TSTP Solution File: SWC204+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC204+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n021.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 11:01:36 EDT 2023

% Result   : Theorem 10.53s 3.37s
% Output   : CNFRefutation 10.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   86
% Syntax   : Number of formulae    :  176 (  54 unt;  75 typ;   0 def)
%            Number of atoms       :  200 (  86 equ)
%            Maximal formula atoms :   16 (   1 avg)
%            Number of connectives :  174 (  75   ~;  69   |;   8   &)
%                                         (   1 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   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    :   56 (  56 usr;   7 con; 0-2 aty)
%            Number of variables   :   41 (;  37   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > cons > app > #nlpp > tl > hd > nil > #skF_36 > #skF_25 > #skF_5 > #skF_44 > #skF_21 > #skF_16 > #skF_6 > #skF_49 > #skF_18 > #skF_24 > #skF_35 > #skF_19 > #skF_31 > #skF_22 > #skF_37 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_51 > #skF_28 > #skF_10 > #skF_41 > #skF_2 > #skF_38 > #skF_43 > #skF_1 > #skF_8 > #skF_39 > #skF_23 > #skF_33 > #skF_26 > #skF_50 > #skF_13 > #skF_17 > #skF_11 > #skF_14 > #skF_27 > #skF_12 > #skF_7 > #skF_46 > #skF_42 > #skF_45 > #skF_9 > #skF_30 > #skF_4 > #skF_20 > #skF_47

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_36',type,
    '#skF_36': $i > $i ).

tff(segmentP,type,
    segmentP: ( $i * $i ) > $o ).

tff('#skF_25',type,
    '#skF_25': $i > $i ).

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

tff('#skF_5',type,
    '#skF_5': $i > $i ).

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

tff('#skF_44',type,
    '#skF_44': $i > $i ).

tff('#skF_21',type,
    '#skF_21': $i > $i ).

tff('#skF_16',type,
    '#skF_16': $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

tff('#skF_49',type,
    '#skF_49': $i ).

tff('#skF_18',type,
    '#skF_18': $i > $i ).

tff('#skF_24',type,
    '#skF_24': $i > $i ).

tff('#skF_35',type,
    '#skF_35': $i > $i ).

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

tff('#skF_19',type,
    '#skF_19': $i > $i ).

tff('#skF_31',type,
    '#skF_31': $i > $i ).

tff('#skF_22',type,
    '#skF_22': $i > $i ).

tff(frontsegP,type,
    frontsegP: ( $i * $i ) > $o ).

tff('#skF_37',type,
    '#skF_37': $i > $i ).

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

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

tff('#skF_40',type,
    '#skF_40': $i > $i ).

tff('#skF_48',type,
    '#skF_48': $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i ) > $i ).

tff('#skF_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_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_1019,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ( ( ~ neq(V,nil)
                          | ? [Y] :
                              ( ssList(Y)
                              & ( X != Y )
                              & ? [Z] :
                                  ( ssList(Z)
                                  & ( tl(X) = Z )
                                  & ( app(W,Z) = Y )
                                  & neq(nil,X) ) )
                          | neq(U,nil) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f_779,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssList(V)
            & ( tl(U) = V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).

tff(f_311,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> ( U != V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

tff(f_769,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssItem(V)
            & ( hd(U) = V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax75) ).

tff(f_371,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssItem(hd(U)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).

tff(f_385,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssList(tl(U)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).

tff(f_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(f_399,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).

tff(f_413,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(nil,U) = U ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

tff(f_803,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ( cons(hd(U),tl(U)) = U ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).

tff(f_327,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( cons(V,U) != U ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).

tff(c_388,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_390,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_4751,plain,
    ! [U_1493] :
      ( ( tl(U_1493) = '#skF_47'(U_1493) )
      | ( nil = U_1493 )
      | ~ ssList(U_1493) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_4864,plain,
    ( ( tl('#skF_50') = '#skF_47'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_390,c_4751]) ).

tff(c_5084,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_4864]) ).

tff(c_4861,plain,
    ( ( tl('#skF_51') = '#skF_47'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_4751]) ).

tff(c_4865,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_4861]) ).

tff(c_386,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_406,plain,
    neq('#skF_49',nil),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_411,plain,
    neq('#skF_51',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).

tff(c_4900,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_4865,c_411]) ).

tff(c_164,plain,
    ! [V_858] :
      ( ~ neq(V_858,V_858)
      | ~ ssList(V_858) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_4926,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_4900,c_164]) ).

tff(c_4931,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_4926]) ).

tff(c_4933,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_4861]) ).

tff(c_5085,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5084,c_4933]) ).

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_5145,plain,
    ! [U_1499] :
      ( ( hd(U_1499) = '#skF_46'(U_1499) )
      | ( U_1499 = '#skF_50' )
      | ~ ssList(U_1499) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5084,c_330]) ).

tff(c_5214,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_388,c_5145]) ).

tff(c_5242,plain,
    hd('#skF_51') = '#skF_46'('#skF_51'),
    inference(negUnitSimplification,[status(thm)],[c_5085,c_5214]) ).

