TSTP Solution File: SWC297+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC297+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 20:21:27 EDT 2023

% Result   : Theorem 0.20s 0.75s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :  104
% Syntax   : Number of formulae    :  234 (  29 unt;  80 typ;   0 def)
%            Number of atoms       :  582 ( 181 equ)
%            Maximal formula atoms :   27 (   3 avg)
%            Number of connectives :  717 ( 289   ~; 303   |;  49   &)
%                                         (   7 <=>;  69  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   61 (  61 usr;  12 con; 0-2 aty)
%            Number of variables   :  208 (   0 sgn; 113   !;   6   ?;   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_0: $i ).

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

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

tff(decl_100,type,
    esk55_0: $i ).

tff(decl_101,type,
    esk56_0: $i ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssItem(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ! [X7] :
                                ( ssList(X7)
                               => ( app(app(X6,cons(X5,nil)),X7) != X1
                                  | ! [X8] :
                                      ( ssItem(X8)
                                     => ( ( ~ memberP(X6,X8)
                                          | lt(X8,X5) )
                                        & ( ~ memberP(X7,X8)
                                          | lt(X5,X8) ) ) ) ) ) ) )
                    | ( nil != X3
                      & nil = X4 )
                    | ( ! [X9] :
                          ( ssItem(X9)
                         => ( cons(X9,nil) != X3
                            | ~ memberP(X4,X9) ) )
                      & neq(X4,nil) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).

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

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

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

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

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

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

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

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

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

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

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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).

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

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

fof(ax3,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( memberP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).

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

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/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).

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

fof(ax37,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(cons(X2,X3),X1)
              <=> ( X1 = X2
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).

fof(ax54,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( ( segmentP(X1,X2)
              & segmentP(X2,X1) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).

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

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

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

fof(c_0_24,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ! [X7] :
                                  ( ssList(X7)
                                 => ( app(app(X6,cons(X5,nil)),X7) != X1
                                    | ! [X8] :
                                        ( ssItem(X8)
                                       => ( ( ~ memberP(X6,X8)
                                            | lt(X8,X5) )
                                          & ( ~ memberP(X7,X8)
                                            | lt(X5,X8) ) ) ) ) ) ) )
                      | ( nil != X3
                        & nil = X4 )
                      | ( ! [X9] :
                            ( ssItem(X9)
                           => ( cons(X9,nil) != X3
                              | ~ memberP(X4,X9) ) )
                        & neq(X4,nil) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_25,negated_conjecture,
    ( ssList(esk48_0)
    & ssList(esk49_0)
    & ssList(esk50_0)
    & ssList(esk51_0)
    & esk49_0 = esk51_0
    & esk48_0 = esk50_0
    & ssItem(esk52_0)
    & ssList(esk53_0)
    & ssList(esk54_0)
    & app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0
    & ssItem(esk55_0)
    & ( memberP(esk54_0,esk55_0)
      | memberP(esk53_0,esk55_0) )
    & ( ~ lt(esk52_0,esk55_0)
      | memberP(esk53_0,esk55_0) )
    & ( memberP(esk54_0,esk55_0)
      | ~ lt(esk55_0,esk52_0) )
    & ( ~ lt(esk52_0,esk55_0)
      | ~ lt(esk55_0,esk52_0) )
    & ( nil = esk50_0
      | nil != esk51_0 )
    & ( ssItem(esk56_0)
      | ~ neq(esk51_0,nil) )
    & ( cons(esk56_0,nil) = esk50_0
      | ~ neq(esk51_0,nil) )
    & ( memberP(esk51_0,esk56_0)
      | ~ neq(esk51_0,nil) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).

cnf(c_0_26,negated_conjecture,
    app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_27,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_28,plain,
    ! [X225,X226,X227] :
      ( ~ ssList(X225)
      | ~ ssList(X226)
      | ~ ssList(X227)
      | app(app(X225,X226),X227) = app(X225,app(X226,X227)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_29,negated_conjecture,
    app(app(esk53_0,cons(esk52_0,nil)),esk54_0) = esk50_0,
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    ssList(esk54_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,negated_conjecture,
    ssList(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_33,plain,
    ! [X114,X115] :
      ( ~ ssList(X114)
      | ~ ssItem(X115)
      | ssList(cons(X115,X114)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_34,plain,
    ! [X23,X24,X26] :
      ( ( ssList(esk6_2(X23,X24))
        | ~ frontsegP(X23,X24)
        | ~ ssList(X24)
        | ~ ssList(X23) )
      & ( app(X24,esk6_2(X23,X24)) = X23
        | ~ frontsegP(X23,X24)
        | ~ ssList(X24)
        | ~ ssList(X23) )
      & ( ~ ssList(X26)
        | app(X24,X26) != X23
        | frontsegP(X23,X24)
        | ~ ssList(X24)
        | ~ ssList(X23) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).

