','#skF_53'),'#skF_53') = cons('#skF_52','#skF_53'),
    inference(resolution,[status(thm)],[c_25313,c_3074]) ).

tff(c_25357,plain,
    cons('#skF_52','#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_3069,c_25340]) ).

tff(c_25379,plain,
    ( ( tl('#skF_51') = '#skF_53' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_25357,c_190]) ).

tff(c_25425,plain,
    '#skF_47'('#skF_51') = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2330,c_2860,c_25379]) ).

tff(c_25427,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_15375,c_25425]) ).

tff(c_25429,plain,
    nil != '#skF_53',
    inference(splitRight,[status(thm)],[c_2984]) ).

tff(c_25518,plain,
    '#skF_55' != '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_25517,c_25429]) ).

tff(c_26368,plain,
    ( ( hd('#skF_47'('#skF_51')) = '#skF_46'('#skF_47'('#skF_51')) )
    | ( '#skF_47'('#skF_51') = '#skF_55' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_25517,c_3031]) ).

tff(c_26369,plain,
    '#skF_47'('#skF_51') = '#skF_55',
    inference(splitLeft,[status(thm)],[c_26368]) ).

tff(c_26374,plain,
    tl('#skF_51') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_26369,c_2860]) ).

tff(c_32469,plain,
    ! [V_2291,U_2292] :
      ( ( app(cons(V_2291,'#skF_55'),U_2292) = cons(V_2291,U_2292) )
      | ~ ssItem(V_2291)
      | ~ ssList(U_2292) ),
    inference(demodulation,[status(thm),theory(equality)],[c_25517,c_346]) ).

tff(c_25532,plain,
    app(cons('#skF_52','#skF_55'),'#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_25517,c_2492]) ).

tff(c_32479,plain,
    ( ( cons('#skF_52','#skF_53') = '#skF_51' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_32469,c_25532]) ).

tff(c_32503,plain,
    cons('#skF_52','#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2330,c_32479]) ).

tff(c_32516,plain,
    ( ( tl('#skF_51') = '#skF_53' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_32503,c_190]) ).

tff(c_32533,plain,
    '#skF_55' = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2330,c_26374,c_32516]) ).

tff(c_32535,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_25518,c_32533]) ).

tff(c_32537,plain,
    '#skF_47'('#skF_51') != '#skF_55',
    inference(splitRight,[status(thm)],[c_26368]) ).

tff(c_25553,plain,
    app(cons('#skF_54','#skF_55'),'#skF_55') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_25517,c_2345]) ).

tff(c_42332,plain,
    ! [U_2583,V_2584] :
      ( ( hd(app(U_2583,V_2584)) = hd(U_2583) )
      | ( U_2583 = '#skF_55' )
      | ~ ssList(V_2584)
      | ~ ssList(U_2583) ),
    inference(demodulation,[status(thm),theory(equality)],[c_25517,c_358]) ).

tff(c_42491,plain,
    ( ( hd(cons('#skF_54','#skF_55')) = hd('#skF_51') )
    | ( cons('#skF_54','#skF_55') = '#skF_55' )
    | ~ ssList('#skF_55')
    | ~ ssList(cons('#skF_54','#skF_55')) ),
    inference(superposition,[status(thm),theory(equality)],[c_25553,c_42332]) ).

tff(c_42659,plain,
    ( ( hd(cons('#skF_54','#skF_55')) = '#skF_46'('#skF_51') )
    | ( cons('#skF_54','#skF_55') = '#skF_55' )
    | ~ ssList(cons('#skF_54','#skF_55')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2992,c_42491]) ).

tff(c_42771,plain,
    ~ ssList(cons('#skF_54','#skF_55')),
    inference(splitLeft,[status(thm)],[c_42659]) ).

tff(c_42774,plain,
    ( ~ ssItem('#skF_54')
    | ~ ssList('#skF_55') ),
    inference(resolution,[status(thm)],[c_166,c_42771]) ).

tff(c_42778,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2328,c_42774]) ).

tff(c_42780,plain,
    ssList(cons('#skF_54','#skF_55')),
    inference(splitRight,[status(thm)],[c_42659]) ).

