TSTP Solution File: SWC389+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC389+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 : 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 11:02:26 EDT 2023

% Result   : Theorem 78.71s 61.52s
% Output   : CNFRefutation 78.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  176 (  44 unt;  78 typ;   0 def)
%            Number of atoms       :  211 (  70 equ)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives :  197 (  84   ~;  79   |;   9   &)
%                                         (   3 <=>;  22  =>;   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   :   51 (;  47   !;   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_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_1038,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 ) ) )
                    | ( segmentP(V,U)
                      & ( ~ neq(V,nil)
                        | singletonP(U) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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

tff(f_686,axiom,
    ! [U] :
      ( ssList(U)
     => segmentP(U,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).

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

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

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

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

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/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).

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(c_390,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

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

tff(c_422,plain,
    ( ssList('#skF_54')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_443,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_422]) ).

tff(c_408,plain,
    ( ssList('#skF_54')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_459,plain,
    ( ssList('#skF_54')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_408]) ).

tff(c_460,plain,
    '#skF_51' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_459]) ).

tff(c_424,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_477,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_460,c_424]) ).

tff(c_478,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_477]) ).

tff(c_274,plain,
    ! [U_1030] :
      ( segmentP(U_1030,nil)
      | ~ ssList(U_1030) ),
    inference(cnfTransformation,[status(thm)],[f_686]) ).

tff(c_491,plain,
    ! [U_1030] :
      ( segmentP(U_1030,'#skF_50')
      | ~ ssList(U_1030) ),
    inference(demodulation,[status(thm),theory(equality)],[c_478,c_274]) ).

tff(c_384,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_386,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_398,plain,
    ( neq('#skF_49',nil)
    | ~ segmentP('#skF_49','#skF_48') ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_428,plain,
    ( neq('#skF_51',nil)
    | ~ segmentP('#skF_51','#skF_48') ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_386,c_398]) ).

tff(c_433,plain,
    ( neq('#skF_51',nil)
    | ~ segmentP('#skF_51','#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_428]) ).

tff(c_519,plain,
    ( neq('#skF_50','#skF_50')
    | ~ segmentP('#skF_50','#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_460,c_478,c_460,c_433]) ).

tff(c_520,plain,
    ~ segmentP('#skF_50','#skF_50'),
    inference(splitLeft,[status(thm)],[c_519]) ).

tff(c_523,plain,
    ~ ssList('#skF_50'),
    inference(resolution,[status(thm)],[c_491,c_520]) ).

tff(c_530,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_523]) ).

tff(c_531,plain,
    neq('#skF_50','#skF_50'),
    inference(splitRight,[status(thm)],[c_519]) ).

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

tff(c_538,plain,
    ~ ssList('#skF_50'),
    inference(resolution,[status(thm)],[c_531,c_164]) ).

tff(c_543,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_538]) ).

tff(c_545,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_477]) ).

tff(c_469,plain,
    nil = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_460,c_443]) ).

tff(c_550,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_545,c_469]) ).

tff(c_552,plain,
    '#skF_51' != '#skF_50',
    inference(splitRight,[status(thm)],[c_459]) ).

tff(c_551,plain,
    ssList('#skF_54'),
    inference(splitRight,[status(thm)],[c_459]) ).

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

tff(c_609,plain,
    ! [U_1526] :
      ( ( app('#skF_51',U_1526) = U_1526 )
      | ~ ssList(U_1526) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_196]) ).

tff(c_624,plain,
    app('#skF_51','#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_390,c_609]) ).

tff(c_410,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_559,plain,
    ( ssList('#skF_53')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_410]) ).

tff(c_560,plain,
    ssList('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_552,c_559]) ).

