TSTP Solution File: SWC181+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC181+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 : n025.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 11:01:30 EDT 2023

% Result   : Theorem 33.62s 18.67s
% Output   : CNFRefutation 33.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  168 (  36 unt;  77 typ;   0 def)
%            Number of atoms       :  271 (  25 equ)
%            Maximal formula atoms :   27 (   2 avg)
%            Number of connectives :  302 ( 122   ~; 117   |;  15   &)
%                                         (   4 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   4 avg)
%            Maximal term depth    :    5 (   2 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   :   91 (;  81   !;  10   ?;   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_1049,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ! [Y] :
                          ( ssList(Y)
                         => ! [Z] :
                              ( ssList(Z)
                             => ( ( app(app(Y,W),Z) != X )
                                | ~ strictorderedP(W)
                                | ? [X1] :
                                    ( ssItem(X1)
                                    & ? [X2] :
                                        ( ssList(X2)
                                        & ( app(X2,cons(X1,nil)) = Y )
                                        & ? [X3] :
                                            ( ssItem(X3)
                                            & ? [X4] :
                                                ( ssList(X4)
                                                & ( app(cons(X3,nil),X4) = W )
                                                & lt(X1,X3) ) ) ) )
                                | ? [X5] :
                                    ( ssItem(X5)
                                    & ? [X6] :
                                        ( ssList(X6)
                                        & ( app(cons(X5,nil),X6) = Z )
                                        & ? [X7] :
                                            ( ssItem(X7)
                                            & ? [X8] :
                                                ( ssList(X8)
                                                & ( app(X8,cons(X7,nil)) = W )
                                                & lt(X7,X5) ) ) ) ) ) ) )
                      | duplicatefreeP(U)
                      | ( ( nil != X )
                        & ( nil = W ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_281,axiom,
    ! [U] :
      ( ssList(U)
     => ( duplicatefreeP(U)
      <=> ! [V] :
            ( ssItem(V)
           => ! [W] :
                ( ssItem(W)
               => ! [X] :
                    ( ssList(X)
                   => ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( ( app(app(X,cons(V,Y)),cons(W,Z)) = U )
                             => ( V != W ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax13) ).

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_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_399,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).

tff(f_498,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( memberP(app(V,W),U)
              <=> ( memberP(V,U)
                  | memberP(W,U) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).

tff(f_844,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( app(app(U,V),W) = app(U,app(V,W)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).

tff(f_87,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( memberP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ? [X] :
                    ( ssList(X)
                    & ( app(W,cons(V,X)) = U ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).

tff(f_628,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ( rearsegP(U,V)
               => rearsegP(app(W,U),V) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax50) ).

tff(f_257,axiom,
    ! [U] :
      ( ssList(U)
     => ( strictorderedP(U)
      <=> ! [V] :
            ( ssItem(V)
           => ! [W] :
                ( ssItem(W)
               => ! [X] :
                    ( ssList(X)
                   => ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( ( app(app(X,cons(V,Y)),cons(W,Z)) = U )
                             => lt(V,W) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).

tff(f_461,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ( lt(U,V)
           => ~ lt(V,U) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax33) ).

tff(c_400,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1049]) ).

tff(c_386,plain,
    ~ duplicatefreeP('#skF_48'),
    inference(cnfTransformation,[status(thm)],[f_1049]) ).

tff(c_415,plain,
    ~ duplicatefreeP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_386]) ).

tff(c_406,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1049]) ).

tff(c_875,plain,
    ! [U_3180] :
      ( ( '#skF_36'(U_3180) = '#skF_35'(U_3180) )
      | duplicatefreeP(U_3180)
      | ~ ssList(U_3180) ),
    inference(cnfTransformation,[status(thm)],[f_281]) ).

tff(c_965,plain,
    ( ( '#skF_36'('#skF_50') = '#skF_35'('#skF_50') )
    | duplicatefreeP('#skF_50') ),
    inference(resolution,[status(thm)],[c_406,c_875]) ).

