TSTP Solution File: SWC248+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC248+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n002.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 : Thu Aug 31 20:21:05 EDT 2023

% Result   : Theorem 38.66s 38.81s
% Output   : CNFRefutation 38.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :  102
% Syntax   : Number of formulae    :  220 (  38 unt;  78 typ;   0 def)
%            Number of atoms       :  536 ( 165 equ)
%            Maximal formula atoms :   52 (   3 avg)
%            Number of connectives :  660 ( 266   ~; 270   |;  61   &)
%                                         (   3 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   37 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   88 (  69   >;  19   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   59 (  59 usr;   9 con; 0-3 aty)
%            Number of variables   :  234 (   0 sgn; 112   !;  24   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ssItem: $i > $o ).

tff(decl_23,type,
    neq: ( $i * $i ) > $o ).

tff(decl_24,type,
    ssList: $i > $o ).

tff(decl_25,type,
    memberP: ( $i * $i ) > $o ).

tff(decl_26,type,
    cons: ( $i * $i ) > $i ).

tff(decl_27,type,
    app: ( $i * $i ) > $i ).

tff(decl_28,type,
    singletonP: $i > $o ).

tff(decl_29,type,
    nil: $i ).

tff(decl_30,type,
    frontsegP: ( $i * $i ) > $o ).

tff(decl_31,type,
    rearsegP: ( $i * $i ) > $o ).

tff(decl_32,type,
    segmentP: ( $i * $i ) > $o ).

tff(decl_33,type,
    cyclefreeP: $i > $o ).

tff(decl_34,type,
    leq: ( $i * $i ) > $o ).

tff(decl_35,type,
    totalorderP: $i > $o ).

tff(decl_36,type,
    strictorderP: $i > $o ).

tff(decl_37,type,
    lt: ( $i * $i ) > $o ).

tff(decl_38,type,
    totalorderedP: $i > $o ).

tff(decl_39,type,
    strictorderedP: $i > $o ).

tff(decl_40,type,
    duplicatefreeP: $i > $o ).

tff(decl_41,type,
    equalelemsP: $i > $o ).

tff(decl_42,type,
    hd: $i > $i ).

tff(decl_43,type,
    tl: $i > $i ).

tff(decl_44,type,
    geq: ( $i * $i ) > $o ).

tff(decl_45,type,
    gt: ( $i * $i ) > $o ).

tff(decl_46,type,
    esk1_0: $i ).

tff(decl_47,type,
    esk2_0: $i ).

tff(decl_48,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk5_1: $i > $i ).

tff(decl_51,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk10_1: $i > $i ).

tff(decl_56,type,
    esk11_1: $i > $i ).

tff(decl_57,type,
    esk12_1: $i > $i ).

tff(decl_58,type,
    esk13_1: $i > $i ).

tff(decl_59,type,
    esk14_1: $i > $i ).

tff(decl_60,type,
    esk15_1: $i > $i ).

tff(decl_61,type,
    esk16_1: $i > $i ).

tff(decl_62,type,
    esk17_1: $i > $i ).

tff(decl_63,type,
    esk18_1: $i > $i ).

tff(decl_64,type,
    esk19_1: $i > $i ).

tff(decl_65,type,
    esk20_1: $i > $i ).

tff(decl_66,type,
    esk21_1: $i > $i ).

tff(decl_67,type,
    esk22_1: $i > $i ).

tff(decl_68,type,
    esk23_1: $i > $i ).

tff(decl_69,type,
    esk24_1: $i > $i ).

tff(decl_70,type,
    esk25_1: $i > $i ).

tff(decl_71,type,
    esk26_1: $i > $i ).

tff(decl_72,type,
    esk27_1: $i > $i ).

tff(decl_73,type,
    esk28_1: $i > $i ).

tff(decl_74,type,
    esk29_1: $i > $i ).

tff(decl_75,type,
    esk30_1: $i > $i ).

