TSTP Solution File: SWC419+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC419+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 : n027.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 11:02:36 EDT 2023

% Result   : Theorem 17.82s 5.75s
% Output   : CNFRefutation 17.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   87
% Syntax   : Number of formulae    :  160 (  39 unt;  77 typ;   0 def)
%            Number of atoms       :  184 (  87 equ)
%            Maximal formula atoms :   19 (   2 avg)
%            Number of connectives :  190 (  89   ~;  73   |;   8   &)
%                                         (   1 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   58 (  58 usr;   9 con; 0-2 aty)
%            Number of variables   :   52 (;  48   !;   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_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_40',type,
    '#skF_40': $i > $i ).

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

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

tff('#skF_34',type,
    '#skF_34': $i > $i ).

tff('#skF_29',type,
    '#skF_29': $i > $i ).

tff('#skF_15',type,
    '#skF_15': $i > $i ).

tff('#skF_32',type,
    '#skF_32': $i > $i ).

tff('#skF_53',type,
    '#skF_53': $i ).

tff('#skF_51',type,
    '#skF_51': $i ).

tff('#skF_28',type,
    '#skF_28': $i > $i ).

tff('#skF_10',type,
    '#skF_10': $i > $i ).

tff('#skF_41',type,
    '#skF_41': $i > $i ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_38',type,
    '#skF_38': $i > $i ).

tff('#skF_43',type,
    '#skF_43': $i > $i ).

tff(hd,type,
    hd: $i > $i ).

tff(app,type,
    app: ( $i * $i ) > $i ).

tff('#skF_1',type,
    '#skF_1': $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

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

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

tff('#skF_39',type,
    '#skF_39': $i > $i ).

tff('#skF_23',type,
    '#skF_23': $i > $i ).

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

tff('#skF_33',type,
    '#skF_33': $i > $i ).

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

tff('#skF_26',type,
    '#skF_26': $i > $i ).

tff('#skF_50',type,
    '#skF_50': $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

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

tff(cons,type,
    cons: ( $i * $i ) > $i ).

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

tff('#skF_17',type,
    '#skF_17': $i > $i ).

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

tff('#skF_11',type,
    '#skF_11': $i > $i ).

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

tff('#skF_14',type,
    '#skF_14': $i > $i ).

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

tff(tl,type,
    tl: $i > $i ).

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

tff('#skF_27',type,
    '#skF_27': $i > $i ).

tff('#skF_12',type,
    '#skF_12': $i > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff('#skF_46',type,
    '#skF_46': $i > $i ).

tff(nil,type,
    nil: $i ).

tff('#skF_42',type,
    '#skF_42': $i > $i ).

tff('#skF_45',type,
    '#skF_45': $i > $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

tff('#skF_30',type,
    '#skF_30': $i > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': $i > $i ).

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

tff('#skF_47',type,
    '#skF_47': $i > $i ).

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

tff(f_1031,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ~ ssList(X)
                    | ( V != X )
                    | ( U != W )
                    | ~ neq(V,nil)
                    | ? [Y] :
                        ( ssItem(Y)
                        & ? [Z] :
                            ( ssList(Z)
                            & ? [X1] :
                                ( ssList(X1)
                                & ( app(app(Z,cons(Y,nil)),X1) = V )
                                & ( app(app(X1,cons(Y,nil)),Z) = U ) ) ) )
                    | ( ( nil != W )
                      & ( nil = X ) )
                    | ( ! [X2] :
                          ( ssItem(X2)
                         => ! [X3] :
                              ( ~ ssList(X3)
                              | ( app(cons(X2,nil),X3) != X )
                              | ( app(X3,cons(X2,nil)) != W ) ) )
                      & neq(X,nil) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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

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_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_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_413,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(nil,U) = U ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).

