TSTP Solution File: SWC409+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC409+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 : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:22:22 EDT 2023

% Result   : Theorem 6.00s 6.08s
% Output   : CNFRefutation 6.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :  100
% Syntax   : Number of formulae    :  230 (  40 unt;  76 typ;   0 def)
%            Number of atoms       :  551 ( 146 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  659 ( 262   ~; 290   |;  41   &)
%                                         (   7 <=>;  59  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   4 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    :   57 (  57 usr;   8 con; 0-2 aty)
%            Number of variables   :  207 (   0 sgn; 102   !;  10   ?;   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 ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(ax36,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(app(X2,X3),X1)
              <=> ( memberP(X2,X1)
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).

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

fof(c_0_25,negated_conjecture,
    ! [X256,X257] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ( ~ ssItem(X256)
        | ~ ssList(X257)
        | app(X257,cons(X256,nil)) = esk50_0
        | app(cons(X256,nil),X257) != esk51_0 )
      & ssItem(esk52_0)
      & memberP(esk49_0,esk52_0)
      & ~ memberP(esk48_0,esk52_0)
      & ( nil = esk50_0
        | nil != esk51_0 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).

fof(c_0_26,plain,
    ! [X21,X22,X24] :
      ( ( ssList(esk6_2(X21,X22))
        | ~ frontsegP(X21,X22)
        | ~ ssList(X22)
        | ~ ssList(X21) )
      & ( app(X22,esk6_2(X21,X22)) = X21
        | ~ frontsegP(X21,X22)
        | ~ ssList(X22)
        | ~ ssList(X21) )
      & ( ~ ssList(X24)
        | app(X22,X24) != X21
        | frontsegP(X21,X22)
        | ~ ssList(X22)
        | ~ ssList(X21) ) ),
    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_27,plain,
    ! [X131,X132] :
      ( ~ ssList(X131)
      | ~ ssList(X132)
      | ssList(app(X131,X132)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

fof(c_0_28,plain,
    ! [X12,X13,X16,X17] :
      ( ( ssList(esk3_2(X12,X13))
        | ~ memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) )
      & ( ssList(esk4_2(X12,X13))
        | ~ memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) )
      & ( app(esk3_2(X12,X13),cons(X13,esk4_2(X12,X13))) = X12
        | ~ memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) )
      & ( ~ ssList(X16)
        | ~ ssList(X17)
        | app(X16,cons(X13,X17)) != X12
        | memberP(X12,X13)
        | ~ ssItem(X13)
        | ~ ssList(X12) ) ),
    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_29,negated_conjecture,
    memberP(esk49_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_31,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_34,plain,
    ( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    memberP(esk51_0,esk52_0),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_36,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_31,c_0_30]) ).

cnf(c_0_37,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_38,plain,
    ( ssList(esk3_2(X1,X2))
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_39,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_33]) ).

cnf(c_0_40,negated_conjecture,
    app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]) ).

cnf(c_0_41,negated_conjecture,
    ssList(esk3_2(esk51_0,esk52_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_36]),c_0_37])]) ).

fof(c_0_42,plain,
    ! [X112,X113] :
      ( ~ ssList(X112)
      | ~ ssItem(X113)
      | ssList(cons(X113,X112)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_43,plain,
    ( ssList(esk4_2(X1,X2))
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_44,plain,
    ! [X165,X166,X167] :
      ( ~ ssList(X165)
      | ~ ssList(X166)
      | ~ ssList(X167)
      | ~ frontsegP(X165,X166)
      | frontsegP(app(X165,X167),X166) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).

fof(c_0_45,plain,
    ! [X172] :
      ( ~ ssList(X172)
      | frontsegP(X172,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).

cnf(c_0_46,negated_conjecture,
    ( frontsegP(esk51_0,esk3_2(esk51_0,esk52_0))
    | ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

cnf(c_0_47,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,negated_conjecture,
    ssList(esk4_2(esk51_0,esk52_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_36]),c_0_37])]) ).

fof(c_0_49,plain,
    ! [X226,X227] :
      ( ( nil = X227
        | nil != app(X226,X227)
        | ~ ssList(X227)
        | ~ ssList(X226) )
      & ( nil = X226
        | nil != app(X226,X227)
        | ~ ssList(X227)
        | ~ ssList(X226) )
      & ( nil != X227
        | nil != X226
        | nil = app(X226,X227)
        | ~ ssList(X227)
        | ~ ssList(X226) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_50,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_51,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_52,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_53,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_54,negated_conjecture,
    frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_37])]) ).