fof(c_0_35,plain,
    ! [X133,X134] :
      ( ~ ssList(X133)
      | ~ ssList(X134)
      | ssList(app(X133,X134)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_36,negated_conjecture,
    ( app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).

cnf(c_0_37,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_38,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_39,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_40,plain,
    ! [X223,X224] :
      ( ~ ssList(X223)
      | ~ ssItem(X224)
      | cons(X224,X223) = app(cons(X224,nil),X223) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_41,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_42,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_43,negated_conjecture,
    app(esk53_0,app(cons(esk52_0,nil),esk54_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]) ).

cnf(c_0_44,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_45,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42]) ).

cnf(c_0_46,negated_conjecture,
    app(esk53_0,cons(esk52_0,esk54_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_31]),c_0_39])]) ).

cnf(c_0_47,negated_conjecture,
    ( frontsegP(esk50_0,esk53_0)
    | ~ ssList(cons(esk52_0,esk54_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32])]) ).

cnf(c_0_48,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_49,plain,
    ! [X220,X221,X222] :
      ( ~ ssList(X220)
      | ~ ssList(X221)
      | ~ ssList(X222)
      | app(X221,X222) != app(X221,X220)
      | X222 = X220 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).

cnf(c_0_50,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_51,negated_conjecture,
    frontsegP(esk50_0,esk53_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_31]),c_0_39])]) ).

cnf(c_0_52,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_48,c_0_27]) ).

cnf(c_0_53,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_54,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X2,X3) != app(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_55,negated_conjecture,
    app(esk53_0,esk6_2(esk50_0,esk53_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_32])]) ).

cnf(c_0_56,negated_conjecture,
    ssList(esk6_2(esk50_0,esk53_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_32]),c_0_52])]) ).

cnf(c_0_57,negated_conjecture,
    ( X1 = esk6_2(esk50_0,esk53_0)
    | app(esk53_0,X1) != esk50_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_32])]) ).

fof(c_0_58,plain,
    ! [X112,X113] :
      ( ( ~ neq(X112,X113)
        | X112 != X113
        | ~ ssList(X113)
        | ~ ssList(X112) )
      & ( X112 = X113
        | neq(X112,X113)
        | ~ ssList(X113)
        | ~ ssList(X112) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_59,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_60,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_61,negated_conjecture,
    ( esk6_2(esk50_0,esk53_0) = cons(esk52_0,esk54_0)
    | ~ ssList(cons(esk52_0,esk54_0)) ),
    inference(spm,[status(thm)],[c_0_57,c_0_46]) ).

fof(c_0_62,plain,
    ! [X20,X22] :
      ( ( ssItem(esk5_1(X20))
        | ~ singletonP(X20)
        | ~ ssList(X20) )
      & ( cons(esk5_1(X20),nil) = X20
        | ~ singletonP(X20)
        | ~ ssList(X20) )
      & ( ~ ssItem(X22)
        | cons(X22,nil) != X20
        | singletonP(X20)
        | ~ 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)],[ax4])])])])]) ).

fof(c_0_63,plain,
    ! [X131,X132] :
      ( ~ ssList(X131)
      | ~ ssItem(X132)
      | tl(cons(X132,X131)) = X131 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).

cnf(c_0_64,negated_conjecture,
    ( cons(esk56_0,nil) = esk50_0
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_65,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_66,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_67,negated_conjecture,
    ( ssItem(esk56_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_68,negated_conjecture,
    esk6_2(esk50_0,esk53_0) = cons(esk52_0,esk54_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_37]),c_0_31]),c_0_39])]) ).