tff(c_25537,plain,
    ! [U_1080] :
      ( ( app(U_1080,'#skF_55') = U_1080 )
      | ~ ssList(U_1080) ),
    inference(demodulation,[status(thm),theory(equality)],[c_25517,c_356]) ).

tff(c_42801,plain,
    app(cons('#skF_54','#skF_55'),'#skF_55') = cons('#skF_54','#skF_55'),
    inference(resolution,[status(thm)],[c_42780,c_25537]) ).

tff(c_42818,plain,
    cons('#skF_54','#skF_55') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_25553,c_42801]) ).

tff(c_42834,plain,
    ( ( tl('#skF_51') = '#skF_55' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_42818,c_190]) ).

tff(c_42874,plain,
    '#skF_47'('#skF_51') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2328,c_2860,c_42834]) ).

tff(c_42876,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32537,c_42874]) ).

tff(c_42878,plain,
    nil != '#skF_55',
    inference(splitRight,[status(thm)],[c_2983]) ).

tff(c_42877,plain,
    hd('#skF_55') = '#skF_46'('#skF_55'),
    inference(splitRight,[status(thm)],[c_2983]) ).

tff(c_56253,plain,
    ! [U_2952,V_2953] :
      ( ( hd(app(U_2952,V_2953)) = hd(U_2952) )
      | ( nil = U_2952 )
      | ~ ssList(V_2953)
      | ~ ssList(U_2952) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_56448,plain,
    ( ( hd('#skF_55') = hd('#skF_50') )
    | ( nil = '#skF_55' )
    | ~ ssList(cons('#skF_54',nil))
    | ~ ssList('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_2360,c_56253]) ).

tff(c_56634,plain,
    ( ( '#skF_46'('#skF_55') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_55' )
    | ~ ssList(cons('#skF_54',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2989,c_42877,c_56448]) ).

tff(c_56635,plain,
    ( ( '#skF_46'('#skF_55') = '#skF_46'('#skF_50') )
    | ~ ssList(cons('#skF_54',nil)) ),
    inference(negUnitSimplification,[status(thm)],[c_42878,c_56634]) ).

tff(c_56638,plain,
    ~ ssList(cons('#skF_54',nil)),
    inference(splitLeft,[status(thm)],[c_56635]) ).

tff(c_56641,plain,
    ( ~ ssItem('#skF_54')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_56638]) ).

tff(c_56645,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_2328,c_56641]) ).

tff(c_56647,plain,
    ssList(cons('#skF_54',nil)),
    inference(splitRight,[status(thm)],[c_56635]) ).

tff(c_56451,plain,
    ( ( hd(cons('#skF_54',nil)) = hd('#skF_51') )
    | ( cons('#skF_54',nil) = nil )
    | ~ ssList('#skF_55')
    | ~ ssList(cons('#skF_54',nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2345,c_56253]) ).

tff(c_56637,plain,
    ( ( hd(cons('#skF_54',nil)) = '#skF_46'('#skF_51') )
    | ( cons('#skF_54',nil) = nil )
    | ~ ssList(cons('#skF_54',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2992,c_56451]) ).

tff(c_56693,plain,
    ( ( hd(cons('#skF_54',nil)) = '#skF_46'('#skF_51') )
    | ( cons('#skF_54',nil) = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56647,c_56637]) ).

tff(c_56694,plain,
    cons('#skF_54',nil) = nil,
    inference(splitLeft,[status(thm)],[c_56693]) ).

tff(c_56705,plain,
    ( singletonP(nil)
    | ~ ssItem('#skF_54') ),
    inference(superposition,[status(thm),theory(equality)],[c_56694,c_54100]) ).

tff(c_56749,plain,
    singletonP(nil),
    inference(demodulation,[status(thm),theory(equality)],[c_2328,c_56705]) ).

tff(c_56751,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_230,c_56749]) ).

tff(c_56752,plain,
    hd(cons('#skF_54',nil)) = '#skF_46'('#skF_51'),
    inference(splitRight,[status(thm)],[c_56693]) ).

tff(c_56801,plain,
    ( ( '#skF_46'('#skF_51') = '#skF_54' )
    | ~ ssItem('#skF_54')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_56752,c_186]) ).

tff(c_56814,plain,
    '#skF_46'('#skF_51') = '#skF_54',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_2328,c_56801]) ).