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

tff(c_392,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_388,plain,
    neq('#skF_49',nil),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_413,plain,
    neq('#skF_51',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_388]) ).

tff(c_404,plain,
    ( ( app(cons('#skF_52',nil),'#skF_53') = '#skF_51' )
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_421,plain,
    app(cons('#skF_52',nil),'#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_413,c_404]) ).

tff(c_396,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_492,plain,
    ! [U_1311] :
      ( ( app(U_1311,nil) = U_1311 )
      | ~ ssList(U_1311) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_508,plain,
    app('#skF_50',nil) = '#skF_50',
    inference(resolution,[status(thm)],[c_396,c_492]) ).

tff(c_408,plain,
    ( ssItem('#skF_52')
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_415,plain,
    ssItem('#skF_52'),
    inference(demodulation,[status(thm),theory(equality)],[c_413,c_408]) ).

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_406,plain,
    ( ssList('#skF_53')
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_419,plain,
    ssList('#skF_53'),
    inference(demodulation,[status(thm),theory(equality)],[c_413,c_406]) ).

tff(c_864,plain,
    ! [U_1362] :
      ( ( hd(U_1362) = '#skF_46'(U_1362) )
      | ( nil = U_1362 )
      | ~ ssList(U_1362) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_975,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( nil = '#skF_53' ) ),
    inference(resolution,[status(thm)],[c_419,c_864]) ).

tff(c_990,plain,
    nil = '#skF_53',
    inference(splitLeft,[status(thm)],[c_975]) ).

tff(c_1004,plain,
    app('#skF_50','#skF_53') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_990,c_508]) ).

tff(c_402,plain,
    ( ( app('#skF_53',cons('#skF_52',nil)) = '#skF_50' )
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_417,plain,
    app('#skF_53',cons('#skF_52',nil)) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_413,c_402]) ).

tff(c_390,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_386,plain,
    ! [X1_1289,Y_1283,Z_1287] :
      ( ( app(app(X1_1289,cons(Y_1283,nil)),Z_1287) != '#skF_48' )
      | ( app(app(Z_1287,cons(Y_1283,nil)),X1_1289) != '#skF_49' )
      | ~ ssList(X1_1289)
      | ~ ssList(Z_1287)
      | ~ ssItem(Y_1283) ),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_578,plain,
    ! [X1_1320,Y_1321,Z_1322] :
      ( ( app(app(X1_1320,cons(Y_1321,nil)),Z_1322) != '#skF_50' )
      | ( app(app(Z_1322,cons(Y_1321,nil)),X1_1320) != '#skF_51' )
      | ~ ssList(X1_1320)
      | ~ ssList(Z_1322)
      | ~ ssItem(Y_1321) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_390,c_386]) ).

tff(c_580,plain,
    ! [Z_1322] :
      ( ( app('#skF_50',Z_1322) != '#skF_50' )
      | ( app(app(Z_1322,cons('#skF_52',nil)),'#skF_53') != '#skF_51' )
      | ~ ssList('#skF_53')
      | ~ ssList(Z_1322)
      | ~ ssItem('#skF_52') ),
    inference(superposition,[status(thm),theory(equality)],[c_417,c_578]) ).

tff(c_624,plain,
    ! [Z_1332] :
      ( ( app('#skF_50',Z_1332) != '#skF_50' )
      | ( app(app(Z_1332,cons('#skF_52',nil)),'#skF_53') != '#skF_51' )
      | ~ ssList(Z_1332) ),
    inference(demodulation,[status(thm),theory(equality)],[c_415,c_419,c_580]) ).

tff(c_627,plain,
    ( ( app('#skF_50','#skF_53') != '#skF_50' )
    | ( app('#skF_50','#skF_53') != '#skF_51' )
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_417,c_624]) ).

tff(c_629,plain,
    ( ( app('#skF_50','#skF_53') != '#skF_50' )
    | ( app('#skF_50','#skF_53') != '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_419,c_627]) ).

tff(c_695,plain,
    app('#skF_50','#skF_53') != '#skF_51',
    inference(splitLeft,[status(thm)],[c_629]) ).

tff(c_2464,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_1004,c_695]) ).

