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

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%------------------------------------------------------------------------------
% 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 : n006.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   : Unsatisfiable 9.44s 9.54s
% Output   : CNFRefutation 9.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :  126
% Syntax   : Number of formulae    :  287 (  58 unt;  73 typ;   0 def)
%            Number of atoms       :  563 ( 190 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  681 ( 332   ~; 349   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   82 (  65   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   54 (  54 usr;   8 con; 0-2 aty)
%            Number of variables   :  313 (  46 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    nil: $i ).

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

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

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

tff(decl_26,type,
    totalorderedP: $i > $o ).

tff(decl_27,type,
    strictorderP: $i > $o ).

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

tff(decl_29,type,
    cyclefreeP: $i > $o ).

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

tff(decl_31,type,
    skac3: $i ).

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

tff(decl_33,type,
    skac2: $i ).

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

tff(decl_35,type,
    skaf83: $i > $i ).

tff(decl_36,type,
    skaf82: $i > $i ).

tff(decl_37,type,
    skaf81: $i > $i ).

tff(decl_38,type,
    skaf80: $i > $i ).

tff(decl_39,type,
    skaf79: $i > $i ).

tff(decl_40,type,
    skaf78: $i > $i ).

tff(decl_41,type,
    skaf77: $i > $i ).

tff(decl_42,type,
    skaf76: $i > $i ).

tff(decl_43,type,
    skaf75: $i > $i ).

tff(decl_44,type,
    skaf74: $i > $i ).

tff(decl_45,type,
    skaf73: $i > $i ).

tff(decl_46,type,
    skaf72: $i > $i ).

tff(decl_47,type,
    skaf71: $i > $i ).

tff(decl_48,type,
    skaf70: $i > $i ).

tff(decl_49,type,
    skaf69: $i > $i ).

tff(decl_50,type,
    skaf68: $i > $i ).

tff(decl_51,type,
    skaf67: $i > $i ).

tff(decl_52,type,
    skaf66: $i > $i ).

tff(decl_53,type,
    skaf65: $i > $i ).

tff(decl_54,type,
    skaf64: $i > $i ).

tff(decl_55,type,
    skaf63: $i > $i ).

tff(decl_56,type,
    skaf62: $i > $i ).

tff(decl_57,type,
    skaf61: $i > $i ).

tff(decl_58,type,
    skaf60: $i > $i ).

tff(decl_59,type,
    skaf59: $i > $i ).

tff(decl_60,type,
    skaf58: $i > $i ).

tff(decl_61,type,
    skaf57: $i > $i ).

tff(decl_62,type,
    skaf56: $i > $i ).

tff(decl_63,type,
    skaf55: $i > $i ).

tff(decl_64,type,
    skaf54: $i > $i ).

tff(decl_65,type,
    skaf53: $i > $i ).

tff(decl_66,type,
    skaf52: $i > $i ).

tff(decl_67,type,
    skaf51: $i > $i ).

tff(decl_68,type,
    skaf50: $i > $i ).

tff(decl_69,type,
    skaf49: $i > $i ).

tff(decl_70,type,
    skaf44: $i > $i ).

tff(decl_71,type,
    skaf48: ( $i * $i ) > $i ).

tff(decl_72,type,
    skaf47: ( $i * $i ) > $i ).

tff(decl_73,type,
    skaf46: ( $i * $i ) > $i ).

tff(decl_74,type,
    skaf45: ( $i * $i ) > $i ).

tff(decl_75,type,
    skaf43: ( $i * $i ) > $i ).

tff(decl_76,type,
    skaf42: ( $i * $i ) > $i ).

tff(decl_77,type,
    geq: ( $i * $i ) > $o ).

tff(decl_78,type,
    segmentP: ( $i * $i ) > $o ).

tff(decl_79,type,
    rearsegP: ( $i * $i ) > $o ).

tff(decl_80,type,
    frontsegP: ( $i * $i ) > $o ).

tff(decl_81,type,
    leq: ( $i * $i ) > $o ).

tff(decl_82,type,
    lt: ( $i * $i ) > $o ).

tff(decl_83,type,
    cons: ( $i * $i ) > $i ).

tff(decl_84,type,
    memberP: ( $i * $i ) > $o ).

tff(decl_85,type,
    app: ( $i * $i ) > $i ).