cnf(c_0_55,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_56,plain,
    ! [X223,X224,X225] :
      ( ~ ssList(X223)
      | ~ ssList(X224)
      | ~ ssList(X225)
      | app(app(X223,X224),X225) = app(X223,app(X224,X225)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_57,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_58,plain,
    ( frontsegP(app(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).

cnf(c_0_59,negated_conjecture,
    app(esk3_2(esk51_0,esk52_0),esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_36]),c_0_41])]) ).

cnf(c_0_60,negated_conjecture,
    ssList(esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_41]),c_0_36])]) ).

fof(c_0_61,plain,
    ! [X29,X30,X33,X34] :
      ( ( ssList(esk8_2(X29,X30))
        | ~ segmentP(X29,X30)
        | ~ ssList(X30)
        | ~ ssList(X29) )
      & ( ssList(esk9_2(X29,X30))
        | ~ segmentP(X29,X30)
        | ~ ssList(X30)
        | ~ ssList(X29) )
      & ( app(app(esk8_2(X29,X30),X30),esk9_2(X29,X30)) = X29
        | ~ segmentP(X29,X30)
        | ~ ssList(X30)
        | ~ ssList(X29) )
      & ( ~ ssList(X33)
        | ~ ssList(X34)
        | app(app(X33,X30),X34) != X29
        | segmentP(X29,X30)
        | ~ ssList(X30)
        | ~ ssList(X29) ) ),
    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_62,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_63,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_57])]),c_0_52])]) ).

cnf(c_0_64,negated_conjecture,
    frontsegP(esk51_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_41])]) ).

cnf(c_0_65,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_61]) ).

cnf(c_0_66,plain,
    ( app(nil,app(nil,X1)) = app(nil,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_52])]) ).

cnf(c_0_67,negated_conjecture,
    app(nil,esk6_2(esk51_0,nil)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_64]),c_0_36]),c_0_52])]) ).

cnf(c_0_68,negated_conjecture,
    ssList(esk6_2(esk51_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_64]),c_0_52]),c_0_36])]) ).

cnf(c_0_69,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_65]) ).

cnf(c_0_70,negated_conjecture,
    app(nil,esk51_0) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).

fof(c_0_71,plain,
    ! [X228] :
      ( ~ ssList(X228)
      | app(X228,nil) = X228 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_72,negated_conjecture,
    ( segmentP(app(esk51_0,X1),esk51_0)
    | ~ ssList(app(esk51_0,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_36]),c_0_52])]) ).

cnf(c_0_73,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_74,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_61]) ).

cnf(c_0_75,negated_conjecture,
    segmentP(esk51_0,esk51_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_36]),c_0_52])]) ).

cnf(c_0_76,plain,
    ( ssList(esk9_2(X1,X2))
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_77,plain,
    ( ssList(esk8_2(X1,X2))
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_78,negated_conjecture,
    app(app(esk8_2(esk51_0,esk51_0),esk51_0),esk9_2(esk51_0,esk51_0)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_36])]) ).

cnf(c_0_79,negated_conjecture,
    ssList(esk9_2(esk51_0,esk51_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_36])]) ).

cnf(c_0_80,negated_conjecture,
    ssList(esk8_2(esk51_0,esk51_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_75]),c_0_36])]) ).

fof(c_0_81,plain,
    ! [X229,X230] :
      ( ~ ssList(X229)
      | ~ ssList(X230)
      | nil = X229
      | hd(app(X229,X230)) = hd(X229) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).

cnf(c_0_82,negated_conjecture,
    app(esk8_2(esk51_0,esk51_0),app(esk51_0,esk9_2(esk51_0,esk51_0))) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_78]),c_0_79]),c_0_36]),c_0_80])]) ).

fof(c_0_83,plain,
    ! [X125] :
      ( ~ ssList(X125)
      | nil = X125
      | ssItem(hd(X125)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_84,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

fof(c_0_85,plain,
    ! [X180,X181,X182] :
      ( ~ ssList(X180)
      | ~ ssList(X181)
      | ~ ssList(X182)
      | ~ rearsegP(X180,X181)
      | rearsegP(app(X182,X180),X181) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).

fof(c_0_86,plain,
    ! [X183] :
      ( ~ ssList(X183)
      | rearsegP(X183,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).

cnf(c_0_87,negated_conjecture,
    ( frontsegP(esk51_0,esk8_2(esk51_0,esk51_0))
    | ~ ssList(app(esk51_0,esk9_2(esk51_0,esk51_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_82]),c_0_80])]) ).

cnf(c_0_88,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_83]) ).

cnf(c_0_89,negated_conjecture,
    ( hd(esk3_2(esk51_0,esk52_0)) = hd(esk51_0)
    | esk3_2(esk51_0,esk52_0) = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_59]),c_0_60]),c_0_41])]) ).