tff(c_56418,plain,
    ( ( hd(cons('#skF_52',nil)) = hd('#skF_51') )
    | ( cons('#skF_52',nil) = nil )
    | ~ ssList('#skF_53')
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2492,c_56253]) ).

tff(c_56605,plain,
    ( ( hd(cons('#skF_52',nil)) = '#skF_46'('#skF_51') )
    | ( cons('#skF_52',nil) = nil )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2992,c_56418]) ).

tff(c_57013,plain,
    ( ( hd(cons('#skF_52',nil)) = '#skF_54' )
    | ( cons('#skF_52',nil) = nil )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56814,c_56605]) ).

tff(c_57014,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_57013]) ).

tff(c_57017,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_57014]) ).

tff(c_57021,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_2330,c_57017]) ).

tff(c_57023,plain,
    ssList(cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_57013]) ).

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_49883,plain,
    ! [U_2779] :
      ( ( cons('#skF_5'(U_2779),nil) = U_2779 )
      | ~ singletonP(U_2779)
      | ~ ssList(U_2779) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

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

tff(c_50338,plain,
    ! [U_2801] :
      ( equalelemsP(U_2801)
      | ~ ssItem('#skF_5'(U_2801))
      | ~ singletonP(U_2801)
      | ~ ssList(U_2801) ),
    inference(superposition,[status(thm),theory(equality)],[c_49883,c_326]) ).

tff(c_50342,plain,
    ! [U_30] :
      ( equalelemsP(U_30)
      | ~ singletonP(U_30)
      | ~ ssList(U_30) ),
    inference(resolution,[status(thm)],[c_24,c_50338]) ).

tff(c_57060,plain,
    ( equalelemsP(cons('#skF_52',nil))
    | ~ singletonP(cons('#skF_52',nil)) ),
    inference(resolution,[status(thm)],[c_57023,c_50342]) ).

tff(c_57142,plain,
    ~ singletonP(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_57060]) ).

tff(c_57145,plain,
    ~ ssItem('#skF_52'),
    inference(resolution,[status(thm)],[c_54100,c_57142]) ).

tff(c_57149,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2330,c_57145]) ).

tff(c_57151,plain,
    singletonP(cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_57060]) ).

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

tff(c_49896,plain,
    ! [U_2779] :
      ( ( nil != U_2779 )
      | ~ ssItem('#skF_5'(U_2779))
      | ~ ssList(nil)
      | ~ singletonP(U_2779)
      | ~ ssList(U_2779) ),
    inference(superposition,[status(thm),theory(equality)],[c_49883,c_182]) ).

tff(c_50018,plain,
    ! [U_2795] :
      ( ( nil != U_2795 )
      | ~ ssItem('#skF_5'(U_2795))
      | ~ singletonP(U_2795)
      | ~ ssList(U_2795) ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_49896]) ).

tff(c_50022,plain,
    ! [U_30] :
      ( ( nil != U_30 )
      | ~ singletonP(U_30)
      | ~ ssList(U_30) ),
    inference(resolution,[status(thm)],[c_24,c_50018]) ).

tff(c_57061,plain,
    ( ( cons('#skF_52',nil) != nil )
    | ~ singletonP(cons('#skF_52',nil)) ),
    inference(resolution,[status(thm)],[c_57023,c_50022]) ).

tff(c_57189,plain,
    cons('#skF_52',nil) != nil,
    inference(demodulation,[status(thm),theory(equality)],[c_57151,c_57061]) ).

tff(c_57022,plain,
    ( ( cons('#skF_52',nil) = nil )
    | ( hd(cons('#skF_52',nil)) = '#skF_54' ) ),
    inference(splitRight,[status(thm)],[c_57013]) ).

tff(c_57190,plain,
    hd(cons('#skF_52',nil)) = '#skF_54',
    inference(negUnitSimplification,[status(thm)],[c_57189,c_57022]) ).

tff(c_57197,plain,
    ( ( '#skF_52' = '#skF_54' )
    | ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_57190,c_186]) ).

tff(c_57210,plain,
    '#skF_52' = '#skF_54',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_2330,c_57197]) ).

tff(c_57225,plain,
    app('#skF_53',cons('#skF_54',nil)) != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_57210,c_2587]) ).