tff(decl_76,type,
    esk31_1: $i > $i ).

tff(decl_77,type,
    esk32_1: $i > $i ).

tff(decl_78,type,
    esk33_1: $i > $i ).

tff(decl_79,type,
    esk34_1: $i > $i ).

tff(decl_80,type,
    esk35_1: $i > $i ).

tff(decl_81,type,
    esk36_1: $i > $i ).

tff(decl_82,type,
    esk37_1: $i > $i ).

tff(decl_83,type,
    esk38_1: $i > $i ).

tff(decl_84,type,
    esk39_1: $i > $i ).

tff(decl_85,type,
    esk40_1: $i > $i ).

tff(decl_86,type,
    esk41_1: $i > $i ).

tff(decl_87,type,
    esk42_1: $i > $i ).

tff(decl_88,type,
    esk43_1: $i > $i ).

tff(decl_89,type,
    esk44_1: $i > $i ).

tff(decl_90,type,
    esk45_1: $i > $i ).

tff(decl_91,type,
    esk46_1: $i > $i ).

tff(decl_92,type,
    esk47_1: $i > $i ).

tff(decl_93,type,
    esk48_0: $i ).

tff(decl_94,type,
    esk49_0: $i ).

tff(decl_95,type,
    esk50_0: $i ).

tff(decl_96,type,
    esk51_0: $i ).

tff(decl_97,type,
    esk52_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk53_0: $i ).

tff(decl_99,type,
    esk54_0: $i ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ~ ssList(X4)
                  | X2 != X4
                  | X1 != X3
                  | nil = X1
                  | ? [X5] :
                      ( ssItem(X5)
                      & ? [X6] :
                          ( ssList(X6)
                          & ? [X7] :
                              ( ssList(X7)
                              & app(app(X6,cons(X5,nil)),X7) = X1
                              & ! [X8] :
                                  ( ~ ssItem(X8)
                                  | ~ memberP(X6,X8)
                                  | ~ memberP(X7,X8)
                                  | ~ lt(X5,X8)
                                  | leq(X5,X8) ) ) ) )
                  | ! [X9] :
                      ( ssList(X9)
                     => ! [X10] :
                          ( ~ ssList(X10)
                          | app(app(X9,X3),X10) != X4
                          | ~ totalorderedP(X3)
                          | ? [X11] :
                              ( ssItem(X11)
                              & ? [X12] :
                                  ( ssList(X12)
                                  & app(X12,cons(X11,nil)) = X9
                                  & ? [X13] :
                                      ( ssItem(X13)
                                      & ? [X14] :
                                          ( ssList(X14)
                                          & app(cons(X13,nil),X14) = X3
                                          & leq(X11,X13) ) ) ) )
                          | ? [X15] :
                              ( ssItem(X15)
                              & ? [X16] :
                                  ( ssList(X16)
                                  & app(cons(X15,nil),X16) = X10
                                  & ? [X17] :
                                      ( ssItem(X17)
                                      & ? [X18] :
                                          ( ssList(X18)
                                          & app(X18,cons(X17,nil)) = X3
                                          & leq(X17,X15) ) ) ) ) ) )
                  | ( nil != X4
                    & nil = X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax43,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( frontsegP(X1,X2)
               => frontsegP(app(X1,X3),X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).

fof(ax42,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).

fof(ax82,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).

fof(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).

fof(ax5,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).

fof(ax80,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X2,X3) = app(X2,X1)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).

fof(ax50,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( rearsegP(X1,X2)
               => rearsegP(app(X3,X1),X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax50) ).

fof(ax51,axiom,
    ! [X1] :
      ( ssList(X1)
     => rearsegP(X1,nil) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax51) ).