tff(c_998,plain,
    '#skF_36'('#skF_50') = '#skF_35'('#skF_50'),
    inference(negUnitSimplification,[status(thm)],[c_415,c_965]) ).

tff(c_144,plain,
    ! [U_679] :
      ( ssItem('#skF_36'(U_679))
      | duplicatefreeP(U_679)
      | ~ ssList(U_679) ),
    inference(cnfTransformation,[status(thm)],[f_281]) ).

tff(c_1002,plain,
    ( ssItem('#skF_35'('#skF_50'))
    | duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_998,c_144]) ).

tff(c_1006,plain,
    ( ssItem('#skF_35'('#skF_50'))
    | duplicatefreeP('#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_1002]) ).

tff(c_1007,plain,
    ssItem('#skF_35'('#skF_50')),
    inference(negUnitSimplification,[status(thm)],[c_415,c_1006]) ).

tff(c_138,plain,
    ! [U_679] :
      ( ssList('#skF_39'(U_679))
      | duplicatefreeP(U_679)
      | ~ ssList(U_679) ),
    inference(cnfTransformation,[status(thm)],[f_281]) ).

tff(c_140,plain,
    ! [U_679] :
      ( ssList('#skF_38'(U_679))
      | duplicatefreeP(U_679)
      | ~ ssList(U_679) ),
    inference(cnfTransformation,[status(thm)],[f_281]) ).

tff(c_142,plain,
    ! [U_679] :
      ( ssList('#skF_37'(U_679))
      | duplicatefreeP(U_679)
      | ~ ssList(U_679) ),
    inference(cnfTransformation,[status(thm)],[f_281]) ).

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_55379,plain,
    ! [U_4693] :
      ( ( app(app('#skF_37'(U_4693),cons('#skF_35'(U_4693),'#skF_38'(U_4693))),cons('#skF_36'(U_4693),'#skF_39'(U_4693))) = U_4693 )
      | duplicatefreeP(U_4693)
      | ~ ssList(U_4693) ),
    inference(cnfTransformation,[status(thm)],[f_281]) ).

tff(c_55464,plain,
    ( ( app(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50'))) = '#skF_50' )
    | duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_998,c_55379]) ).

tff(c_55468,plain,
    ( ( app(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50'))) = '#skF_50' )
    | duplicatefreeP('#skF_50') ),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_55464]) ).

tff(c_55469,plain,
    app(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50'))) = '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_415,c_55468]) ).

tff(c_272,plain,
    ! [W_1027,U_1015,X_1029,V_1023] :
      ( segmentP(app(app(W_1027,U_1015),X_1029),V_1023)
      | ~ segmentP(U_1015,V_1023)
      | ~ ssList(X_1029)
      | ~ ssList(W_1027)
      | ~ ssList(V_1023)
      | ~ ssList(U_1015) ),
    inference(cnfTransformation,[status(thm)],[f_682]) ).

tff(c_55486,plain,
    ! [V_1023] :
      ( segmentP('#skF_50',V_1023)
      | ~ segmentP(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')),V_1023)
      | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))
      | ~ ssList('#skF_37'('#skF_50'))
      | ~ ssList(V_1023)
      | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_55469,c_272]) ).

tff(c_55656,plain,
    ~ ssList(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),
    inference(splitLeft,[status(thm)],[c_55486]) ).

tff(c_55659,plain,
    ( ~ ssItem('#skF_35'('#skF_50'))
    | ~ ssList('#skF_38'('#skF_50')) ),
    inference(resolution,[status(thm)],[c_166,c_55656]) ).

tff(c_55662,plain,
    ~ ssList('#skF_38'('#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_1007,c_55659]) ).

tff(c_55665,plain,
    ( duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_140,c_55662]) ).

tff(c_55668,plain,
    duplicatefreeP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_55665]) ).

tff(c_55670,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_415,c_55668]) ).

tff(c_55672,plain,
    ssList(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),
    inference(splitRight,[status(thm)],[c_55486]) ).