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

tff(c_5692,plain,
    ! [U_1523] :
      ( ssItem(hd(U_1523))
      | ( U_1523 = '#skF_50' )
      | ~ ssList(U_1523) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5084,c_184]) ).

tff(c_5695,plain,
    ( ssItem('#skF_46'('#skF_51'))
    | ( '#skF_51' = '#skF_50' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_5242,c_5692]) ).

tff(c_5697,plain,
    ( ssItem('#skF_46'('#skF_51'))
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_5695]) ).

tff(c_5698,plain,
    ssItem('#skF_46'('#skF_51')),
    inference(negUnitSimplification,[status(thm)],[c_5085,c_5697]) ).

tff(c_4932,plain,
    tl('#skF_51') = '#skF_47'('#skF_51'),
    inference(splitRight,[status(thm)],[c_4861]) ).

tff(c_4279,plain,
    ! [U_1431] :
      ( ssList(tl(U_1431))
      | ( nil = U_1431 )
      | ~ ssList(U_1431) ),
    inference(cnfTransformation,[status(thm)],[f_385]) ).

tff(c_2587,plain,
    ! [U_1358] :
      ( ( hd(U_1358) = '#skF_46'(U_1358) )
      | ( nil = U_1358 )
      | ~ ssList(U_1358) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_2701,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_2587]) ).

tff(c_2705,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_2701]) ).

tff(c_2857,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_2705,c_411]) ).

tff(c_2922,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_2857,c_164]) ).

tff(c_2927,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_2922]) ).

tff(c_2929,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_2701]) ).

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

tff(c_4164,plain,
    ! [U_1412,V_1413] :
      ( neq(U_1412,V_1413)
      | ( V_1413 = U_1412 )
      | ~ ssList(V_1413)
      | ~ ssList(U_1412) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_772,plain,
    ! [U_1248] :
      ( ( hd(U_1248) = '#skF_46'(U_1248) )
      | ( nil = U_1248 )
      | ~ ssList(U_1248) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_874,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_772]) ).

tff(c_878,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_874]) ).

tff(c_908,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_878,c_411]) ).

tff(c_1144,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_908,c_164]) ).

tff(c_1149,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_1144]) ).

tff(c_1151,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_874]) ).

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

tff(c_1998,plain,
    ! [U_1287,V_1288] :
      ( ssList(app(U_1287,V_1288))
      | ~ ssList(V_1288)
      | ~ ssList(U_1287) ),
    inference(cnfTransformation,[status(thm)],[f_399]) ).

tff(c_398,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssList(tl('#skF_51'))
    | ( app('#skF_50',tl('#skF_51')) = '#skF_51' )
    | ~ ssList(app('#skF_50',tl('#skF_51')))
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_416,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssList(tl('#skF_51'))
    | ( app('#skF_50',tl('#skF_51')) = '#skF_51' )
    | ~ ssList(app('#skF_50',tl('#skF_51'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_398]) ).

tff(c_429,plain,
    ~ ssList(app('#skF_50',tl('#skF_51'))),
    inference(splitLeft,[status(thm)],[c_416]) ).

tff(c_2013,plain,
    ( ~ ssList(tl('#skF_51'))
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_1998,c_429]) ).

tff(c_2035,plain,
    ~ ssList(tl('#skF_51')),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_2013]) ).

tff(c_2048,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_188,c_2035]) ).

tff(c_2051,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_2048]) ).

tff(c_2053,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1151,c_2051]) ).

tff(c_2054,plain,
    ( ~ ssList(tl('#skF_51'))
    | ~ neq(nil,'#skF_51')
    | ( app('#skF_50',tl('#skF_51')) = '#skF_51' ) ),
    inference(splitRight,[status(thm)],[c_416]) ).

tff(c_2062,plain,
    ~ neq(nil,'#skF_51'),
    inference(splitLeft,[status(thm)],[c_2054]) ).

tff(c_4171,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_4164,c_2062]) ).

tff(c_4183,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_4171]) ).

tff(c_4185,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2929,c_4183]) ).

tff(c_4186,plain,
    ( ~ ssList(tl('#skF_51'))
    | ( app('#skF_50',tl('#skF_51')) = '#skF_51' ) ),
    inference(splitRight,[status(thm)],[c_2054]) ).

tff(c_4190,plain,
    ~ ssList(tl('#skF_51')),
    inference(splitLeft,[status(thm)],[c_4186]) ).

tff(c_4288,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_4279,c_4190]) ).

tff(c_4293,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_4288]) ).

tff(c_4317,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_4293,c_411]) ).

tff(c_4338,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_4317,c_164]) ).

tff(c_4343,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_4338]) ).

tff(c_4344,plain,
    app('#skF_50',tl('#skF_51')) = '#skF_51',
    inference(splitRight,[status(thm)],[c_4186]) ).

tff(c_4936,plain,
    app('#skF_50','#skF_47'('#skF_51')) = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_4932,c_4344]) ).