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

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

tff(decl_88,type,
    neq: ( $i * $i ) > $o ).

tff(decl_89,type,
    gt: ( $i * $i ) > $o ).

tff(decl_90,type,
    sk1: $i ).

tff(decl_91,type,
    sk2: $i ).

tff(decl_92,type,
    sk3: $i ).

tff(decl_93,type,
    sk4: $i ).

tff(decl_94,type,
    sk5: $i ).

cnf(co1_9,negated_conjecture,
    memberP(sk2,sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

cnf(co1_5,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).

cnf(co1_2,negated_conjecture,
    ssList(sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).

cnf(clause179,axiom,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).

cnf(clause169,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).

cnf(co1_8,negated_conjecture,
    ssItem(sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

cnf(clause52,axiom,
    ssList(skaf43(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).

cnf(clause53,axiom,
    ssList(skaf42(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).

cnf(clause99,axiom,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).

cnf(clause104,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).

cnf(clause75,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).

cnf(clause76,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).

cnf(clause116,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).

cnf(clause72,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).

cnf(clause133,axiom,
    ( nil = X2
    | tl(app(X2,X1)) = app(tl(X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).

cnf(clause85,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).

cnf(clause118,axiom,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).

cnf(clause96,axiom,
    ( tl(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).

cnf(clause101,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).

cnf(clause47,axiom,
    ssItem(skaf44(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).

cnf(clause8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).

cnf(clause86,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).

cnf(clause73,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).

cnf(clause98,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).

cnf(clause120,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).

cnf(co1_7,negated_conjecture,
    ( app(X2,cons(X1,nil)) = sk3
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != sk4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

cnf(clause131,axiom,
    ( app(skaf46(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause131) ).

cnf(clause58,axiom,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause58) ).

cnf(clause136,axiom,
    ( rearsegP(app(X3,X1),X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause136) ).

cnf(clause109,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).

cnf(clause13,axiom,
    ssList(skaf82(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).

cnf(clause151,axiom,
    ( X1 = X3
    | app(X1,X2) != app(X3,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause151) ).

cnf(clause50,axiom,
    ssList(skaf46(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).

cnf(co1_1,negated_conjecture,
    ssList(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).

cnf(co1_6,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

cnf(clause137,axiom,
    ( frontsegP(app(X1,X3),X2)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause137) ).

cnf(clause60,axiom,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).

cnf(clause144,axiom,
    ( frontsegP(X3,X1)
    | app(X1,X2) != X3
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).

cnf(clause149,axiom,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).

cnf(clause74,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).

cnf(clause145,axiom,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).

cnf(clause119,axiom,
    ( nil = X2
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).

cnf(clause157,axiom,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).

cnf(clause132,axiom,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).

cnf(clause138,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).

cnf(clause97,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).

cnf(clause51,axiom,
    ssList(skaf45(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).

cnf(clause175,axiom,
    ( memberP(X4,X2)
    | app(X1,cons(X2,X3)) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ ssList(X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).

cnf(clause161,axiom,
    ( memberP(X2,X3)
    | X3 = X1
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).

cnf(clause71,axiom,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).

cnf(clause123,axiom,
    ( nil = X2
    | hd(app(X2,X1)) = hd(X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause123) ).

cnf(clause140,axiom,
    ( memberP(app(X1,X3),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause140) ).

cnf(co1_10,negated_conjecture,
    ~ memberP(sk1,sk5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

cnf(c_0_53,negated_conjecture,
    memberP(sk2,sk5),
    co1_9 ).

cnf(c_0_54,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_55,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_56,axiom,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    clause179 ).

cnf(c_0_57,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    clause169 ).

cnf(c_0_58,negated_conjecture,
    memberP(sk4,sk5),
    inference(rw,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_59,negated_conjecture,
    ssItem(sk5),
    co1_8 ).

cnf(c_0_60,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_55,c_0_54]) ).

cnf(c_0_61,plain,
    ( ~ ssItem(X1)
    | ~ ssList(app(app(X2,cons(X1,X3)),cons(X1,X4)))
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ duplicatefreeP(app(app(X2,cons(X1,X3)),cons(X1,X4))) ),
    inference(er,[status(thm)],[c_0_56]) ).

cnf(c_0_62,negated_conjecture,
    app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60])]) ).

cnf(c_0_63,axiom,
    ssList(skaf43(X1,X2)),
    clause52 ).

cnf(c_0_64,axiom,
    ssList(skaf42(X1,X2)),
    clause53 ).

cnf(c_0_65,axiom,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause99 ).

cnf(c_0_66,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause104 ).

cnf(c_0_67,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause75 ).

cnf(c_0_68,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause76 ).