cnf(c_0_69,plain,
    ( singletonP(X2)
    | ~ ssItem(X1)
    | cons(X1,nil) != X2
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

fof(c_0_70,plain,
    ! [X216] :
      ( ~ ssList(X216)
      | nil = X216
      | cons(hd(X216),tl(X216)) = X216 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

cnf(c_0_71,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_72,negated_conjecture,
    ( cons(esk56_0,nil) = esk50_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_38]),c_0_66])]) ).

cnf(c_0_73,negated_conjecture,
    ( esk51_0 = nil
    | ssItem(esk56_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_65]),c_0_38]),c_0_66])]) ).

fof(c_0_74,plain,
    ! [X31,X32,X35,X36] :
      ( ( ssList(esk8_2(X31,X32))
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( ssList(esk9_2(X31,X32))
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( app(app(esk8_2(X31,X32),X32),esk9_2(X31,X32)) = X31
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( ~ ssList(X35)
        | ~ ssList(X36)
        | app(app(X35,X32),X36) != X31
        | segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) ) ),
    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_75,negated_conjecture,
    ( X1 = cons(esk52_0,esk54_0)
    | app(esk53_0,X1) != esk50_0
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[c_0_57,c_0_68]) ).

fof(c_0_76,plain,
    ! [X128,X129] :
      ( ~ ssList(X128)
      | ~ ssItem(X129)
      | hd(cons(X129,X128)) = X129 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).

cnf(c_0_77,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_69]) ).

cnf(c_0_78,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_70]) ).

cnf(c_0_79,negated_conjecture,
    ( tl(esk50_0) = nil
    | esk51_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_38])]),c_0_73]) ).

cnf(c_0_80,negated_conjecture,
    ( nil = esk50_0
    | nil != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_81,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[ax38]) ).

fof(c_0_82,plain,
    ! [X14,X15,X18,X19] :
      ( ( ssList(esk3_2(X14,X15))
        | ~ memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) )
      & ( ssList(esk4_2(X14,X15))
        | ~ memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) )
      & ( app(esk3_2(X14,X15),cons(X15,esk4_2(X14,X15))) = X14
        | ~ memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) )
      & ( ~ ssList(X18)
        | ~ ssList(X19)
        | app(X18,cons(X15,X19)) != X14
        | memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).

cnf(c_0_83,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_74]) ).

fof(c_0_84,plain,
    ! [X138] :
      ( ~ ssList(X138)
      | app(nil,X138) = X138 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_85,negated_conjecture,
    ( app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0)
    | ~ ssList(app(cons(esk52_0,nil),esk54_0)) ),
    inference(spm,[status(thm)],[c_0_75,c_0_43]) ).

fof(c_0_86,plain,
    ! [X118,X119,X120,X121] :
      ( ( X120 = X121
        | cons(X120,X118) != cons(X121,X119)
        | ~ ssItem(X121)
        | ~ ssItem(X120)
        | ~ ssList(X119)
        | ~ ssList(X118) )
      & ( X119 = X118
        | cons(X120,X118) != cons(X121,X119)
        | ~ ssItem(X121)
        | ~ ssItem(X120)
        | ~ ssList(X119)
        | ~ ssList(X118) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).

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

cnf(c_0_88,plain,
    ( cons(esk5_1(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_89,plain,
    ( ssItem(esk5_1(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_90,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_37]),c_0_38])]) ).

cnf(c_0_91,negated_conjecture,
    ( cons(hd(esk50_0),nil) = esk50_0
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_52])]),c_0_80]) ).

fof(c_0_92,plain,
    ! [X127] :
      ( ~ ssList(X127)
      | nil = X127
      | ssItem(hd(X127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

fof(c_0_93,plain,
    ! [X157,X158,X159] :
      ( ( ~ memberP(cons(X158,X159),X157)
        | X157 = X158
        | memberP(X159,X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) )
      & ( X157 != X158
        | memberP(cons(X158,X159),X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) )
      & ( ~ memberP(X159,X157)
        | memberP(cons(X158,X159),X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).

fof(c_0_94,plain,
    ! [X160] :
      ( ~ ssItem(X160)
      | ~ memberP(nil,X160) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_81])]) ).

cnf(c_0_95,plain,
    ( memberP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X1,cons(X3,X2)) != X4
    | ~ ssItem(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

cnf(c_0_96,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_83]) ).

cnf(c_0_97,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_98,negated_conjecture,
    ( app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0)
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_42]),c_0_31])]) ).