tff(c_4345,plain,
    ssList(tl('#skF_51')),
    inference(splitRight,[status(thm)],[c_4186]) ).

tff(c_4389,plain,
    ! [U_1442] :
      ( ( app(nil,U_1442) = U_1442 )
      | ~ ssList(U_1442) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_4402,plain,
    app(nil,tl('#skF_51')) = tl('#skF_51'),
    inference(resolution,[status(thm)],[c_4345,c_4389]) ).

tff(c_4935,plain,
    app(nil,'#skF_47'('#skF_51')) = '#skF_47'('#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_4932,c_4932,c_4402]) ).

tff(c_5282,plain,
    '#skF_47'('#skF_51') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_4936,c_5084,c_4935]) ).

tff(c_5285,plain,
    tl('#skF_51') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_5282,c_4932]) ).

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_6612,plain,
    ! [U_1581] :
      ( ( cons(hd(U_1581),tl(U_1581)) = U_1581 )
      | ( U_1581 = '#skF_50' )
      | ~ ssList(U_1581) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5084,c_340]) ).

tff(c_6643,plain,
    ( ( cons(hd('#skF_51'),'#skF_51') = '#skF_51' )
    | ( '#skF_51' = '#skF_50' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_5285,c_6612]) ).

tff(c_6652,plain,
    ( ( cons('#skF_46'('#skF_51'),'#skF_51') = '#skF_51' )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_5242,c_6643]) ).

tff(c_6653,plain,
    cons('#skF_46'('#skF_51'),'#skF_51') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_5085,c_6652]) ).

tff(c_170,plain,
    ! [V_864,U_862] :
      ( ( cons(V_864,U_862) != U_862 )
      | ~ ssItem(V_864)
      | ~ ssList(U_862) ),
    inference(cnfTransformation,[status(thm)],[f_327]) ).

tff(c_6673,plain,
    ( ~ ssItem('#skF_46'('#skF_51'))
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_6653,c_170]) ).

tff(c_6689,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_5698,c_6673]) ).

tff(c_6691,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_4864]) ).

tff(c_7166,plain,
    ! [U_1601,V_1602] :
      ( neq(U_1601,V_1602)
      | ( V_1602 = U_1601 )
      | ~ ssList(V_1602)
      | ~ ssList(U_1601) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_384,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_396,plain,
    ( ~ neq('#skF_48',nil)
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_414,plain,
    ~ neq('#skF_48',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_396]) ).

tff(c_418,plain,
    ~ neq('#skF_50',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_414]) ).

tff(c_7177,plain,
    ( ( nil = '#skF_50' )
    | ~ ssList(nil)
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_7166,c_418]) ).

tff(c_7184,plain,
    nil = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_168,c_7177]) ).

tff(c_7186,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6691,c_7184]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC204+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.35  % Computer : n021.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 21:40:22 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 10.53/3.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.53/3.38  
% 10.53/3.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.53/3.42  
% 10.53/3.42  Inference rules
% 10.53/3.42  ----------------------
% 10.53/3.42  #Ref     : 0
% 10.53/3.42  #Sup     : 1479
% 10.53/3.42  #Fact    : 0
% 10.53/3.42  #Define  : 0
% 10.53/3.42  #Split   : 33
% 10.53/3.42  #Chain   : 0
% 10.53/3.42  #Close   : 0
% 10.53/3.42  
% 10.53/3.42  Ordering : KBO
% 10.53/3.42  
% 10.53/3.42  Simplification rules
% 10.53/3.42  ----------------------
% 10.53/3.42  #Subsume      : 32
% 10.53/3.42  #Demod        : 787
% 10.53/3.42  #Tautology    : 392
% 10.53/3.42  #SimpNegUnit  : 43
% 10.53/3.42  #BackRed      : 331
% 10.53/3.42  
% 10.53/3.42  #Partial instantiations: 0
% 10.53/3.42  #Strategies tried      : 1
% 10.53/3.42  
% 10.53/3.42  Timing (in seconds)
% 10.53/3.42  ----------------------
% 10.53/3.42  Preprocessing        : 0.89
% 10.53/3.42  Parsing              : 0.41
% 10.53/3.42  CNF conversion       : 0.11
% 10.53/3.42  Main loop            : 1.45
% 10.53/3.42  Inferencing          : 0.48
% 10.53/3.42  Reduction            : 0.44
% 10.53/3.42  Demodulation         : 0.29
% 10.53/3.42  BG Simplification    : 0.09
% 10.53/3.42  Subsumption          : 0.30
% 10.53/3.42  Abstraction          : 0.06
% 10.53/3.42  MUC search           : 0.00
% 10.53/3.42  Cooper               : 0.00
% 10.53/3.42  Total                : 2.41
% 10.53/3.42  Index Insertion      : 0.00
% 10.53/3.42  Index Deletion       : 0.00
% 10.53/3.42  Index Matching       : 0.00
% 10.53/3.42  BG Taut test         : 0.00
%------------------------------------------------------------------------------