cnf(c_0_90,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_91,plain,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_92,negated_conjecture,
    frontsegP(esk51_0,esk8_2(esk51_0,esk51_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_33]),c_0_79]),c_0_36])]) ).

fof(c_0_93,plain,
    ! [X25,X26,X28] :
      ( ( ssList(esk7_2(X25,X26))
        | ~ rearsegP(X25,X26)
        | ~ ssList(X26)
        | ~ ssList(X25) )
      & ( app(esk7_2(X25,X26),X26) = X25
        | ~ rearsegP(X25,X26)
        | ~ ssList(X26)
        | ~ ssList(X25) )
      & ( ~ ssList(X28)
        | app(X28,X26) != X25
        | rearsegP(X25,X26)
        | ~ ssList(X26)
        | ~ ssList(X25) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).

fof(c_0_94,plain,
    ! [X136] :
      ( ~ ssList(X136)
      | app(nil,X136) = X136 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_95,negated_conjecture,
    ( esk3_2(esk51_0,esk52_0) = nil
    | ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_41])]) ).

cnf(c_0_96,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_52])]) ).

cnf(c_0_97,negated_conjecture,
    app(esk8_2(esk51_0,esk51_0),esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_92]),c_0_36]),c_0_80])]) ).

cnf(c_0_98,negated_conjecture,
    ssList(esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_92]),c_0_80]),c_0_36])]) ).

cnf(c_0_99,plain,
    ( app(esk7_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_100,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

fof(c_0_101,plain,
    ! [X221,X222] :
      ( ~ ssList(X221)
      | ~ ssItem(X222)
      | cons(X222,X221) = app(cons(X222,nil),X221) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_102,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_103,negated_conjecture,
    ( app(nil,cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0
    | ssItem(hd(esk51_0)) ),
    inference(spm,[status(thm)],[c_0_40,c_0_95]) ).

fof(c_0_104,plain,
    ! [X214] :
      ( ~ ssList(X214)
      | nil = X214
      | cons(hd(X214),tl(X214)) = X214 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

cnf(c_0_105,negated_conjecture,
    rearsegP(esk51_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_80]),c_0_98])]) ).

cnf(c_0_106,plain,
    ( app(esk7_2(X1,nil),nil) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_91]),c_0_52])]) ).

cnf(c_0_107,plain,
    ( ssList(esk7_2(X1,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_91]),c_0_52])]) ).

cnf(c_0_108,negated_conjecture,
    ( app(X2,cons(X1,nil)) = esk50_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_109,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_101]) ).

cnf(c_0_110,negated_conjecture,
    ( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
    | ssItem(hd(esk51_0))
    | ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_111,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_112,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_113,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_99,c_0_105]),c_0_52]),c_0_36])]) ).

cnf(c_0_114,plain,
    ( esk7_2(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_106]),c_0_107]) ).

cnf(c_0_115,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_28]) ).

cnf(c_0_116,negated_conjecture,
    ( app(X1,cons(X2,nil)) = esk50_0
    | cons(X2,X1) != esk51_0
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[c_0_108,c_0_109]) ).

cnf(c_0_117,negated_conjecture,
    ( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
    | ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_47]),c_0_48]),c_0_37])]) ).

cnf(c_0_118,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_119,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_120,negated_conjecture,
    ~ memberP(esk48_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_121,plain,
    ! [X155,X156,X157] :
      ( ( ~ memberP(cons(X156,X157),X155)
        | X155 = X156
        | memberP(X157,X155)
        | ~ ssList(X157)
        | ~ ssItem(X156)
        | ~ ssItem(X155) )
      & ( X155 != X156
        | memberP(cons(X156,X157),X155)
        | ~ ssList(X157)
        | ~ ssItem(X156)
        | ~ ssItem(X155) )
      & ( ~ memberP(X157,X155)
        | memberP(cons(X156,X157),X155)
        | ~ ssList(X157)
        | ~ ssItem(X156)
        | ~ ssItem(X155) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).

fof(c_0_122,plain,
    ! [X128] :
      ( ~ ssList(X128)
      | nil = X128
      | ssList(tl(X128)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

fof(c_0_123,plain,
    ! [X231,X232] :
      ( ~ ssList(X231)
      | ~ ssList(X232)
      | nil = X231
      | tl(app(X231,X232)) = app(tl(X231),X232) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).

cnf(c_0_124,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_111,c_0_84]),c_0_33]),c_0_112]) ).

cnf(c_0_125,negated_conjecture,
    app(esk51_0,nil) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_36])]) ).

cnf(c_0_126,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_115]) ).

cnf(c_0_127,negated_conjecture,
    ( app(esk4_2(esk51_0,esk52_0),cons(esk52_0,nil)) = esk50_0
    | ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_48]),c_0_37])]) ).