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

fof(ax6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( rearsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).

fof(ax28,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).

fof(ax79,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X3,X2) = app(X1,X2)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).

fof(ax83,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).

fof(ax27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).

fof(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).

fof(ax86,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).

fof(ax24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).

fof(ax85,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => hd(app(X1,X2)) = hd(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).

fof(ax78,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).

fof(ax81,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).

fof(ax22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).

fof(ax38,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).

fof(c_0_24,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ~ ssList(X4)
                    | X2 != X4
                    | X1 != X3
                    | nil = X1
                    | ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & app(app(X6,cons(X5,nil)),X7) = X1
                                & ! [X8] :
                                    ( ~ ssItem(X8)
                                    | ~ memberP(X6,X8)
                                    | ~ memberP(X7,X8)
                                    | ~ lt(X5,X8)
                                    | leq(X5,X8) ) ) ) )
                    | ! [X9] :
                        ( ssList(X9)
                       => ! [X10] :
                            ( ~ ssList(X10)
                            | app(app(X9,X3),X10) != X4
                            | ~ totalorderedP(X3)
                            | ? [X11] :
                                ( ssItem(X11)
                                & ? [X12] :
                                    ( ssList(X12)
                                    & app(X12,cons(X11,nil)) = X9
                                    & ? [X13] :
                                        ( ssItem(X13)
                                        & ? [X14] :
                                            ( ssList(X14)
                                            & app(cons(X13,nil),X14) = X3
                                            & leq(X11,X13) ) ) ) )
                            | ? [X15] :
                                ( ssItem(X15)
                                & ? [X16] :
                                    ( ssList(X16)
                                    & app(cons(X15,nil),X16) = X10
                                    & ? [X17] :
                                        ( ssItem(X17)
                                        & ? [X18] :
                                            ( ssList(X18)
                                            & app(X18,cons(X17,nil)) = X3
                                            & leq(X17,X15) ) ) ) ) ) )
                    | ( nil != X4
                      & nil = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_25,negated_conjecture,
    ! [X267,X268,X269,X273,X274,X275,X276,X277,X278,X279,X280] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & nil != esk48_0
      & ( ssItem(esk52_3(X267,X268,X269))
        | ~ ssList(X269)
        | app(app(X268,cons(X267,nil)),X269) != esk48_0
        | ~ ssList(X268)
        | ~ ssItem(X267) )
      & ( memberP(X268,esk52_3(X267,X268,X269))
        | ~ ssList(X269)
        | app(app(X268,cons(X267,nil)),X269) != esk48_0
        | ~ ssList(X268)
        | ~ ssItem(X267) )
      & ( memberP(X269,esk52_3(X267,X268,X269))
        | ~ ssList(X269)
        | app(app(X268,cons(X267,nil)),X269) != esk48_0
        | ~ ssList(X268)
        | ~ ssItem(X267) )
      & ( lt(X267,esk52_3(X267,X268,X269))
        | ~ ssList(X269)
        | app(app(X268,cons(X267,nil)),X269) != esk48_0
        | ~ ssList(X268)
        | ~ ssItem(X267) )
      & ( ~ leq(X267,esk52_3(X267,X268,X269))
        | ~ ssList(X269)
        | app(app(X268,cons(X267,nil)),X269) != esk48_0
        | ~ ssList(X268)
        | ~ ssItem(X267) )
      & ssList(esk53_0)
      & ssList(esk54_0)
      & app(app(esk53_0,esk50_0),esk54_0) = esk51_0
      & totalorderedP(esk50_0)
      & ( ~ ssItem(X273)
        | ~ ssList(X274)
        | app(X274,cons(X273,nil)) != esk53_0
        | ~ ssItem(X275)
        | ~ ssList(X276)
        | app(cons(X275,nil),X276) != esk50_0
        | ~ leq(X273,X275) )
      & ( ~ ssItem(X277)
        | ~ ssList(X278)
        | app(cons(X277,nil),X278) != esk54_0
        | ~ ssItem(X279)
        | ~ ssList(X280)
        | app(X280,cons(X279,nil)) != esk50_0
        | ~ leq(X279,X277) )
      & ( nil = esk51_0
        | nil != esk50_0 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])]) ).