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_218,plain,
    ! [W_940,U_934,V_938] :
      ( ~ memberP(W_940,U_934)
      | memberP(app(V_938,W_940),U_934)
      | ~ ssList(W_940)
      | ~ ssList(V_938)
      | ~ ssItem(U_934) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_55516,plain,
    ! [U_934] :
      ( ~ memberP(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')),U_934)
      | memberP('#skF_50',U_934)
      | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))
      | ~ ssList(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))))
      | ~ ssItem(U_934) ),
    inference(superposition,[status(thm),theory(equality)],[c_55469,c_218]) ).

tff(c_56018,plain,
    ~ ssList(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')))),
    inference(splitLeft,[status(thm)],[c_55516]) ).

tff(c_56139,plain,
    ( ~ ssList(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')))
    | ~ ssList('#skF_37'('#skF_50')) ),
    inference(resolution,[status(thm)],[c_192,c_56018]) ).

tff(c_56142,plain,
    ~ ssList('#skF_37'('#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_55672,c_56139]) ).

tff(c_56145,plain,
    ( duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_142,c_56142]) ).

tff(c_56148,plain,
    duplicatefreeP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_56145]) ).

tff(c_56150,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_415,c_56148]) ).

tff(c_56152,plain,
    ssList(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')))),
    inference(splitRight,[status(thm)],[c_55516]) ).

tff(c_348,plain,
    ! [U_1070,V_1074,W_1076] :
      ( ( app(app(U_1070,V_1074),W_1076) = app(U_1070,app(V_1074,W_1076)) )
      | ~ ssList(W_1076)
      | ~ ssList(V_1074)
      | ~ ssList(U_1070) ),
    inference(cnfTransformation,[status(thm)],[f_844]) ).

tff(c_55548,plain,
    ( ( app('#skF_37'('#skF_50'),app(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')),cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))) = '#skF_50' )
    | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))
    | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')))
    | ~ ssList('#skF_37'('#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_348,c_55469]) ).

tff(c_57775,plain,
    ( ( app('#skF_37'('#skF_50'),app(cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')),cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))) = '#skF_50' )
    | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))
    | ~ ssList('#skF_37'('#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_55672,c_55548]) ).

tff(c_57776,plain,
    ~ ssList('#skF_37'('#skF_50')),
    inference(splitLeft,[status(thm)],[c_57775]) ).

tff(c_57779,plain,
    ( duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_142,c_57776]) ).

tff(c_57782,plain,
    duplicatefreeP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_57779]) ).

tff(c_57784,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_415,c_57782]) ).

tff(c_57786,plain,
    ssList('#skF_37'('#skF_50')),
    inference(splitRight,[status(thm)],[c_57775]) ).

tff(c_12,plain,
    ! [W_27,V_19,X_29] :
      ( memberP(app(W_27,cons(V_19,X_29)),V_19)
      | ~ ssList(X_29)
      | ~ ssList(W_27)
      | ~ ssItem(V_19)
      | ~ ssList(app(W_27,cons(V_19,X_29))) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_258,plain,
    ! [W_1001,U_995,V_999] :
      ( rearsegP(app(W_1001,U_995),V_999)
      | ~ rearsegP(U_995,V_999)
      | ~ ssList(W_1001)
      | ~ ssList(V_999)
      | ~ ssList(U_995) ),
    inference(cnfTransformation,[status(thm)],[f_628]) ).

tff(c_55510,plain,
    ! [V_999] :
      ( rearsegP('#skF_50',V_999)
      | ~ rearsegP(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')),V_999)
      | ~ ssList(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))))
      | ~ ssList(V_999)
      | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_55469,c_258]) ).

tff(c_56701,plain,
    ! [V_999] :
      ( rearsegP('#skF_50',V_999)
      | ~ rearsegP(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')),V_999)
      | ~ ssList(V_999)
      | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56152,c_55510]) ).

tff(c_56702,plain,
    ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50'))),
    inference(splitLeft,[status(thm)],[c_56701]) ).