cnf(c_0_128,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_118,c_0_119]) ).

cnf(c_0_129,negated_conjecture,
    ~ memberP(esk50_0,esk52_0),
    inference(rw,[status(thm)],[c_0_120,c_0_119]) ).

cnf(c_0_130,plain,
    ( X3 = X1
    | memberP(X2,X3)
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_121]) ).

cnf(c_0_131,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_122]) ).

cnf(c_0_132,plain,
    ( nil = X1
    | tl(app(X1,X2)) = app(tl(X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

cnf(c_0_133,negated_conjecture,
    ( cons(hd(esk51_0),tl(esk51_0)) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_52]),c_0_36])]) ).

cnf(c_0_134,negated_conjecture,
    ssItem(hd(esk51_0)),
    inference(sr,[status(thm)],[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_126,c_0_127]),c_0_128]),c_0_52]),c_0_48]),c_0_37])]),c_0_129]) ).

fof(c_0_135,plain,
    ! [X152,X153,X154] :
      ( ( ~ memberP(app(X153,X154),X152)
        | memberP(X153,X152)
        | memberP(X154,X152)
        | ~ ssList(X154)
        | ~ ssList(X153)
        | ~ ssItem(X152) )
      & ( ~ memberP(X153,X152)
        | memberP(app(X153,X154),X152)
        | ~ ssList(X154)
        | ~ ssList(X153)
        | ~ ssItem(X152) )
      & ( ~ memberP(X154,X152)
        | memberP(app(X153,X154),X152)
        | ~ ssList(X154)
        | ~ ssList(X153)
        | ~ ssItem(X152) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).

cnf(c_0_136,plain,
    ( hd(X1) = X2
    | nil = X1
    | memberP(tl(X1),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_111]),c_0_88]),c_0_131]) ).

cnf(c_0_137,plain,
    ( nil = X1
    | ssList(app(tl(X1),X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_33]),c_0_112]) ).

cnf(c_0_138,negated_conjecture,
    ( app(tl(esk51_0),nil) = tl(esk51_0)
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_125]),c_0_52]),c_0_36])]) ).

cnf(c_0_139,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
    | esk51_0 = nil
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_133]),c_0_134])]) ).

cnf(c_0_140,plain,
    ( memberP(app(X1,X3),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_135]) ).

cnf(c_0_141,negated_conjecture,
    ( hd(esk51_0) = esk52_0
    | esk51_0 = nil
    | memberP(tl(esk51_0),esk52_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_35]),c_0_36]),c_0_37])]) ).

cnf(c_0_142,negated_conjecture,
    ( esk51_0 = nil
    | ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_52]),c_0_36])]) ).

cnf(c_0_143,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_131]),c_0_36])]) ).

cnf(c_0_144,negated_conjecture,
    ( hd(esk51_0) = esk52_0
    | esk51_0 = nil
    | memberP(app(tl(esk51_0),X1),esk52_0)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_37])]),c_0_142]) ).

cnf(c_0_145,negated_conjecture,
    ( esk51_0 = nil
    | memberP(esk50_0,hd(esk51_0))
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_143]),c_0_128]),c_0_52]),c_0_134])]) ).

cnf(c_0_146,negated_conjecture,
    ( hd(esk51_0) = esk52_0
    | esk51_0 = nil
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_143]),c_0_129]) ).

cnf(c_0_147,negated_conjecture,
    ( esk51_0 = nil
    | memberP(esk50_0,hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_131]),c_0_36])]) ).

cnf(c_0_148,negated_conjecture,
    ( hd(esk51_0) = esk52_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_47]),c_0_52]),c_0_134])]) ).

cnf(c_0_149,negated_conjecture,
    ( nil = esk50_0
    | nil != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_150,negated_conjecture,
    esk51_0 = nil,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_129]) ).

cnf(c_0_151,negated_conjecture,
    esk50_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150])]) ).

cnf(c_0_152,negated_conjecture,
    ~ memberP(nil,esk52_0),
    inference(rw,[status(thm)],[c_0_129,c_0_151]) ).

cnf(c_0_153,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_150]),c_0_152]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC409+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 : n025.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 17:29:24 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 6.00/6.08  % Version  : CSE_E---1.5
% 6.00/6.08  % Problem  : theBenchmark.p
% 6.00/6.08  % Proof found
% 6.00/6.08  % SZS status Theorem for theBenchmark.p
% 6.00/6.08  % SZS output start Proof
% See solution above
% 6.00/6.09  % Total time : 5.509000 s
% 6.00/6.09  % SZS output end Proof
% 6.00/6.09  % Total time : 5.513000 s
%------------------------------------------------------------------------------