TSTP Solution File: SWC117+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC117+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 : n005.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 20:19:57 EDT 2023

% Result   : Theorem 1.32s 1.45s
% Output   : CNFRefutation 1.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :  106
% Syntax   : Number of formulae    :  263 (  45 unt;  75 typ;   0 def)
%            Number of atoms       :  624 ( 164 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  760 ( 324   ~; 316   |;  46   &)
%                                         (   6 <=>;  68  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Maximal term depth    :    5 (   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    :   56 (  56 usr;   7 con; 0-2 aty)
%            Number of variables   :  248 (   0 sgn; 118   !;   9   ?;   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 ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ segmentP(X4,X3)
                    | ~ equalelemsP(X3)
                    | ? [X5] :
                        ( ssList(X5)
                        & neq(X3,X5)
                        & segmentP(X4,X5)
                        & segmentP(X5,X3)
                        & equalelemsP(X5) )
                    | ( nil = X2
                      & nil = X1 )
                    | ( neq(X1,nil)
                      & segmentP(X2,X1) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

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

fof(ax7,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).

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

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

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

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(ax19,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => ! [X4] :
                  ( ssItem(X4)
                 => ( cons(X3,X1) = cons(X4,X2)
                   => ( X3 = X4
                      & X2 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).

fof(ax20,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).

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

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).

fof(ax4,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( singletonP(X1)
      <=> ? [X2] :
            ( ssItem(X2)
            & cons(X2,nil) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).

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

fof(ax25,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => tl(cons(X2,X1)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).

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

fof(ax23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => hd(cons(X2,X1)) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).

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(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).

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

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(ax57,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,nil) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).

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(ax45,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,nil) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).

fof(ax73,axiom,
    ! [X1] :
      ( ssItem(X1)
     => equalelemsP(cons(X1,nil)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).

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(c_0_31,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ segmentP(X4,X3)
                      | ~ equalelemsP(X3)
                      | ? [X5] :
                          ( ssList(X5)
                          & neq(X3,X5)
                          & segmentP(X4,X5)
                          & segmentP(X5,X3)
                          & equalelemsP(X5) )
                      | ( nil = X2
                        & nil = X1 )
                      | ( neq(X1,nil)
                        & segmentP(X2,X1) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_32,negated_conjecture,
    ! [X255] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & segmentP(esk51_0,esk50_0)
      & equalelemsP(esk50_0)
      & ( ~ ssList(X255)
        | ~ neq(esk50_0,X255)
        | ~ segmentP(esk51_0,X255)
        | ~ segmentP(X255,esk50_0)
        | ~ equalelemsP(X255) )
      & ( nil != esk49_0
        | nil != esk48_0 )
      & ( ~ neq(esk48_0,nil)
        | ~ segmentP(esk49_0,esk48_0) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ neq(esk48_0,nil)
    | ~ segmentP(esk49_0,esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_34,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    segmentP(esk51_0,esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_37,plain,
    ! [X109,X110] :
      ( ( ~ neq(X109,X110)
        | X109 != X110
        | ~ ssList(X110)
        | ~ ssList(X109) )
      & ( X109 = X110
        | neq(X109,X110)
        | ~ ssList(X110)
        | ~ ssList(X109) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_38,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_39,negated_conjecture,
    ~ neq(esk50_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_34]),c_0_36])]) ).

cnf(c_0_40,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_41,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_42,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_38,c_0_34]) ).

fof(c_0_43,plain,
    ! [X28,X29,X32,X33] :
      ( ( ssList(esk8_2(X28,X29))
        | ~ segmentP(X28,X29)
        | ~ ssList(X29)
        | ~ ssList(X28) )
      & ( ssList(esk9_2(X28,X29))
        | ~ segmentP(X28,X29)
        | ~ ssList(X29)
        | ~ ssList(X28) )
      & ( app(app(esk8_2(X28,X29),X29),esk9_2(X28,X29)) = X28
        | ~ segmentP(X28,X29)
        | ~ ssList(X29)
        | ~ ssList(X28) )
      & ( ~ ssList(X32)
        | ~ ssList(X33)
        | app(app(X32,X29),X33) != X28
        | segmentP(X28,X29)
        | ~ ssList(X29)
        | ~ ssList(X28) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).