tff(c_57760,plain,
    ( ~ ssItem('#skF_35'('#skF_50'))
    | ~ ssList('#skF_39'('#skF_50')) ),
    inference(resolution,[status(thm)],[c_166,c_56702]) ).

tff(c_57763,plain,
    ~ ssList('#skF_39'('#skF_50')),
    inference(demodulation,[status(thm),theory(equality)],[c_1007,c_57760]) ).

tff(c_57766,plain,
    ( duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_138,c_57763]) ).

tff(c_57769,plain,
    duplicatefreeP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_57766]) ).

tff(c_57771,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_415,c_57769]) ).

tff(c_57773,plain,
    ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50'))),
    inference(splitRight,[status(thm)],[c_56701]) ).

tff(c_220,plain,
    ! [V_938,U_934,W_940] :
      ( ~ memberP(V_938,U_934)
      | memberP(app(V_938,W_940),U_934)
      | ~ ssList(W_940)
      | ~ ssList(V_938)
      | ~ ssItem(U_934) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_55513,plain,
    ! [U_934] :
      ( ~ memberP(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),U_934)
      | memberP('#skF_50',U_934)
      | ~ ssList(cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))
      | ~ ssList(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))))
      | ~ ssItem(U_934) ),
    inference(superposition,[status(thm),theory(equality)],[c_55469,c_220]) ).

tff(c_62791,plain,
    ! [U_4756] :
      ( ~ memberP(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),U_4756)
      | memberP('#skF_50',U_4756)
      | ~ ssItem(U_4756) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56152,c_57773,c_55513]) ).

tff(c_62795,plain,
    ( memberP('#skF_50','#skF_35'('#skF_50'))
    | ~ ssList('#skF_38'('#skF_50'))
    | ~ ssList('#skF_37'('#skF_50'))
    | ~ ssItem('#skF_35'('#skF_50'))
    | ~ ssList(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50')))) ),
    inference(resolution,[status(thm)],[c_12,c_62791]) ).

tff(c_62806,plain,
    ( memberP('#skF_50','#skF_35'('#skF_50'))
    | ~ ssList('#skF_38'('#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56152,c_1007,c_57786,c_62795]) ).

tff(c_62813,plain,
    ~ ssList('#skF_38'('#skF_50')),
    inference(splitLeft,[status(thm)],[c_62806]) ).

tff(c_62816,plain,
    ( duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_140,c_62813]) ).

tff(c_62819,plain,
    duplicatefreeP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_62816]) ).

tff(c_62821,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_415,c_62819]) ).

tff(c_62823,plain,
    ssList('#skF_38'('#skF_50')),
    inference(splitRight,[status(thm)],[c_62806]) ).

tff(c_392,plain,
    strictorderedP('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1049]) ).

tff(c_59218,plain,
    ! [V_4725,Y_4727,W_4724,X_4723,Z_4726] :
      ( lt(V_4725,W_4724)
      | ~ ssList(Z_4726)
      | ~ ssList(Y_4727)
      | ~ ssList(X_4723)
      | ~ ssItem(W_4724)
      | ~ ssItem(V_4725)
      | ~ strictorderedP(app(app(X_4723,cons(V_4725,Y_4727)),cons(W_4724,Z_4726)))
      | ~ ssList(app(app(X_4723,cons(V_4725,Y_4727)),cons(W_4724,Z_4726))) ),
    inference(cnfTransformation,[status(thm)],[f_257]) ).

tff(c_59230,plain,
    ( lt('#skF_35'('#skF_50'),'#skF_35'('#skF_50'))
    | ~ ssList('#skF_39'('#skF_50'))
    | ~ ssList('#skF_38'('#skF_50'))
    | ~ ssList('#skF_37'('#skF_50'))
    | ~ ssItem('#skF_35'('#skF_50'))
    | ~ ssItem('#skF_35'('#skF_50'))
    | ~ strictorderedP('#skF_50')
    | ~ ssList(app(app('#skF_37'('#skF_50'),cons('#skF_35'('#skF_50'),'#skF_38'('#skF_50'))),cons('#skF_35'('#skF_50'),'#skF_39'('#skF_50')))) ),
    inference(superposition,[status(thm),theory(equality)],[c_55469,c_59218]) ).