cnf(c_0_99,plain,
    ( X1 = X2
    | cons(X1,X3) != cons(X2,X4)
    | ~ ssItem(X2)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_100,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_87,c_0_88]),c_0_38])]),c_0_89]) ).

cnf(c_0_101,negated_conjecture,
    ( esk50_0 = nil
    | singletonP(esk50_0)
    | ~ ssItem(hd(esk50_0)) ),
    inference(spm,[status(thm)],[c_0_90,c_0_91]) ).

cnf(c_0_102,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_92]) ).

cnf(c_0_103,plain,
    ( X3 = X1
    | memberP(X2,X3)
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_104,plain,
    ( ~ ssItem(X1)
    | ~ memberP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_105,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(er,[status(thm)],[c_0_95]) ).

cnf(c_0_106,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_96,c_0_97]),c_0_38])]),c_0_42]) ).

cnf(c_0_107,negated_conjecture,
    app(cons(esk52_0,nil),esk54_0) = cons(esk52_0,esk54_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_37]),c_0_38]),c_0_39])]) ).

cnf(c_0_108,plain,
    ( esk5_1(cons(X1,X2)) = X1
    | ~ singletonP(cons(X1,X2))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_88]),c_0_38])])]),c_0_89]),c_0_37]) ).

cnf(c_0_109,plain,
    ( ssItem(hd(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_89,c_0_100]) ).

cnf(c_0_110,negated_conjecture,
    ( esk50_0 = nil
    | singletonP(esk50_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_52])]) ).

cnf(c_0_111,plain,
    ( esk5_1(X1) = X2
    | ~ singletonP(X1)
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_88]),c_0_38])]),c_0_89]),c_0_104]) ).

cnf(c_0_112,negated_conjecture,
    memberP(esk50_0,esk52_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_46]),c_0_52]),c_0_31]),c_0_32]),c_0_39])]) ).

fof(c_0_113,plain,
    ! [X190,X191] :
      ( ~ ssList(X190)
      | ~ ssList(X191)
      | ~ segmentP(X190,X191)
      | ~ segmentP(X191,X190)
      | X190 = X191 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).

cnf(c_0_114,negated_conjecture,
    ( segmentP(cons(esk52_0,esk54_0),cons(esk52_0,nil))
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_31])]) ).

cnf(c_0_115,plain,
    ( esk5_1(cons(X1,nil)) = X1
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_90]),c_0_38])]) ).

cnf(c_0_116,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_52])]) ).

cnf(c_0_117,negated_conjecture,
    ( esk5_1(esk50_0) = esk52_0
    | ~ singletonP(esk50_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_52]),c_0_39])]) ).

fof(c_0_118,plain,
    ! [X230] :
      ( ~ ssList(X230)
      | app(X230,nil) = X230 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

fof(c_0_119,plain,
    ! [X228,X229] :
      ( ( nil = X229
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil = X228
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil != X229
        | nil != X228
        | nil = app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

fof(c_0_120,plain,
    ! [X217,X218,X219] :
      ( ~ ssList(X217)
      | ~ ssList(X218)
      | ~ ssList(X219)
      | app(X219,X218) != app(X217,X218)
      | X219 = X217 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).

cnf(c_0_121,plain,
    ( X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ segmentP(X1,X2)
    | ~ segmentP(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_113]) ).

cnf(c_0_122,negated_conjecture,
    segmentP(cons(esk52_0,esk54_0),cons(esk52_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_37]),c_0_38]),c_0_39])]) ).

cnf(c_0_123,negated_conjecture,
    ssList(cons(esk52_0,esk54_0)),
    inference(rw,[status(thm)],[c_0_56,c_0_68]) ).

cnf(c_0_124,negated_conjecture,
    ( esk5_1(esk50_0) = hd(esk50_0)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_91]),c_0_116]) ).

cnf(c_0_125,negated_conjecture,
    ( esk5_1(esk50_0) = esk52_0
    | esk50_0 = nil ),
    inference(spm,[status(thm)],[c_0_117,c_0_110]) ).

cnf(c_0_126,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_118]) ).

cnf(c_0_127,plain,
    ( nil = X1
    | nil != app(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_119]) ).

cnf(c_0_128,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X3,X2) != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_120]) ).

cnf(c_0_129,negated_conjecture,
    ( cons(esk52_0,esk54_0) = cons(esk52_0,nil)
    | ~ segmentP(cons(esk52_0,nil),cons(esk52_0,esk54_0))
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).