cnf(c_0_44,negated_conjecture,
    esk50_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).

cnf(c_0_45,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_46,plain,
    ! [X179,X180,X181] :
      ( ~ ssList(X179)
      | ~ ssList(X180)
      | ~ ssList(X181)
      | ~ rearsegP(X179,X180)
      | rearsegP(app(X181,X179),X180) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).

fof(c_0_47,plain,
    ! [X182] :
      ( ~ ssList(X182)
      | rearsegP(X182,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).

cnf(c_0_48,plain,
    ( app(app(esk8_2(X1,X2),X2),esk9_2(X1,X2)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_49,negated_conjecture,
    segmentP(esk51_0,nil),
    inference(rw,[status(thm)],[c_0_36,c_0_44]) ).

cnf(c_0_50,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_45,c_0_35]) ).

fof(c_0_51,plain,
    ! [X227] :
      ( ~ ssList(X227)
      | app(X227,nil) = X227 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_52,plain,
    ( ssList(esk8_2(X1,X2))
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_53,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_54,plain,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_55,negated_conjecture,
    app(app(esk8_2(esk51_0,nil),nil),esk9_2(esk51_0,nil)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_41]),c_0_50])]) ).

cnf(c_0_56,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_57,negated_conjecture,
    ssList(esk8_2(esk51_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_49]),c_0_41]),c_0_50])]) ).

cnf(c_0_58,plain,
    ( ssList(esk9_2(X1,X2))
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

fof(c_0_59,plain,
    ! [X24,X25,X27] :
      ( ( ssList(esk7_2(X24,X25))
        | ~ rearsegP(X24,X25)
        | ~ ssList(X25)
        | ~ ssList(X24) )
      & ( app(esk7_2(X24,X25),X25) = X24
        | ~ rearsegP(X24,X25)
        | ~ ssList(X25)
        | ~ ssList(X24) )
      & ( ~ ssList(X27)
        | app(X27,X25) != X24
        | rearsegP(X24,X25)
        | ~ ssList(X25)
        | ~ ssList(X24) ) ),
    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_60,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_41])]) ).

cnf(c_0_61,negated_conjecture,
    app(esk8_2(esk51_0,nil),esk9_2(esk51_0,nil)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).

cnf(c_0_62,negated_conjecture,
    ssList(esk9_2(esk51_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_41]),c_0_50])]) ).

cnf(c_0_63,plain,
    ( app(esk7_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_64,negated_conjecture,
    rearsegP(esk51_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_57]),c_0_62])]) ).

cnf(c_0_65,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

fof(c_0_66,plain,
    ! [X213] :
      ( ~ ssList(X213)
      | nil = X213
      | cons(hd(X213),tl(X213)) = X213 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

fof(c_0_67,plain,
    ! [X228,X229] :
      ( ~ ssList(X228)
      | ~ ssList(X229)
      | nil = X228
      | hd(app(X228,X229)) = hd(X228) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).

fof(c_0_68,plain,
    ! [X130,X131] :
      ( ~ ssList(X130)
      | ~ ssList(X131)
      | ssList(app(X130,X131)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

fof(c_0_69,plain,
    ! [X225,X226] :
      ( ( nil = X226
        | nil != app(X225,X226)
        | ~ ssList(X226)
        | ~ ssList(X225) )
      & ( nil = X225
        | nil != app(X225,X226)
        | ~ ssList(X226)
        | ~ ssList(X225) )
      & ( nil != X226
        | nil != X225
        | nil = app(X225,X226)
        | ~ ssList(X226)
        | ~ ssList(X225) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_70,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_63,c_0_64]),c_0_41]),c_0_50])]) ).

cnf(c_0_71,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_65,c_0_64]),c_0_41]),c_0_50])]) ).

