TSTP Solution File: SWC109+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC109+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 : n024.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 11:01:12 EDT 2023

% Result   : Theorem 233.27s 208.85s
% Output   : CNFRefutation 233.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   89
% Syntax   : Number of formulae    :  192 (  55 unt;  78 typ;   0 def)
%            Number of atoms       :  240 (  99 equ)
%            Maximal formula atoms :   24 (   2 avg)
%            Number of connectives :  222 (  96   ~;  92   |;   9   &)
%                                         (   2 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   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    :   59 (  59 usr;  10 con; 0-2 aty)
%            Number of variables   :   56 (;  53   !;   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_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_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_1043,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)
                                  | ( cons(Y,nil) != W )
                                  | ( app(app(Z,W),X1) != X )
                                  | ? [X2] :
                                      ( ssItem(X2)
                                      & memberP(Z,X2)
                                      & lt(Y,X2) )
                                  | ? [X3] :
                                      ( ssItem(X3)
                                      & memberP(X1,X3)
                                      & lt(X3,Y) ) ) ) )
                      & ( ( nil != X )
                        | ( nil != W ) ) )
                    | ( ( ( nil != V )
                        | ( nil = U ) )
                      & ( ~ neq(V,nil)
                        | ( neq(U,nil)
                          & segmentP(V,U) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f_667,axiom,
    ! [U] :
      ( ssList(U)
     => segmentP(U,U) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).

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_859,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(U,nil) = U ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).

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_413,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(nil,U) = U ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

tff(f_855,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( nil = app(U,V) )
          <=> ( ( nil = V )
              & ( nil = U ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).

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_327,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( cons(V,U) != U ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).

tff(f_682,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( segmentP(U,V)
                   => segmentP(app(app(W,U),X),V) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).

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

tff(c_390,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_270,plain,
    ! [U_1014] :
      ( segmentP(U_1014,U_1014)
      | ~ ssList(U_1014) ),
    inference(cnfTransformation,[status(thm)],[f_667]) ).

tff(c_412,plain,
    ( ssList('#skF_54')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_5931,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_412]) ).

tff(c_414,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_484,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_414]) ).

tff(c_426,plain,
    ( ssList('#skF_54')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_450,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_426]) ).

tff(c_416,plain,
    ( ssItem('#skF_52')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_466,plain,
    ( ssItem('#skF_52')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_416]) ).

tff(c_467,plain,
    '#skF_51' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_466]) ).

tff(c_384,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_386,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_400,plain,
    ( ( nil != '#skF_48' )
    | neq('#skF_49',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_433,plain,
    ( ( nil != '#skF_48' )
    | neq('#skF_51',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_400]) ).

tff(c_438,plain,
    ( ( nil != '#skF_50' )
    | neq('#skF_51',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_433]) ).

tff(c_505,plain,
    neq('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_484,c_467,c_484,c_438]) ).

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

tff(c_511,plain,
    ~ ssList('#skF_50'),
    inference(resolution,[status(thm)],[c_505,c_164]) ).

tff(c_516,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_511]) ).

tff(c_518,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_414]) ).

tff(c_476,plain,
    nil = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_467,c_450]) ).

tff(c_523,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_518,c_476]) ).

tff(c_525,plain,
    '#skF_51' != '#skF_50',
    inference(splitRight,[status(thm)],[c_466]) ).

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

tff(c_551,plain,
    ! [U_1515] :
      ( ( app(U_1515,'#skF_51') = U_1515 )
      | ~ ssList(U_1515) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_356]) ).

tff(c_567,plain,
    app('#skF_50','#skF_51') = '#skF_50',
    inference(resolution,[status(thm)],[c_390,c_551]) ).

tff(c_526,plain,
    ( ssList('#skF_54')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_412]) ).

tff(c_527,plain,
    ssList('#skF_54'),
    inference(negUnitSimplification,[status(thm)],[c_525,c_526]) ).

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_1021,plain,
    ! [U_1572] :
      ( ( hd(U_1572) = '#skF_46'(U_1572) )
      | ( U_1572 = '#skF_51' )
      | ~ ssList(U_1572) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_330]) ).

tff(c_1131,plain,
    ( ( hd('#skF_54') = '#skF_46'('#skF_54') )
    | ( '#skF_54' = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_527,c_1021]) ).

tff(c_1188,plain,
    '#skF_54' = '#skF_51',
    inference(splitLeft,[status(thm)],[c_1131]) ).