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_1050,plain,
    ! [U_1580] :
      ( ( hd(U_1580) = '#skF_46'(U_1580) )
      | ( U_1580 = '#skF_51' )
      | ~ ssList(U_1580) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_330]) ).

tff(c_1159,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( '#skF_53' = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_560,c_1050]) ).

tff(c_1176,plain,
    '#skF_53' = '#skF_51',
    inference(splitLeft,[status(thm)],[c_1159]) ).

tff(c_404,plain,
    ( ( app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_668,plain,
    ( ( app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51' )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_404]) ).

tff(c_669,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_552,c_668]) ).

tff(c_1178,plain,
    app(app('#skF_51','#skF_50'),'#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1176,c_669]) ).

tff(c_1182,plain,
    app('#skF_50','#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_624,c_1178]) ).

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_2605,plain,
    ! [U_1632,V_1633] :
      ( ( U_1632 = '#skF_51' )
      | ( app(U_1632,V_1633) != '#skF_51' )
      | ~ ssList(V_1633)
      | ~ ssList(U_1632) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_443,c_352]) ).

tff(c_2607,plain,
    ( ( '#skF_51' = '#skF_50' )
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_1182,c_2605]) ).

tff(c_2620,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_551,c_2607]) ).

tff(c_2622,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_552,c_2620]) ).

tff(c_2624,plain,
    '#skF_53' != '#skF_51',
    inference(splitRight,[status(thm)],[c_1159]) ).

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_5731,plain,
    ! [U_1749,V_1750] :
      ( ( U_1749 = '#skF_51' )
      | ( app(U_1749,V_1750) != '#skF_51' )
      | ~ ssList(V_1750)
      | ~ ssList(U_1749) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_443,c_352]) ).

tff(c_5739,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_51' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_669,c_5731]) ).

tff(c_5762,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_51' )
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_551,c_5739]) ).

tff(c_5779,plain,
    ~ ssList(app('#skF_53','#skF_50')),
    inference(splitLeft,[status(thm)],[c_5762]) ).

tff(c_5782,plain,
    ( ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_5779]) ).

tff(c_5786,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_560,c_390,c_5782]) ).

tff(c_5787,plain,
    app('#skF_53','#skF_50') = '#skF_51',
    inference(splitRight,[status(thm)],[c_5762]) ).

tff(c_5730,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_443,c_443,c_352]) ).

tff(c_5792,plain,
    ( ( '#skF_53' = '#skF_51' )
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_5787,c_5730]) ).

tff(c_5800,plain,
    '#skF_53' = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_560,c_390,c_5792]) ).

tff(c_5802,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2624,c_5800]) ).

tff(c_5804,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_422]) ).

tff(c_5805,plain,
    ssList('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_5804,c_424]) ).

tff(c_5803,plain,
    ssList('#skF_54'),
    inference(splitRight,[status(thm)],[c_422]) ).

tff(c_418,plain,
    ( ( app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51' )
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_5983,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_5804,c_418]) ).

tff(c_194615,plain,
    ! [W_4845,U_4846,X_4847,V_4848] :
      ( segmentP(app(app(W_4845,U_4846),X_4847),V_4848)
      | ~ segmentP(U_4846,V_4848)
      | ~ ssList(X_4847)
      | ~ ssList(W_4845)
      | ~ ssList(V_4848)
      | ~ ssList(U_4846) ),
    inference(cnfTransformation,[status(thm)],[f_682]) ).

tff(c_194836,plain,
    ! [V_4848] :
      ( segmentP('#skF_51',V_4848)
      | ~ segmentP('#skF_50',V_4848)
      | ~ ssList('#skF_54')
      | ~ ssList('#skF_53')
      | ~ ssList(V_4848)
      | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_5983,c_194615]) ).

tff(c_195533,plain,
    ! [V_4854] :
      ( segmentP('#skF_51',V_4854)
      | ~ segmentP('#skF_50',V_4854)
      | ~ ssList(V_4854) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_5805,c_5803,c_194836]) ).

tff(c_396,plain,
    ( ~ singletonP('#skF_48')
    | ~ segmentP('#skF_49','#skF_48') ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_429,plain,
    ( ~ singletonP('#skF_48')
    | ~ segmentP('#skF_51','#skF_48') ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_396]) ).