cnf(c_0_72,negated_conjecture,
    ( nil != esk49_0
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_73,plain,
    ! [X115,X116,X117,X118] :
      ( ( X117 = X118
        | cons(X117,X115) != cons(X118,X116)
        | ~ ssItem(X118)
        | ~ ssItem(X117)
        | ~ ssList(X116)
        | ~ ssList(X115) )
      & ( X116 = X115
        | cons(X117,X115) != cons(X118,X116)
        | ~ ssItem(X118)
        | ~ ssItem(X117)
        | ~ ssList(X116)
        | ~ ssList(X115) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).

fof(c_0_74,plain,
    ! [X119] :
      ( ( ssList(esk44_1(X119))
        | nil = X119
        | ~ ssList(X119) )
      & ( ssItem(esk45_1(X119))
        | nil = X119
        | ~ ssList(X119) )
      & ( cons(esk45_1(X119),esk44_1(X119)) = X119
        | nil = X119
        | ~ ssList(X119) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).

fof(c_0_75,plain,
    ! [X111,X112] :
      ( ~ ssList(X111)
      | ~ ssItem(X112)
      | ssList(cons(X112,X111)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_76,plain,
    ! [X122,X123] :
      ( ~ ssList(X122)
      | ~ ssItem(X123)
      | nil != cons(X123,X122) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_77,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_78,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_79,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_80,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_81,negated_conjecture,
    esk7_2(esk51_0,nil) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_70]),c_0_71])]) ).

cnf(c_0_82,negated_conjecture,
    ( esk50_0 != nil
    | esk51_0 != nil ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_34]),c_0_35]) ).

cnf(c_0_83,plain,
    ( X1 = X2
    | cons(X3,X2) != cons(X4,X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_73]) ).

cnf(c_0_84,plain,
    ( cons(esk45_1(X1),esk44_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_85,plain,
    ( ssItem(esk45_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_86,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

cnf(c_0_87,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_88,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_77,c_0_78]),c_0_79]),c_0_80]) ).

cnf(c_0_89,negated_conjecture,
    app(esk51_0,nil) = esk51_0,
    inference(rw,[status(thm)],[c_0_70,c_0_81]) ).

cnf(c_0_90,negated_conjecture,
    esk51_0 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_44])]) ).

cnf(c_0_91,plain,
    ( esk44_1(cons(X1,X2)) = X2
    | ~ ssList(esk44_1(cons(X1,X2)))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84])]),c_0_85]),c_0_86]),c_0_87]) ).

cnf(c_0_92,negated_conjecture,
    cons(hd(esk51_0),tl(esk51_0)) = esk51_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_41]),c_0_50])]),c_0_90]) ).

fof(c_0_93,plain,
    ! [X17,X19] :
      ( ( ssItem(esk5_1(X17))
        | ~ singletonP(X17)
        | ~ ssList(X17) )
      & ( cons(esk5_1(X17),nil) = X17
        | ~ singletonP(X17)
        | ~ ssList(X17) )
      & ( ~ ssItem(X19)
        | cons(X19,nil) != X17
        | singletonP(X17)
        | ~ ssList(X17) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).

cnf(c_0_94,negated_conjecture,
    ( esk44_1(esk51_0) = tl(esk51_0)
    | ~ ssList(esk44_1(esk51_0))
    | ~ ssList(tl(esk51_0))
    | ~ ssItem(hd(esk51_0)) ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_95,plain,
    ( ssList(esk44_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

fof(c_0_96,plain,
    ! [X127] :
      ( ~ ssList(X127)
      | nil = X127
      | ssList(tl(X127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

fof(c_0_97,plain,
    ! [X128,X129] :
      ( ~ ssList(X128)
      | ~ ssItem(X129)
      | tl(cons(X129,X128)) = X128 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).

cnf(c_0_98,plain,
    ( singletonP(X2)
    | ~ ssItem(X1)
    | cons(X1,nil) != X2
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_99,negated_conjecture,
    ( esk44_1(esk51_0) = tl(esk51_0)
    | ~ ssList(tl(esk51_0))
    | ~ ssItem(hd(esk51_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_50])]),c_0_90]) ).

cnf(c_0_100,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_96]) ).