fof(c_0_26,plain,
    ! [X176,X177,X178] :
      ( ~ ssList(X176)
      | ~ ssList(X177)
      | ~ ssList(X178)
      | ~ frontsegP(X176,X177)
      | frontsegP(app(X176,X178),X177) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).

fof(c_0_27,plain,
    ! [X175] :
      ( ~ ssList(X175)
      | frontsegP(X175,X175) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).

cnf(c_0_28,negated_conjecture,
    app(app(esk53_0,esk50_0),esk54_0) = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_30,plain,
    ! [X234,X235,X236] :
      ( ~ ssList(X234)
      | ~ ssList(X235)
      | ~ ssList(X236)
      | app(app(X234,X235),X236) = app(X234,app(X235,X236)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_31,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_32,plain,
    ( frontsegP(X1,X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,negated_conjecture,
    app(app(esk53_0,esk48_0),esk54_0) = esk51_0,
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    ssList(esk54_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_36,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_37,negated_conjecture,
    ssList(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_38,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_39,negated_conjecture,
    app(esk53_0,app(esk48_0,esk54_0)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]),c_0_37])]) ).

fof(c_0_40,plain,
    ! [X142,X143] :
      ( ~ ssList(X142)
      | ~ ssList(X143)
      | ssList(app(X142,X143)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

fof(c_0_41,plain,
    ! [X32,X33,X35] :
      ( ( ssList(esk6_2(X32,X33))
        | ~ frontsegP(X32,X33)
        | ~ ssList(X33)
        | ~ ssList(X32) )
      & ( app(X33,esk6_2(X32,X33)) = X32
        | ~ frontsegP(X32,X33)
        | ~ ssList(X33)
        | ~ ssList(X32) )
      & ( ~ ssList(X35)
        | app(X33,X35) != X32
        | frontsegP(X32,X33)
        | ~ ssList(X33)
        | ~ ssList(X32) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).

cnf(c_0_42,negated_conjecture,
    ( frontsegP(esk51_0,esk53_0)
    | ~ ssList(app(esk48_0,esk54_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_37])]) ).

cnf(c_0_43,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_45,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_46,plain,
    ! [X229,X230,X231] :
      ( ~ ssList(X229)
      | ~ ssList(X230)
      | ~ ssList(X231)
      | app(X230,X231) != app(X230,X229)
      | X231 = X229 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).

cnf(c_0_47,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_48,negated_conjecture,
    frontsegP(esk51_0,esk53_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_35]),c_0_36])]) ).

cnf(c_0_49,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_50,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_51,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X2,X3) != app(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_52,negated_conjecture,
    app(esk53_0,esk6_2(esk51_0,esk53_0)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_37])]) ).

cnf(c_0_53,negated_conjecture,
    ssList(esk6_2(esk51_0,esk53_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_48]),c_0_37]),c_0_49])]) ).

cnf(c_0_54,negated_conjecture,
    ( X1 = esk6_2(esk51_0,esk53_0)
    | app(esk53_0,X1) != esk51_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_37])]) ).

fof(c_0_55,plain,
    ! [X191,X192,X193] :
      ( ~ ssList(X191)
      | ~ ssList(X192)
      | ~ ssList(X193)
      | ~ rearsegP(X191,X192)
      | rearsegP(app(X193,X191),X192) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).

fof(c_0_56,plain,
    ! [X194] :
      ( ~ ssList(X194)
      | rearsegP(X194,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).

cnf(c_0_57,negated_conjecture,
    ( esk6_2(esk51_0,esk53_0) = app(esk48_0,esk54_0)
    | ~ ssList(app(esk48_0,esk54_0)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_39]) ).

cnf(c_0_58,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_59,plain,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_60,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_61,negated_conjecture,
    esk6_2(esk51_0,esk53_0) = app(esk48_0,esk54_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_43]),c_0_35]),c_0_36])]) ).