cnf(c_0_130,negated_conjecture,
    ( hd(esk50_0) = esk52_0
    | esk50_0 = nil ),
    inference(spm,[status(thm)],[c_0_124,c_0_125]) ).

cnf(c_0_131,plain,
    ( segmentP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_126]),c_0_38])]),c_0_42]) ).

cnf(c_0_132,negated_conjecture,
    ( esk54_0 = nil
    | esk50_0 != nil
    | ~ ssList(app(esk53_0,cons(esk52_0,nil))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_29]),c_0_31])]) ).

cnf(c_0_133,plain,
    ( X1 = nil
    | app(X1,X2) != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_97]),c_0_38])]) ).

cnf(c_0_134,plain,
    ( X1 = X2
    | cons(X3,X2) != cons(X4,X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_135,negated_conjecture,
    ( cons(esk52_0,esk54_0) = cons(esk52_0,nil)
    | ~ segmentP(cons(esk52_0,nil),cons(esk52_0,esk54_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_37]),c_0_38]),c_0_39])]) ).

cnf(c_0_136,negated_conjecture,
    ( cons(esk52_0,nil) = esk50_0
    | esk50_0 = nil ),
    inference(spm,[status(thm)],[c_0_91,c_0_130]) ).

cnf(c_0_137,negated_conjecture,
    segmentP(esk50_0,cons(esk52_0,esk54_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_46]),c_0_123]),c_0_32])]) ).

cnf(c_0_138,negated_conjecture,
    ( esk54_0 = nil
    | esk50_0 != nil
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_42]),c_0_32])]) ).

cnf(c_0_139,negated_conjecture,
    ( esk53_0 = nil
    | cons(esk52_0,esk54_0) != esk50_0
    | ~ ssList(cons(esk52_0,esk54_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_46]),c_0_32])]) ).

cnf(c_0_140,negated_conjecture,
    ( esk50_0 = nil
    | X1 = nil
    | cons(X2,X1) != esk50_0
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_91]),c_0_38])]),c_0_116]) ).

cnf(c_0_141,negated_conjecture,
    ( cons(esk52_0,esk54_0) = esk50_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137])]) ).

cnf(c_0_142,negated_conjecture,
    ( esk54_0 = nil
    | esk50_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_37]),c_0_38]),c_0_39])]) ).

cnf(c_0_143,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_119]) ).

cnf(c_0_144,negated_conjecture,
    ( esk53_0 = nil
    | cons(esk52_0,esk54_0) != esk50_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_37]),c_0_31]),c_0_39])]) ).

cnf(c_0_145,negated_conjecture,
    esk54_0 = nil,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_31]),c_0_39])]),c_0_142]) ).

cnf(c_0_146,negated_conjecture,
    ( esk53_0 = nil
    | esk50_0 != nil
    | ~ ssList(cons(esk52_0,esk54_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_46]),c_0_32])]) ).

cnf(c_0_147,negated_conjecture,
    ( esk53_0 = nil
    | cons(esk52_0,nil) != esk50_0 ),
    inference(rw,[status(thm)],[c_0_144,c_0_145]) ).

cnf(c_0_148,negated_conjecture,
    ( esk53_0 = nil
    | esk50_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_37]),c_0_31]),c_0_39])]) ).

cnf(c_0_149,negated_conjecture,
    ( memberP(esk54_0,esk55_0)
    | memberP(esk53_0,esk55_0) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_150,negated_conjecture,
    esk53_0 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_136]),c_0_148]) ).

cnf(c_0_151,negated_conjecture,
    memberP(nil,esk55_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_145]),c_0_150])]) ).

cnf(c_0_152,negated_conjecture,
    ssItem(esk55_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_153,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_151]),c_0_152])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC297+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Aug 28 17:08:02 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.75  % Version  : CSE_E---1.5
% 0.20/0.75  % Problem  : theBenchmark.p
% 0.20/0.75  % Proof found
% 0.20/0.75  % SZS status Theorem for theBenchmark.p
% 0.20/0.75  % SZS output start Proof
% See solution above
% 0.20/0.76  % Total time : 0.200000 s
% 0.20/0.76  % SZS output end Proof
% 0.20/0.76  % Total time : 0.205000 s
%------------------------------------------------------------------------------