fof(c_0_101,plain,
    ! [X124] :
      ( ~ ssList(X124)
      | nil = X124
      | ssItem(hd(X124)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

fof(c_0_102,plain,
    ! [X125,X126] :
      ( ~ ssList(X125)
      | ~ ssItem(X126)
      | hd(cons(X126,X125)) = X126 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).

cnf(c_0_103,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_104,plain,
    ( cons(esk5_1(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_105,plain,
    ( ssItem(esk5_1(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_106,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_98]) ).

cnf(c_0_107,negated_conjecture,
    ( esk44_1(esk51_0) = tl(esk51_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_50])]),c_0_90]) ).

cnf(c_0_108,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_101]) ).

cnf(c_0_109,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_102]) ).

fof(c_0_110,plain,
    ! [X132,X133,X134] :
      ( ~ ssList(X132)
      | ~ ssList(X133)
      | ~ ssItem(X134)
      | cons(X134,app(X133,X132)) = app(cons(X134,X133),X132) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).

fof(c_0_111,plain,
    ! [X113,X114] :
      ( ~ ssList(X113)
      | ~ ssItem(X114)
      | cons(X114,X113) != X113 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_112,plain,
    ( tl(X1) = nil
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_41])]),c_0_105]) ).

cnf(c_0_113,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_86]),c_0_41])]) ).

cnf(c_0_114,negated_conjecture,
    esk44_1(esk51_0) = tl(esk51_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_50])]),c_0_90]) ).

cnf(c_0_115,plain,
    ( esk5_1(X1) = hd(X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_104]),c_0_41])]),c_0_105]) ).

cnf(c_0_116,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_110]) ).

cnf(c_0_117,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_118,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_111]) ).

cnf(c_0_119,plain,
    ( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_109]),c_0_86]),c_0_87]) ).

cnf(c_0_120,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_112,c_0_113]) ).

cnf(c_0_121,negated_conjecture,
    cons(esk45_1(esk51_0),tl(esk51_0)) = esk51_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_114]),c_0_50])]),c_0_90]) ).

cnf(c_0_122,negated_conjecture,
    ssList(tl(esk51_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_114]),c_0_50])]),c_0_90]) ).

cnf(c_0_123,plain,
    ( ssItem(hd(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_105,c_0_115]) ).

fof(c_0_124,plain,
    ! [X220,X221] :
      ( ~ ssList(X220)
      | ~ ssItem(X221)
      | cons(X221,X220) = app(cons(X221,nil),X220) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_125,plain,
    ( ssList(cons(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_116]),c_0_86]) ).

cnf(c_0_126,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_117])]),c_0_41])]) ).

cnf(c_0_127,plain,
    ( tl(cons(X1,X2)) != cons(X1,X2)
    | ~ ssList(tl(cons(X1,X2)))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_118,c_0_119]) ).

cnf(c_0_128,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_86]),c_0_41])]) ).

cnf(c_0_129,negated_conjecture,
    ( esk45_1(esk51_0) = hd(esk51_0)
    | ~ ssItem(esk45_1(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_121]),c_0_122])]) ).

cnf(c_0_130,plain,
    ( ssItem(hd(cons(X1,nil)))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_123,c_0_113]) ).

cnf(c_0_131,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

cnf(c_0_132,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_41])]) ).

cnf(c_0_133,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_41])]) ).

cnf(c_0_134,negated_conjecture,
    esk45_1(esk51_0) = hd(esk51_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_85]),c_0_50])]),c_0_90]) ).

cnf(c_0_135,plain,
    ( segmentP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(app(X1,X3),X2) != X4
    | ~ ssList(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

fof(c_0_136,plain,
    ! [X135] :
      ( ~ ssList(X135)
      | app(nil,X135) = X135 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_137,plain,
    ( cons(hd(cons(X1,X2)),X2) = cons(X1,X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_103]),c_0_86]),c_0_87]) ).

cnf(c_0_138,plain,
    ( ssItem(hd(cons(X1,nil)))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_86]),c_0_41])]) ).

cnf(c_0_139,plain,
    ( cons(hd(cons(X1,nil)),tl(cons(X1,X2))) = cons(X1,X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_131]),c_0_132]),c_0_133]) ).