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

tff(c_605,plain,
    ! [U_1518] :
      ( ( app('#skF_51',U_1518) = U_1518 )
      | ~ ssList(U_1518) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_196]) ).

tff(c_622,plain,
    app('#skF_51','#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_390,c_605]) ).

tff(c_528,plain,
    ( ssList('#skF_53')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_414]) ).

tff(c_529,plain,
    ssList('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_525,c_528]) ).

tff(c_1130,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( '#skF_53' = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_529,c_1021]) ).

tff(c_1147,plain,
    '#skF_53' = '#skF_51',
    inference(splitLeft,[status(thm)],[c_1130]) ).

tff(c_408,plain,
    ( ( app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_635,plain,
    ( ( app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51' )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_408]) ).

tff(c_636,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_525,c_635]) ).

tff(c_1167,plain,
    app(app('#skF_51','#skF_50'),'#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1147,c_636]) ).

tff(c_1171,plain,
    app('#skF_50','#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_622,c_1167]) ).

tff(c_1190,plain,
    app('#skF_50','#skF_51') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1188,c_1171]) ).

tff(c_1195,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_567,c_1190]) ).

tff(c_1197,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_525,c_1195]) ).

tff(c_1199,plain,
    '#skF_54' != '#skF_51',
    inference(splitRight,[status(thm)],[c_1131]) ).

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_2252,plain,
    ! [V_1614,U_1615] :
      ( ( V_1614 = '#skF_51' )
      | ( app(U_1615,V_1614) != '#skF_51' )
      | ~ ssList(V_1614)
      | ~ ssList(U_1615) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_450,c_354]) ).

tff(c_2258,plain,
    ( ( '#skF_54' = '#skF_51' )
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_1171,c_2252]) ).

tff(c_2276,plain,
    '#skF_54' = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_527,c_2258]) ).

tff(c_2278,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1199,c_2276]) ).

tff(c_2280,plain,
    '#skF_53' != '#skF_51',
    inference(splitRight,[status(thm)],[c_1130]) ).

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_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_5866,plain,
    ! [U_1742,V_1743] :
      ( ( U_1742 = '#skF_51' )
      | ( app(U_1742,V_1743) != '#skF_51' )
      | ~ ssList(V_1743)
      | ~ ssList(U_1742) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_450,c_352]) ).

tff(c_5868,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_51' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_636,c_5866]) ).

tff(c_5885,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_51' )
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_527,c_5868]) ).

tff(c_5905,plain,
    ~ ssList(app('#skF_53','#skF_50')),
    inference(splitLeft,[status(thm)],[c_5885]) ).

tff(c_5908,plain,
    ( ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_5905]) ).

tff(c_5912,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_529,c_390,c_5908]) ).

tff(c_5913,plain,
    app('#skF_53','#skF_50') = '#skF_51',
    inference(splitRight,[status(thm)],[c_5885]) ).

tff(c_5865,plain,
    ! [U_1077,V_1079] :
      ( ( U_1077 = '#skF_51' )
      | ( app(U_1077,V_1079) != '#skF_51' )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(demodulation,[status(thm),theory(equality)],[c_450,c_450,c_352]) ).

tff(c_5918,plain,
    ( ( '#skF_53' = '#skF_51' )
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_5913,c_5865]) ).

tff(c_5926,plain,
    '#skF_53' = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_529,c_390,c_5918]) ).

tff(c_5928,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2280,c_5926]) ).

tff(c_5930,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_426]) ).

tff(c_5932,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_5931,c_5930]) ).

tff(c_430,plain,
    ( ssItem('#skF_52')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_5950,plain,
    ( ssItem('#skF_52')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5931,c_430]) ).

tff(c_5951,plain,
    ssItem('#skF_52'),
    inference(negUnitSimplification,[status(thm)],[c_5932,c_5950]) ).

tff(c_424,plain,
    ( ( cons('#skF_52',nil) = '#skF_50' )
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_5972,plain,
    ( ( cons('#skF_52','#skF_50') = '#skF_50' )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5931,c_5931,c_424]) ).

tff(c_5973,plain,
    cons('#skF_52','#skF_50') = '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_5932,c_5972]) ).

tff(c_6526,plain,
    ! [V_1812,U_1813] :
      ( ( cons(V_1812,U_1813) != U_1813 )
      | ~ ssItem(V_1812)
      | ~ ssList(U_1813) ),
    inference(cnfTransformation,[status(thm)],[f_327]) ).

tff(c_6528,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_5973,c_6526]) ).

tff(c_6532,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_5951,c_6528]) ).

tff(c_6534,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_412]) ).

tff(c_6536,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_414]) ).

tff(c_6537,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6534,c_6536]) ).

tff(c_6538,plain,
    ssList('#skF_53'),
    inference(splitRight,[status(thm)],[c_414]) ).

tff(c_5929,plain,
    ssList('#skF_54'),
    inference(splitRight,[status(thm)],[c_426]) ).

tff(c_6601,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_6534,c_408]) ).

tff(c_350099,plain,
    ! [W_6647,U_6648,X_6649,V_6650] :
      ( segmentP(app(app(W_6647,U_6648),X_6649),V_6650)
      | ~ segmentP(U_6648,V_6650)
      | ~ ssList(X_6649)
      | ~ ssList(W_6647)
      | ~ ssList(V_6650)
      | ~ ssList(U_6648) ),
    inference(cnfTransformation,[status(thm)],[f_682]) ).

tff(c_350332,plain,
    ! [V_6650] :
      ( segmentP('#skF_51',V_6650)
      | ~ segmentP('#skF_50',V_6650)
      | ~ ssList('#skF_54')
      | ~ ssList('#skF_53')
      | ~ ssList(V_6650)
      | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_6601,c_350099]) ).

tff(c_350500,plain,
    ! [V_6651] :
      ( segmentP('#skF_51',V_6651)
      | ~ segmentP('#skF_50',V_6651)
      | ~ ssList(V_6651) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_6538,c_5929,c_350332]) ).