tff(c_432,plain,
    ( ~ singletonP('#skF_50')
    | ~ segmentP('#skF_51','#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_384,c_429]) ).

tff(c_5817,plain,
    ~ segmentP('#skF_51','#skF_50'),
    inference(splitLeft,[status(thm)],[c_432]) ).

tff(c_195540,plain,
    ( ~ segmentP('#skF_50','#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_195533,c_5817]) ).

tff(c_195549,plain,
    ~ segmentP('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_195540]) ).

tff(c_195552,plain,
    ~ ssList('#skF_50'),
    inference(resolution,[status(thm)],[c_270,c_195549]) ).

tff(c_195556,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_195552]) ).

tff(c_195557,plain,
    ~ singletonP('#skF_50'),
    inference(splitRight,[status(thm)],[c_432]) ).

tff(c_426,plain,
    ( ssItem('#skF_52')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_5808,plain,
    ssItem('#skF_52'),
    inference(negUnitSimplification,[status(thm)],[c_5804,c_426]) ).

tff(c_420,plain,
    ( ( cons('#skF_52',nil) = '#skF_50' )
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1038]) ).

tff(c_5812,plain,
    cons('#skF_52',nil) = '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_5804,c_420]) ).

tff(c_205541,plain,
    ! [V_5280] :
      ( singletonP(cons(V_5280,nil))
      | ~ ssItem(V_5280)
      | ~ ssList(cons(V_5280,nil)) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_205551,plain,
    ( singletonP(cons('#skF_52',nil))
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_5812,c_205541]) ).

tff(c_205556,plain,
    singletonP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_5808,c_5812,c_205551]) ).

tff(c_205558,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_195557,c_205556]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC389+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
% 0.17/0.35  % 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 21:36:06 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 78.71/61.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.71/61.53  
% 78.71/61.53  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 78.97/61.56  
% 78.97/61.56  Inference rules
% 78.97/61.56  ----------------------
% 78.97/61.56  #Ref     : 24
% 78.97/61.56  #Sup     : 44815
% 78.97/61.56  #Fact    : 0
% 78.97/61.56  #Define  : 0
% 78.97/61.56  #Split   : 360
% 78.97/61.56  #Chain   : 0
% 78.97/61.56  #Close   : 0
% 78.97/61.56  
% 78.97/61.56  Ordering : KBO
% 78.97/61.56  
% 78.97/61.56  Simplification rules
% 78.97/61.56  ----------------------
% 78.97/61.56  #Subsume      : 6671
% 78.97/61.56  #Demod        : 42586
% 78.97/61.56  #Tautology    : 10497
% 78.97/61.56  #SimpNegUnit  : 5185
% 78.97/61.56  #BackRed      : 1042
% 78.97/61.56  
% 78.97/61.56  #Partial instantiations: 0
% 78.97/61.56  #Strategies tried      : 1
% 78.97/61.56  
% 78.97/61.56  Timing (in seconds)
% 78.97/61.56  ----------------------
% 78.97/61.57  Preprocessing        : 0.90
% 78.97/61.57  Parsing              : 0.41
% 78.97/61.57  CNF conversion       : 0.12
% 78.97/61.57  Main loop            : 59.58
% 78.97/61.57  Inferencing          : 9.79
% 78.97/61.57  Reduction            : 28.63
% 78.97/61.57  Demodulation         : 20.37
% 78.97/61.57  BG Simplification    : 0.33
% 78.97/61.57  Subsumption          : 15.67
% 78.97/61.57  Abstraction          : 0.53
% 78.97/61.57  MUC search           : 0.00
% 78.97/61.57  Cooper               : 0.00
% 78.97/61.57  Total                : 60.54
% 78.97/61.57  Index Insertion      : 0.00
% 78.97/61.57  Index Deletion       : 0.00
% 78.97/61.57  Index Matching       : 0.00
% 78.97/61.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------