cnf(c_0_140,negated_conjecture,
    ssItem(hd(esk51_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_134]),c_0_50])]),c_0_90]) ).

cnf(c_0_141,plain,
    ( rearsegP(X3,X2)
    | ~ ssList(X1)
    | app(X1,X2) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

fof(c_0_142,plain,
    ! [X230,X231] :
      ( ~ ssList(X230)
      | ~ ssList(X231)
      | nil = X230
      | tl(app(X230,X231)) = app(tl(X230),X231) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).

cnf(c_0_143,plain,
    ( segmentP(app(app(X1,X2),X3),X2)
    | ~ ssList(app(app(X1,X2),X3))
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_135]) ).

cnf(c_0_144,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_136]) ).

cnf(c_0_145,plain,
    ( cons(hd(cons(X1,nil)),X2) = app(cons(X1,nil),X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_137]),c_0_41])]),c_0_138]) ).

cnf(c_0_146,negated_conjecture,
    cons(hd(cons(hd(esk51_0),nil)),tl(esk51_0)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_92]),c_0_122]),c_0_140])]) ).

cnf(c_0_147,plain,
    ( rearsegP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_141]),c_0_79]) ).

cnf(c_0_148,plain,
    ( nil = X1
    | tl(app(X1,X2)) = app(tl(X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_142]) ).

fof(c_0_149,plain,
    ! [X194] :
      ( ~ ssList(X194)
      | segmentP(X194,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).

cnf(c_0_150,plain,
    ( segmentP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_41])]),c_0_79]) ).

cnf(c_0_151,negated_conjecture,
    app(cons(hd(esk51_0),nil),tl(esk51_0)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_122]),c_0_140])]) ).

cnf(c_0_152,plain,
    ( rearsegP(app(X1,app(X2,X3)),X3)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_147]),c_0_79]) ).

cnf(c_0_153,negated_conjecture,
    app(tl(esk51_0),nil) = tl(esk51_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_89]),c_0_41]),c_0_50])]),c_0_90]) ).

cnf(c_0_154,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(esk50_0,X1)
    | ~ segmentP(esk51_0,X1)
    | ~ segmentP(X1,esk50_0)
    | ~ equalelemsP(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_155,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_149]) ).

cnf(c_0_156,negated_conjecture,
    ( segmentP(esk51_0,cons(hd(esk51_0),nil))
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_122])]) ).

fof(c_0_157,plain,
    ! [X164,X165,X166] :
      ( ~ ssList(X164)
      | ~ ssList(X165)
      | ~ ssList(X166)
      | ~ frontsegP(X164,X165)
      | frontsegP(app(X164,X166),X165) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).

fof(c_0_158,plain,
    ! [X171] :
      ( ~ ssList(X171)
      | frontsegP(X171,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).

cnf(c_0_159,negated_conjecture,
    ( rearsegP(app(X1,tl(esk51_0)),nil)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_41]),c_0_122])]) ).

cnf(c_0_160,negated_conjecture,
    ( ~ equalelemsP(X1)
    | ~ segmentP(esk51_0,X1)
    | ~ ssList(X1)
    | ~ neq(nil,X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_44]),c_0_44]),c_0_155]) ).

cnf(c_0_161,negated_conjecture,
    segmentP(esk51_0,cons(hd(esk51_0),nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_86]),c_0_41]),c_0_140])]) ).

cnf(c_0_162,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_157]) ).

cnf(c_0_163,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_158]) ).

cnf(c_0_164,negated_conjecture,
    rearsegP(tl(esk51_0),nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_144]),c_0_41]),c_0_122])]) ).

cnf(c_0_165,plain,
    ( ssList(esk7_2(app(X1,X2),X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_147]),c_0_79]) ).

cnf(c_0_166,negated_conjecture,
    ( ~ equalelemsP(cons(hd(esk51_0),nil))
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ neq(nil,cons(hd(esk51_0),nil)) ),
    inference(spm,[status(thm)],[c_0_160,c_0_161]) ).