tff(c_57575,plain,
    ! [V_2971,U_2972] :
      ( ( app(cons(V_2971,nil),U_2972) = cons(V_2971,U_2972) )
      | ~ ssItem(V_2971)
      | ~ ssList(U_2972) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_57597,plain,
    ( ( cons('#skF_54','#skF_55') = '#skF_51' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_57575,c_2345]) ).

tff(c_57620,plain,
    cons('#skF_54','#skF_55') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2328,c_57597]) ).

tff(c_57647,plain,
    ( ( tl('#skF_51') = '#skF_55' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_55') ),
    inference(superposition,[status(thm),theory(equality)],[c_57620,c_190]) ).

tff(c_57669,plain,
    '#skF_47'('#skF_51') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_2334,c_2328,c_2860,c_57647]) ).

tff(c_57708,plain,
    tl('#skF_51') = '#skF_55',
    inference(demodulation,[status(thm),theory(equality)],[c_57669,c_2860]) ).

tff(c_57226,plain,
    app(cons('#skF_54',nil),'#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_57210,c_2492]) ).

tff(c_57603,plain,
    ( ( cons('#skF_54','#skF_53') = '#skF_51' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_57226,c_57575]) ).

tff(c_57623,plain,
    cons('#skF_54','#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2328,c_57603]) ).

tff(c_57783,plain,
    ( ( tl('#skF_51') = '#skF_53' )
    | ~ ssItem('#skF_54')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_57623,c_190]) ).

tff(c_57805,plain,
    '#skF_55' = '#skF_53',
    inference(demodulation,[status(thm),theory(equality)],[c_2331,c_2328,c_57708,c_57783]) ).

tff(c_57850,plain,
    app('#skF_53',cons('#skF_54',nil)) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_57805,c_2360]) ).

tff(c_57871,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_57225,c_57850]) ).

tff(c_57872,plain,
    nil = '#skF_50',
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_412,plain,
    ( ssItem('#skF_52')
    | ( nil != '#skF_48' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_429,plain,
    ( ssItem('#skF_52')
    | ( nil != '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_412]) ).

tff(c_57916,plain,
    ssItem('#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_429]) ).

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

tff(c_57953,plain,
    ! [U_2991] :
      ( ( app('#skF_50',U_2991) = U_2991 )
      | ~ ssList(U_2991) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_196]) ).

tff(c_57961,plain,
    app('#skF_50','#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_392,c_57953]) ).

tff(c_57918,plain,
    ssList('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_430]) ).

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_58421,plain,
    ! [U_3045] :
      ( ( tl(U_3045) = '#skF_47'(U_3045) )
      | ( U_3045 = '#skF_50' )
      | ~ ssList(U_3045) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_334]) ).

tff(c_58524,plain,
    ( ( tl('#skF_53') = '#skF_47'('#skF_53') )
    | ( '#skF_53' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_57918,c_58421]) ).

tff(c_58527,plain,
    '#skF_53' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_58524]) ).

tff(c_57873,plain,
    nil = '#skF_51',
    inference(splitRight,[status(thm)],[c_384]) ).

tff(c_57886,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_57873]) ).

tff(c_408,plain,
    ( ( app(cons('#skF_52',nil),'#skF_53') = '#skF_49' )
    | ( nil != '#skF_48' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_425,plain,
    ( ( app(cons('#skF_52',nil),'#skF_53') = '#skF_51' )
    | ( nil != '#skF_48' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_408]) ).

tff(c_433,plain,
    ( ( app(cons('#skF_52',nil),'#skF_53') = '#skF_51' )
    | ( nil != '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_425]) ).

tff(c_58128,plain,
    app(cons('#skF_52','#skF_50'),'#skF_53') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_57886,c_57872,c_433]) ).

tff(c_58529,plain,
    app(cons('#skF_52','#skF_50'),'#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_58527,c_58128]) ).