fof(c_0_62,plain,
    ! [X36,X37,X39] :
      ( ( ssList(esk7_2(X36,X37))
        | ~ rearsegP(X36,X37)
        | ~ ssList(X37)
        | ~ ssList(X36) )
      & ( app(esk7_2(X36,X37),X37) = X36
        | ~ rearsegP(X36,X37)
        | ~ ssList(X37)
        | ~ ssList(X36) )
      & ( ~ ssList(X39)
        | app(X39,X37) != X36
        | rearsegP(X36,X37)
        | ~ ssList(X37)
        | ~ ssList(X36) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).

cnf(c_0_63,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).

cnf(c_0_64,negated_conjecture,
    ssList(app(esk48_0,esk54_0)),
    inference(rw,[status(thm)],[c_0_53,c_0_61]) ).

fof(c_0_65,plain,
    ! [X147] :
      ( ~ ssList(X147)
      | app(nil,X147) = X147 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

fof(c_0_66,plain,
    ! [X239] :
      ( ~ ssList(X239)
      | app(X239,nil) = X239 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_67,plain,
    ( app(esk7_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_68,negated_conjecture,
    rearsegP(esk51_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_39]),c_0_37]),c_0_64])]) ).

cnf(c_0_69,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_70,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_71,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_72,negated_conjecture,
    app(esk7_2(esk51_0,nil),nil) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_60]),c_0_49])]) ).

cnf(c_0_73,negated_conjecture,
    ssList(esk7_2(esk51_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_68]),c_0_60]),c_0_49])]) ).

cnf(c_0_74,plain,
    ( app(nil,app(X1,X2)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_70]),c_0_60])]) ).

cnf(c_0_75,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_34]),c_0_60])]),c_0_43]) ).

cnf(c_0_76,negated_conjecture,
    esk7_2(esk51_0,nil) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).

cnf(c_0_77,negated_conjecture,
    ( app(esk53_0,app(app(esk48_0,esk54_0),X1)) = app(esk51_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_39]),c_0_37])]),c_0_64])]) ).

cnf(c_0_78,plain,
    ( app(nil,X1) = app(X1,nil)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_60])]) ).

cnf(c_0_79,negated_conjecture,
    app(esk51_0,nil) = esk51_0,
    inference(rw,[status(thm)],[c_0_72,c_0_76]) ).

fof(c_0_80,plain,
    ! [X226,X227,X228] :
      ( ~ ssList(X226)
      | ~ ssList(X227)
      | ~ ssList(X228)
      | app(X228,X227) != app(X226,X227)
      | X228 = X226 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).

cnf(c_0_81,negated_conjecture,
    ( X1 = app(esk48_0,esk54_0)
    | app(esk53_0,X1) != esk51_0
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[c_0_54,c_0_61]) ).

cnf(c_0_82,negated_conjecture,
    app(esk53_0,app(nil,app(esk48_0,esk54_0))) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_60]),c_0_64])]) ).

cnf(c_0_83,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X3,X2) != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_84,negated_conjecture,
    ( app(nil,app(esk48_0,esk54_0)) = app(esk48_0,esk54_0)
    | ~ ssList(app(nil,app(esk48_0,esk54_0))) ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

fof(c_0_85,plain,
    ! [X237,X238] :
      ( ( nil = X238
        | nil != app(X237,X238)
        | ~ ssList(X238)
        | ~ ssList(X237) )
      & ( nil = X237
        | nil != app(X237,X238)
        | ~ ssList(X238)
        | ~ ssList(X237) )
      & ( nil != X238
        | nil != X237
        | nil = app(X237,X238)
        | ~ ssList(X238)
        | ~ ssList(X237) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_86,plain,
    ( X1 = app(X2,X3)
    | app(X1,X4) != app(X2,app(X3,X4))
    | ~ ssList(X4)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_34]),c_0_43]) ).