cnf(c_0_69,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause116 ).

cnf(c_0_70,negated_conjecture,
    ( ~ ssList(app(sk4,cons(sk5,X1)))
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(sk4,cons(sk5,X1))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_59]),c_0_63]),c_0_64])]) ).

cnf(c_0_71,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    clause72 ).

cnf(c_0_72,plain,
    ( nil = X1
    | tl(X1) != X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]) ).

cnf(c_0_73,axiom,
    ( nil = X2
    | tl(app(X2,X1)) = app(tl(X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause133 ).

cnf(c_0_74,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause85 ).

cnf(c_0_75,axiom,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause118 ).

cnf(c_0_76,axiom,
    ( tl(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause96 ).

cnf(c_0_77,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    clause101 ).

cnf(c_0_78,axiom,
    ssItem(skaf44(X1)),
    clause47 ).

cnf(c_0_79,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_80,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(er,[status(thm)],[c_0_69]) ).

cnf(c_0_81,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause86 ).

cnf(c_0_82,negated_conjecture,
    ( ssItem(X1)
    | ~ ssList(app(sk4,cons(sk5,X2)))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_83,plain,
    ( nil = X1
    | app(tl(X1),X2) != app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_75]) ).

cnf(c_0_84,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    clause73 ).

cnf(c_0_85,plain,
    ( tl(X1) = nil
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79])]) ).

cnf(c_0_86,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_79])]) ).

cnf(c_0_87,negated_conjecture,
    ( ssItem(X1)
    | ~ ssList(cons(sk5,X2))
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_74]),c_0_60])]) ).

cnf(c_0_88,plain,
    ( nil = X1
    | tl(X1) != app(X1,nil)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_79])]),c_0_67]) ).

cnf(c_0_89,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause98 ).

cnf(c_0_90,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_91,negated_conjecture,
    ( ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_81]),c_0_59])]) ).

cnf(c_0_92,plain,
    ( app(cons(X1,X2),nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_76]),c_0_81]),c_0_89]) ).

cnf(c_0_93,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause120 ).

cnf(c_0_94,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_81]),c_0_79])]) ).

cnf(c_0_95,negated_conjecture,
    ssItem(X1),
    inference(spm,[status(thm)],[c_0_91,c_0_64]) ).

cnf(c_0_96,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_79])]) ).

cnf(c_0_97,negated_conjecture,
    ( app(X2,cons(X1,nil)) = sk3
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != sk4 ),
    co1_7 ).

cnf(c_0_98,plain,
    tl(cons(X1,nil)) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).

cnf(c_0_99,plain,
    cons(X1,nil) != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_95])]) ).

cnf(c_0_100,negated_conjecture,
    ( app(X1,cons(X2,nil)) = sk3
    | app(cons(X2,nil),X1) != sk4
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_95])]) ).

cnf(c_0_101,plain,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_95])]) ).

cnf(c_0_102,plain,
    ( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
    | ~ ssList(cons(X1,nil)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_98]),c_0_99]) ).

cnf(c_0_103,plain,
    ( ssList(cons(X1,X2))
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_95])]) ).

cnf(c_0_104,axiom,
    ( app(skaf46(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause131 ).

cnf(c_0_105,axiom,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    clause58 ).

cnf(c_0_106,axiom,
    ( rearsegP(app(X3,X1),X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause136 ).

cnf(c_0_107,negated_conjecture,
    ( app(X1,cons(X2,nil)) = sk3
    | cons(X2,X1) != sk4
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_108,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause109 ).

cnf(c_0_109,axiom,
    ssList(skaf82(X1)),
    clause13 ).

cnf(c_0_110,plain,
    cons(hd(cons(X1,nil)),nil) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_79])]) ).

cnf(c_0_111,axiom,
    ( X1 = X3
    | app(X1,X2) != app(X3,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause151 ).

cnf(c_0_112,plain,
    ( app(skaf46(X1,nil),nil) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_79])]) ).

cnf(c_0_113,axiom,
    ssList(skaf46(X1,X2)),
    clause50 ).

cnf(c_0_114,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_105]),c_0_79])]) ).

cnf(c_0_115,negated_conjecture,
    ( app(skaf82(sk4),cons(skaf83(sk4),nil)) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109])])]),c_0_60])]) ).

cnf(c_0_116,plain,
    ssList(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_110]),c_0_79])]) ).