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_6717,plain,
    ! [V_1627,U_1628] :
      ( ( app(cons(V_1627,'#skF_53'),U_1628) = cons(V_1627,U_1628) )
      | ~ ssItem(V_1627)
      | ~ ssList(U_1628) ),
    inference(demodulation,[status(thm),theory(equality)],[c_990,c_346]) ).

tff(c_1021,plain,
    app(cons('#skF_52','#skF_53'),'#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_990,c_421]) ).

tff(c_6768,plain,
    ( ( cons('#skF_52','#skF_53') = '#skF_51' )
    | ~ ssItem('#skF_52')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_6717,c_1021]) ).

tff(c_6790,plain,
    cons('#skF_52','#skF_53') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_419,c_415,c_6768]) ).

tff(c_1014,plain,
    app('#skF_53',cons('#skF_52','#skF_53')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_990,c_417]) ).

tff(c_6798,plain,
    app('#skF_53','#skF_51') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_6790,c_1014]) ).

tff(c_394,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1031]) ).

tff(c_458,plain,
    ! [U_1309] :
      ( ( app(nil,U_1309) = U_1309 )
      | ~ ssList(U_1309) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_474,plain,
    app(nil,'#skF_51') = '#skF_51',
    inference(resolution,[status(thm)],[c_394,c_458]) ).

tff(c_1007,plain,
    app('#skF_53','#skF_51') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_990,c_474]) ).

tff(c_6914,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_6798,c_1007]) ).

tff(c_6916,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2464,c_6914]) ).

tff(c_6918,plain,
    nil != '#skF_53',
    inference(splitRight,[status(thm)],[c_975]) ).

tff(c_6917,plain,
    hd('#skF_53') = '#skF_46'('#skF_53'),
    inference(splitRight,[status(thm)],[c_975]) ).

tff(c_976,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_396,c_864]) ).

tff(c_6929,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_976]) ).

tff(c_7068,plain,
    app('#skF_53',cons('#skF_52','#skF_50')) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_6929,c_417]) ).

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_8113,plain,
    ! [V_1686,U_1687] :
      ( ( V_1686 = '#skF_50' )
      | ( app(U_1687,V_1686) != '#skF_50' )
      | ~ ssList(V_1686)
      | ~ ssList(U_1687) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6929,c_6929,c_354]) ).

tff(c_8121,plain,
    ( ( cons('#skF_52','#skF_50') = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50'))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_7068,c_8113]) ).

tff(c_8142,plain,
    ( ( cons('#skF_52','#skF_50') = '#skF_50' )
    | ~ ssList(cons('#skF_52','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_419,c_8121]) ).

tff(c_8157,plain,
    ~ ssList(cons('#skF_52','#skF_50')),
    inference(splitLeft,[status(thm)],[c_8142]) ).

tff(c_8160,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_8157]) ).

tff(c_8164,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_415,c_8160]) ).

tff(c_8165,plain,
    cons('#skF_52','#skF_50') = '#skF_50',
    inference(splitRight,[status(thm)],[c_8142]) ).

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_7607,plain,
    ! [V_887,U_885] :
      ( ( cons(V_887,U_885) != '#skF_50' )
      | ~ ssItem(V_887)
      | ~ ssList(U_885) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6929,c_182]) ).

tff(c_8212,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_8165,c_7607]) ).

tff(c_8251,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_415,c_8212]) ).

tff(c_8252,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(splitRight,[status(thm)],[c_976]) ).

tff(c_14646,plain,
    ! [U_1952,V_1953] :
      ( ( hd(app(U_1952,V_1953)) = hd(U_1952) )
      | ( nil = U_1952 )
      | ~ ssList(V_1953)
      | ~ ssList(U_1952) ),
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_14856,plain,
    ( ( hd('#skF_53') = hd('#skF_50') )
    | ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil))
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_417,c_14646]) ).