cnf(c_0_87,negated_conjecture,
    app(nil,app(esk48_0,esk54_0)) = app(esk48_0,esk54_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_43]),c_0_64]),c_0_60])]) ).

fof(c_0_88,plain,
    ! [X144,X145,X146] :
      ( ~ ssList(X144)
      | ~ ssList(X145)
      | ~ ssItem(X146)
      | cons(X146,app(X145,X144)) = app(cons(X146,X145),X144) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).

fof(c_0_89,plain,
    ! [X123,X124] :
      ( ~ ssList(X123)
      | ~ ssItem(X124)
      | ssList(cons(X124,X123)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_90,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_91,negated_conjecture,
    ( X1 = app(nil,esk48_0)
    | app(X1,esk54_0) != app(esk48_0,esk54_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_35]),c_0_36]),c_0_60])]) ).

cnf(c_0_92,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_88]) ).

cnf(c_0_93,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_94,plain,
    ( app(nil,X1) = nil
    | nil != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_90]),c_0_60])]) ).

cnf(c_0_95,negated_conjecture,
    app(nil,esk48_0) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_91]),c_0_36])]) ).

fof(c_0_96,plain,
    ! [X242,X243] :
      ( ~ ssList(X242)
      | ~ ssList(X243)
      | nil = X242
      | tl(app(X242,X243)) = app(tl(X242),X243) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).

fof(c_0_97,plain,
    ! [X139] :
      ( ~ ssList(X139)
      | nil = X139
      | ssList(tl(X139)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

fof(c_0_98,plain,
    ! [X240,X241] :
      ( ~ ssList(X240)
      | ~ ssList(X241)
      | nil = X240
      | hd(app(X240,X241)) = hd(X240) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).

cnf(c_0_99,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_100,plain,
    ( ssList(cons(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_92]),c_0_93]) ).

cnf(c_0_101,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_94]),c_0_60])]) ).

fof(c_0_102,plain,
    ! [X225] :
      ( ~ ssList(X225)
      | nil = X225
      | cons(hd(X225),tl(X225)) = X225 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

cnf(c_0_103,negated_conjecture,
    rearsegP(esk48_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_95]),c_0_60]),c_0_36])]) ).

cnf(c_0_104,plain,
    ( app(esk7_2(X1,nil),nil) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_59]),c_0_60])]) ).

cnf(c_0_105,plain,
    ( ssList(esk7_2(X1,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_59]),c_0_60])]) ).

cnf(c_0_106,plain,
    ( nil = X1
    | tl(app(X1,X2)) = app(tl(X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_96]) ).

cnf(c_0_107,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_108,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_98]) ).

cnf(c_0_109,plain,
    ( app(X1,X2) = nil
    | app(X1,app(X2,X3)) != nil
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_34]),c_0_43]) ).

cnf(c_0_110,negated_conjecture,
    ( memberP(X1,esk52_3(X2,X1,X3))
    | ~ ssList(X3)
    | app(app(X1,cons(X2,nil)),X3) != esk48_0
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_111,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_60])]) ).

fof(c_0_112,plain,
    ! [X232,X233] :
      ( ~ ssList(X232)
      | ~ ssItem(X233)
      | cons(X233,X232) = app(cons(X233,nil),X232) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_113,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_102]) ).

cnf(c_0_114,negated_conjecture,
    app(esk7_2(esk48_0,nil),nil) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_103]),c_0_60]),c_0_36])]) ).

cnf(c_0_115,plain,
    ( esk7_2(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_104]),c_0_105]) ).

cnf(c_0_116,plain,
    ( nil = X1
    | ssList(tl(app(X1,X2)))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_106]),c_0_107]) ).