fof(c_0_167,plain,
    ! [X206] :
      ( ~ ssItem(X206)
      | equalelemsP(cons(X206,nil)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])]) ).

fof(c_0_168,plain,
    ! [X20,X21,X23] :
      ( ( ssList(esk6_2(X20,X21))
        | ~ frontsegP(X20,X21)
        | ~ ssList(X21)
        | ~ ssList(X20) )
      & ( app(X21,esk6_2(X20,X21)) = X20
        | ~ frontsegP(X20,X21)
        | ~ ssList(X21)
        | ~ ssList(X20) )
      & ( ~ ssList(X23)
        | app(X21,X23) != X20
        | frontsegP(X20,X21)
        | ~ ssList(X21)
        | ~ ssList(X20) ) ),
    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_169,plain,
    ( frontsegP(app(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_41])]) ).

cnf(c_0_170,negated_conjecture,
    app(esk7_2(tl(esk51_0),nil),nil) = tl(esk51_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_164]),c_0_41]),c_0_122])]) ).

cnf(c_0_171,negated_conjecture,
    ssList(esk7_2(tl(esk51_0),nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_153]),c_0_41]),c_0_122])]) ).

cnf(c_0_172,negated_conjecture,
    ( ~ equalelemsP(cons(hd(esk51_0),nil))
    | ~ neq(nil,cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_86]),c_0_41]),c_0_140])]) ).

cnf(c_0_173,plain,
    ( equalelemsP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_167]) ).

cnf(c_0_174,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_168]) ).

cnf(c_0_175,negated_conjecture,
    frontsegP(tl(esk51_0),nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_41]),c_0_171])]) ).

cnf(c_0_176,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_168]) ).

cnf(c_0_177,negated_conjecture,
    ~ neq(nil,cons(hd(esk51_0),nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_140])]) ).

cnf(c_0_178,negated_conjecture,
    app(nil,esk6_2(tl(esk51_0),nil)) = tl(esk51_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_122]),c_0_41])]) ).

cnf(c_0_179,negated_conjecture,
    ssList(esk6_2(tl(esk51_0),nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_175]),c_0_41]),c_0_122])]) ).

cnf(c_0_180,negated_conjecture,
    ( tl(esk51_0) != esk51_0
    | ~ ssList(tl(esk51_0))
    | ~ ssItem(hd(esk51_0)) ),
    inference(spm,[status(thm)],[c_0_118,c_0_92]) ).

cnf(c_0_181,negated_conjecture,
    ( cons(hd(esk51_0),nil) = nil
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_40]),c_0_41])]) ).

cnf(c_0_182,negated_conjecture,
    esk6_2(tl(esk51_0),nil) = tl(esk51_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_178]),c_0_179])]) ).

cnf(c_0_183,negated_conjecture,
    ( tl(esk51_0) != esk51_0
    | ~ ssItem(hd(esk51_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_100]),c_0_50])]),c_0_90]) ).

cnf(c_0_184,negated_conjecture,
    cons(hd(esk51_0),nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_86]),c_0_41]),c_0_140])]) ).

cnf(c_0_185,negated_conjecture,
    app(nil,tl(esk51_0)) = tl(esk51_0),
    inference(rw,[status(thm)],[c_0_178,c_0_182]) ).

cnf(c_0_186,negated_conjecture,
    tl(esk51_0) != esk51_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_108]),c_0_50])]),c_0_90]) ).

cnf(c_0_187,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_184]),c_0_185]),c_0_186]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWC117+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n005.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
% 0.19/0.34  % DateTime   : Mon Aug 28 15:59:53 EDT 2023
% 0.19/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 1.32/1.45  % Version  : CSE_E---1.5
% 1.32/1.45  % Problem  : theBenchmark.p
% 1.32/1.45  % Proof found
% 1.32/1.45  % SZS status Theorem for theBenchmark.p
% 1.32/1.45  % SZS output start Proof
% See solution above
% 1.32/1.46  % Total time : 0.868000 s
% 1.32/1.46  % SZS output end Proof
% 1.32/1.46  % Total time : 0.872000 s
%------------------------------------------------------------------------------