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_59519,plain,
    ! [U_3104,V_3105] :
      ( ( U_3104 = '#skF_50' )
      | ( app(U_3104,V_3105) != '#skF_50' )
      | ~ ssList(V_3105)
      | ~ ssList(U_3104) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_57872,c_352]) ).

tff(c_59521,plain,
    ( ( cons('#skF_52','#skF_50') = '#skF_50' )
    | ~ ssList('#skF_50')
    | ~ ssList(cons('#skF_52','#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_58529,c_59519]) ).

tff(c_59526,plain,
    ( ( cons('#skF_52','#skF_50') = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_59521]) ).

tff(c_59531,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(splitLeft,[status(thm)],[c_59526]) ).

tff(c_59534,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_59531]) ).

tff(c_59538,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_57916,c_59534]) ).

tff(c_59539,plain,
    cons('#skF_52','#skF_50') = '#skF_50',
    inference(splitRight,[status(thm)],[c_59526]) ).

tff(c_406,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) != '#skF_48' )
    | ( nil != '#skF_48' ) ),
    inference(cnfTransformation,[status(thm)],[f_1032]) ).

tff(c_431,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) != '#skF_50' )
    | ( nil != '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_386,c_406]) ).

tff(c_58007,plain,
    app('#skF_53',cons('#skF_52','#skF_50')) != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_57872,c_431]) ).

tff(c_58530,plain,
    app('#skF_50',cons('#skF_52','#skF_50')) != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_58527,c_58007]) ).

tff(c_59600,plain,
    app('#skF_50','#skF_50') != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_59539,c_58530]) ).

tff(c_59605,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_57961,c_59600]) ).

tff(c_59607,plain,
    '#skF_53' != '#skF_50',
    inference(splitRight,[status(thm)],[c_58524]) ).

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_60315,plain,
    ! [V_3138,U_3139] :
      ( ( V_3138 = '#skF_50' )
      | ( app(U_3139,V_3138) != '#skF_50' )
      | ~ ssList(V_3138)
      | ~ ssList(U_3139) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57872,c_57872,c_354]) ).

tff(c_60317,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ ssList('#skF_53')
    | ~ ssList(cons('#skF_52','#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_58128,c_60315]) ).

tff(c_60326,plain,
    ( ( '#skF_53' = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57918,c_60317]) ).

tff(c_60327,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(negUnitSimplification,[status(thm)],[c_59607,c_60326]) ).

tff(c_60339,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_60327]) ).

tff(c_60343,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_57916,c_60339]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWC315+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 21:37:31 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 22.68/9.96  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.68/9.98  
% 22.68/9.98  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.84/10.03  
% 22.84/10.03  Inference rules
% 22.84/10.03  ----------------------
% 22.84/10.03  #Ref     : 0
% 22.84/10.03  #Sup     : 13374
% 22.84/10.03  #Fact    : 0
% 22.84/10.03  #Define  : 0
% 22.84/10.03  #Split   : 349
% 22.84/10.03  #Chain   : 0
% 22.84/10.03  #Close   : 0
% 22.84/10.03  
% 22.84/10.03  Ordering : KBO
% 22.84/10.03  
% 22.84/10.03  Simplification rules
% 22.84/10.03  ----------------------
% 22.84/10.03  #Subsume      : 1919
% 22.84/10.03  #Demod        : 11224
% 22.84/10.03  #Tautology    : 5717
% 22.84/10.03  #SimpNegUnit  : 1603
% 22.84/10.03  #BackRed      : 783
% 22.84/10.03  
% 22.84/10.03  #Partial instantiations: 0
% 22.84/10.03  #Strategies tried      : 1
% 22.84/10.03  
% 22.84/10.03  Timing (in seconds)
% 22.84/10.03  ----------------------
% 22.84/10.03  Preprocessing        : 0.88
% 22.84/10.03  Parsing              : 0.42
% 22.84/10.04  CNF conversion       : 0.10
% 22.84/10.04  Main loop            : 7.96
% 22.84/10.04  Inferencing          : 2.29
% 22.84/10.04  Reduction            : 3.06
% 22.84/10.04  Demodulation         : 2.24
% 22.84/10.04  BG Simplification    : 0.14
% 22.84/10.04  Subsumption          : 1.85
% 22.84/10.04  Abstraction          : 0.15
% 22.84/10.04  MUC search           : 0.00
% 22.84/10.04  Cooper               : 0.00
% 22.84/10.04  Total                : 8.94
% 22.84/10.04  Index Insertion      : 0.00
% 22.84/10.04  Index Deletion       : 0.00
% 22.84/10.04  Index Matching       : 0.00
% 22.84/10.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------