fof(c_0_117,plain,
    ! [X136] :
      ( ~ ssList(X136)
      | nil = X136
      | ssItem(hd(X136)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_118,plain,
    ( hd(app(X1,app(X2,X3))) = hd(app(X1,X2))
    | app(X1,X2) = nil
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_34]),c_0_43]) ).

cnf(c_0_119,negated_conjecture,
    nil != esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_120,negated_conjecture,
    ( app(nil,esk48_0) = nil
    | app(esk48_0,esk54_0) != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_87]),c_0_35]),c_0_36]),c_0_60])]) ).

cnf(c_0_121,negated_conjecture,
    ( ssItem(esk52_3(X1,X2,X3))
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_122,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[ax38]) ).

cnf(c_0_123,negated_conjecture,
    ( memberP(nil,esk52_3(X1,nil,X2))
    | app(cons(X1,nil),X2) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_70]),c_0_60])]),c_0_111]) ).

cnf(c_0_124,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_112]) ).

cnf(c_0_125,plain,
    ( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
    | nil = X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_108]),c_0_43]),c_0_99]) ).

cnf(c_0_126,negated_conjecture,
    app(esk48_0,nil) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_36])]) ).

cnf(c_0_127,plain,
    ( nil = X1
    | ssList(tl(app(nil,X1)))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_78]),c_0_60])]) ).

cnf(c_0_128,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_117]) ).

cnf(c_0_129,negated_conjecture,
    hd(app(esk48_0,esk54_0)) = hd(esk48_0),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_87]),c_0_35]),c_0_36]),c_0_60])]),c_0_95]),c_0_95]),c_0_119]) ).

cnf(c_0_130,negated_conjecture,
    app(esk48_0,esk54_0) != nil,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_95]),c_0_119]) ).

cnf(c_0_131,negated_conjecture,
    ( ssItem(esk52_3(X1,nil,X2))
    | app(cons(X1,nil),X2) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_70]),c_0_60])]),c_0_111]) ).

fof(c_0_132,plain,
    ! [X169] :
      ( ~ ssItem(X169)
      | ~ memberP(nil,X169) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_122])]) ).

cnf(c_0_133,negated_conjecture,
    ( memberP(nil,esk52_3(X1,nil,X2))
    | cons(X1,X2) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_123,c_0_124]) ).

cnf(c_0_134,negated_conjecture,
    cons(hd(esk48_0),tl(esk48_0)) = esk48_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_60]),c_0_36])]),c_0_119]) ).

cnf(c_0_135,negated_conjecture,
    ssList(tl(esk48_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_95]),c_0_36])]),c_0_119]) ).

cnf(c_0_136,negated_conjecture,
    ssItem(hd(esk48_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_64])]),c_0_130]) ).

cnf(c_0_137,negated_conjecture,
    ( ssItem(esk52_3(X1,nil,X2))
    | cons(X1,X2) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_131,c_0_124]) ).

cnf(c_0_138,plain,
    ( ~ ssItem(X1)
    | ~ memberP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_132]) ).

cnf(c_0_139,negated_conjecture,
    memberP(nil,esk52_3(hd(esk48_0),nil,tl(esk48_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_136])]) ).

cnf(c_0_140,negated_conjecture,
    ssItem(esk52_3(hd(esk48_0),nil,tl(esk48_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_134]),c_0_135]),c_0_136])]) ).

cnf(c_0_141,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem    : SWC248+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.32  % Computer : n002.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Mon Aug 28 15:45:04 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.15/0.55  start to proof: theBenchmark
% 38.66/38.81  % Version  : CSE_E---1.5
% 38.66/38.81  % Problem  : theBenchmark.p
% 38.66/38.81  % Proof found
% 38.66/38.81  % SZS status Theorem for theBenchmark.p
% 38.66/38.81  % SZS output start Proof
% See solution above
% 38.66/38.82  % Total time : 38.246000 s
% 38.66/38.82  % SZS output end Proof
% 38.66/38.82  % Total time : 38.251000 s
%------------------------------------------------------------------------------