tff(c_15058,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_53' )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_419,c_6917,c_8252,c_14856]) ).

tff(c_15059,plain,
    ( ( '#skF_46'('#skF_53') = '#skF_46'('#skF_50') )
    | ~ ssList(cons('#skF_52',nil)) ),
    inference(negUnitSimplification,[status(thm)],[c_6918,c_15058]) ).

tff(c_15062,plain,
    ~ ssList(cons('#skF_52',nil)),
    inference(splitLeft,[status(thm)],[c_15059]) ).

tff(c_15065,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_166,c_15062]) ).

tff(c_15069,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_415,c_15065]) ).

tff(c_15071,plain,
    ssList(cons('#skF_52',nil)),
    inference(splitRight,[status(thm)],[c_15059]) ).

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

tff(c_15115,plain,
    app(nil,cons('#skF_52',nil)) = cons('#skF_52',nil),
    inference(resolution,[status(thm)],[c_15071,c_196]) ).

tff(c_582,plain,
    ! [Z_1322] :
      ( ( app('#skF_50',Z_1322) != '#skF_50' )
      | ( app(app(Z_1322,cons('#skF_52',nil)),'#skF_53') != '#skF_51' )
      | ~ ssList(Z_1322) ),
    inference(demodulation,[status(thm),theory(equality)],[c_415,c_419,c_580]) ).

tff(c_15422,plain,
    ( ( app('#skF_50',nil) != '#skF_50' )
    | ( app(cons('#skF_52',nil),'#skF_53') != '#skF_51' )
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_15115,c_582]) ).

tff(c_15441,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_421,c_508,c_15422]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC419+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
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 21:39:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 17.82/5.75  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.82/5.76  
% 17.82/5.76  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.82/5.80  
% 17.82/5.80  Inference rules
% 17.82/5.80  ----------------------
% 17.82/5.80  #Ref     : 0
% 17.82/5.80  #Sup     : 3401
% 17.82/5.80  #Fact    : 0
% 17.82/5.80  #Define  : 0
% 17.82/5.80  #Split   : 75
% 17.82/5.80  #Chain   : 0
% 17.82/5.80  #Close   : 0
% 17.82/5.80  
% 17.82/5.80  Ordering : KBO
% 17.82/5.80  
% 17.82/5.80  Simplification rules
% 17.82/5.80  ----------------------
% 17.82/5.80  #Subsume      : 487
% 17.82/5.80  #Demod        : 2485
% 17.82/5.80  #Tautology    : 1278
% 17.82/5.80  #SimpNegUnit  : 278
% 17.82/5.80  #BackRed      : 204
% 17.82/5.80  
% 17.82/5.80  #Partial instantiations: 0
% 17.82/5.80  #Strategies tried      : 1
% 17.82/5.80  
% 17.82/5.80  Timing (in seconds)
% 17.82/5.80  ----------------------
% 17.82/5.80  Preprocessing        : 1.33
% 17.82/5.80  Parsing              : 0.67
% 17.82/5.80  CNF conversion       : 0.17
% 17.82/5.80  Main loop            : 3.25
% 17.82/5.80  Inferencing          : 1.03
% 17.82/5.80  Reduction            : 1.11
% 17.82/5.80  Demodulation         : 0.79
% 17.82/5.80  BG Simplification    : 0.14
% 17.82/5.80  Subsumption          : 0.70
% 17.82/5.80  Abstraction          : 0.09
% 17.82/5.80  MUC search           : 0.00
% 17.82/5.80  Cooper               : 0.00
% 17.82/5.80  Total                : 4.65
% 17.82/5.80  Index Insertion      : 0.00
% 17.82/5.80  Index Deletion       : 0.00
% 17.82/5.80  Index Matching       : 0.00
% 17.82/5.80  BG Taut test         : 0.00
%------------------------------------------------------------------------------