tff(c_59357,plain,
    ( lt('#skF_35'('#skF_50'),'#skF_35'('#skF_50'))
    | ~ ssList('#skF_39'('#skF_50'))
    | ~ ssList('#skF_38'('#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_55469,c_392,c_1007,c_1007,c_57786,c_59230]) ).

tff(c_72353,plain,
    ( lt('#skF_35'('#skF_50'),'#skF_35'('#skF_50'))
    | ~ ssList('#skF_39'('#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_62823,c_59357]) ).

tff(c_72354,plain,
    ~ ssList('#skF_39'('#skF_50')),
    inference(splitLeft,[status(thm)],[c_72353]) ).

tff(c_72357,plain,
    ( duplicatefreeP('#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_138,c_72354]) ).

tff(c_72360,plain,
    duplicatefreeP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_72357]) ).

tff(c_72362,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_415,c_72360]) ).

tff(c_72363,plain,
    lt('#skF_35'('#skF_50'),'#skF_35'('#skF_50')),
    inference(splitRight,[status(thm)],[c_72353]) ).

tff(c_208,plain,
    ! [V_923,U_921] :
      ( ~ lt(V_923,U_921)
      | ~ lt(U_921,V_923)
      | ~ ssItem(V_923)
      | ~ ssItem(U_921) ),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_72503,plain,
    ( ~ lt('#skF_35'('#skF_50'),'#skF_35'('#skF_50'))
    | ~ ssItem('#skF_35'('#skF_50')) ),
    inference(resolution,[status(thm)],[c_72363,c_208]) ).

tff(c_72533,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1007,c_72363,c_72503]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWC181+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
% 0.15/0.36  % Computer : n025.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 21:28:34 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 33.62/18.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.62/18.68  
% 33.62/18.68  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.62/18.72  
% 33.62/18.72  Inference rules
% 33.62/18.72  ----------------------
% 33.62/18.72  #Ref     : 5
% 33.62/18.72  #Sup     : 15986
% 33.62/18.72  #Fact    : 0
% 33.62/18.72  #Define  : 0
% 33.62/18.72  #Split   : 199
% 33.62/18.72  #Chain   : 0
% 33.62/18.72  #Close   : 0
% 33.62/18.72  
% 33.62/18.72  Ordering : KBO
% 33.62/18.72  
% 33.62/18.72  Simplification rules
% 33.62/18.72  ----------------------
% 33.62/18.72  #Subsume      : 3079
% 33.62/18.72  #Demod        : 14556
% 33.62/18.72  #Tautology    : 4071
% 33.62/18.72  #SimpNegUnit  : 1280
% 33.62/18.72  #BackRed      : 527
% 33.62/18.72  
% 33.62/18.72  #Partial instantiations: 0
% 33.62/18.72  #Strategies tried      : 1
% 33.62/18.72  
% 33.62/18.72  Timing (in seconds)
% 33.62/18.72  ----------------------
% 33.62/18.73  Preprocessing        : 0.92
% 33.62/18.73  Parsing              : 0.42
% 33.62/18.73  CNF conversion       : 0.14
% 33.62/18.73  Main loop            : 16.66
% 33.62/18.73  Inferencing          : 3.38
% 33.62/18.73  Reduction            : 7.53
% 33.62/18.73  Demodulation         : 5.60
% 33.62/18.73  BG Simplification    : 0.17
% 33.62/18.73  Subsumption          : 4.18
% 33.62/18.73  Abstraction          : 0.23
% 33.62/18.73  MUC search           : 0.00
% 33.62/18.73  Cooper               : 0.00
% 33.62/18.73  Total                : 17.65
% 33.62/18.73  Index Insertion      : 0.00
% 33.62/18.73  Index Deletion       : 0.00
% 33.62/18.73  Index Matching       : 0.00
% 33.62/18.73  BG Taut test         : 0.00
%------------------------------------------------------------------------------