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

tff(c_10240,plain,
    ! [U_1986,V_1987] :
      ( neq(U_1986,V_1987)
      | ( V_1987 = U_1986 )
      | ~ ssList(V_1987)
      | ~ ssList(U_1986) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_398,plain,
    ( ( nil = '#skF_49' )
    | ~ segmentP('#skF_49','#skF_48')
    | ~ neq('#skF_48',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1043]) ).

tff(c_434,plain,
    ( ( nil = '#skF_51' )
    | ~ segmentP('#skF_51','#skF_48')
    | ~ neq('#skF_48',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_386,c_398]) ).

tff(c_440,plain,
    ( ( nil = '#skF_51' )
    | ~ segmentP('#skF_51','#skF_50')
    | ~ neq('#skF_50',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_384,c_434]) ).

tff(c_6975,plain,
    ( ~ segmentP('#skF_51','#skF_50')
    | ~ neq('#skF_50',nil) ),
    inference(negUnitSimplification,[status(thm)],[c_5930,c_440]) ).

tff(c_6976,plain,
    ~ neq('#skF_50',nil),
    inference(splitLeft,[status(thm)],[c_6975]) ).

tff(c_10243,plain,
    ( ( nil = '#skF_50' )
    | ~ ssList(nil)
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_10240,c_6976]) ).

tff(c_10254,plain,
    nil = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_168,c_10243]) ).

tff(c_10256,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6534,c_10254]) ).

tff(c_10257,plain,
    ~ segmentP('#skF_51','#skF_50'),
    inference(splitRight,[status(thm)],[c_6975]) ).

tff(c_350507,plain,
    ( ~ segmentP('#skF_50','#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_350500,c_10257]) ).

tff(c_350516,plain,
    ~ segmentP('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_350507]) ).

tff(c_350519,plain,
    ~ ssList('#skF_50'),
    inference(resolution,[status(thm)],[c_270,c_350516]) ).

tff(c_350523,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_350519]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : SWC109+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15  % 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
% 0.15/0.36  % Computer : n024.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 21:22:30 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 233.27/208.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 233.38/208.86  
% 233.38/208.86  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 233.38/208.90  
% 233.38/208.90  Inference rules
% 233.38/208.90  ----------------------
% 233.38/208.90  #Ref     : 30
% 233.38/208.90  #Sup     : 75592
% 233.38/208.90  #Fact    : 0
% 233.38/208.90  #Define  : 0
% 233.38/208.90  #Split   : 443
% 233.38/208.90  #Chain   : 0
% 233.38/208.90  #Close   : 0
% 233.38/208.90  
% 233.38/208.90  Ordering : KBO
% 233.38/208.90  
% 233.38/208.90  Simplification rules
% 233.38/208.90  ----------------------
% 233.38/208.90  #Subsume      : 13054
% 233.38/208.90  #Demod        : 93216
% 233.38/208.90  #Tautology    : 12065
% 233.38/208.90  #SimpNegUnit  : 8093
% 233.38/208.90  #BackRed      : 1032
% 233.38/208.90  
% 233.38/208.90  #Partial instantiations: 0
% 233.38/208.90  #Strategies tried      : 1
% 233.38/208.90  
% 233.38/208.90  Timing (in seconds)
% 233.38/208.90  ----------------------
% 233.38/208.90  Preprocessing        : 0.87
% 233.38/208.90  Parsing              : 0.41
% 233.38/208.90  CNF conversion       : 0.11
% 233.38/208.90  Main loop            : 206.94
% 233.38/208.90  Inferencing          : 22.50
% 233.38/208.90  Reduction            : 102.60
% 233.38/208.90  Demodulation         : 73.04
% 233.38/208.90  BG Simplification    : 0.57
% 233.38/208.90  Subsumption          : 63.89
% 233.38/208.90  Abstraction          : 1.12
% 233.38/208.90  MUC search           : 0.00
% 233.38/208.90  Cooper               : 0.00
% 233.38/208.90  Total                : 207.88
% 233.38/208.90  Index Insertion      : 0.00
% 233.38/208.90  Index Deletion       : 0.00
% 233.38/208.90  Index Matching       : 0.00
% 233.38/208.90  BG Taut test         : 0.00
%------------------------------------------------------------------------------