cnf(c_0_117,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_118,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_119,plain,
    ( skaf46(app(X1,nil),nil) = X1
    | ~ ssList(app(X1,nil))
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_79]),c_0_113])])]) ).

cnf(c_0_120,negated_conjecture,
    ( sk4 = nil
    | rearsegP(sk3,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_109]),c_0_116])]) ).

cnf(c_0_121,negated_conjecture,
    ssList(sk3),
    inference(rw,[status(thm)],[c_0_117,c_0_118]) ).

cnf(c_0_122,plain,
    ( skaf46(app(X1,nil),nil) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_74]),c_0_79])]) ).

cnf(c_0_123,axiom,
    ( frontsegP(app(X1,X3),X2)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause137 ).

cnf(c_0_124,axiom,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    clause60 ).

cnf(c_0_125,negated_conjecture,
    ( app(skaf46(sk3,nil),nil) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_120]),c_0_79]),c_0_121])]) ).

cnf(c_0_126,plain,
    ( skaf46(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_112]),c_0_113])]) ).

cnf(c_0_127,axiom,
    ( frontsegP(X3,X1)
    | app(X1,X2) != X3
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    clause144 ).

cnf(c_0_128,axiom,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause149 ).

cnf(c_0_129,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    clause74 ).

cnf(c_0_130,plain,
    skaf46(cons(X1,nil),nil) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_101]),c_0_116]),c_0_79])]) ).

cnf(c_0_131,axiom,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause145 ).

cnf(c_0_132,plain,
    ( frontsegP(app(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_79])]) ).

cnf(c_0_133,negated_conjecture,
    ( app(sk3,nil) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_121])]) ).

cnf(c_0_134,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_127]),c_0_74]) ).

cnf(c_0_135,axiom,
    ( nil = X2
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause119 ).

cnf(c_0_136,plain,
    ( app(nil,app(X1,X2)) = app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_79])]) ).

cnf(c_0_137,plain,
    app(cons(X1,nil),nil) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_130]),c_0_116])]) ).

cnf(c_0_138,axiom,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause157 ).

cnf(c_0_139,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_131])]),c_0_79])]) ).

cnf(c_0_140,axiom,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause132 ).

cnf(c_0_141,negated_conjecture,
    ( sk4 = nil
    | frontsegP(sk3,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_79]),c_0_121])]) ).

cnf(c_0_142,negated_conjecture,
    ( sk4 = nil
    | frontsegP(sk3,sk3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_133]),c_0_79]),c_0_121])]) ).

cnf(c_0_143,plain,
    ( nil = X1
    | app(X2,app(X3,X1)) != nil
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_128]),c_0_74]) ).

cnf(c_0_144,plain,
    app(nil,cons(X1,nil)) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_116]),c_0_79])]) ).

cnf(c_0_145,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    clause138 ).

cnf(c_0_146,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause97 ).

cnf(c_0_147,plain,
    ( app(cons(X1,X2),X3) = cons(X1,app(X2,X3))
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_95])]) ).

cnf(c_0_148,plain,
    ( cons(X1,X2) != nil
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_95])]) ).

cnf(c_0_149,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_128,c_0_139]),c_0_79])]) ).

cnf(c_0_150,negated_conjecture,
    ( app(nil,skaf45(sk3,nil)) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_79]),c_0_121])]) ).

cnf(c_0_151,axiom,
    ssList(skaf45(X1,X2)),
    clause51 ).

cnf(c_0_152,plain,
    ( ssList(app(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_128]),c_0_74]) ).

cnf(c_0_153,negated_conjecture,
    ( app(sk3,skaf45(sk3,sk3)) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_142]),c_0_121])]) ).

cnf(c_0_154,plain,
    ( app(X1,X2) = nil
    | app(X1,app(X2,X3)) != nil
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_128]),c_0_74]) ).

cnf(c_0_155,plain,
    ( app(X1,cons(X2,nil)) != nil
    | ~ ssList(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_116]),c_0_79])]),c_0_99]) ).

cnf(c_0_156,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_145]) ).

cnf(c_0_157,plain,
    ( X1 = nil
    | app(X1,nil) != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_139]),c_0_79])]) ).

cnf(c_0_158,plain,
    ( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
    | nil = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_73]),c_0_74]),c_0_75]) ).

cnf(c_0_159,plain,
    ( tl(cons(X1,X2)) = X2
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_95])]) ).

cnf(c_0_160,plain,
    ( hd(cons(X1,X2)) = X1
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_95])]) ).

cnf(c_0_161,plain,
    ( tl(cons(X1,app(X2,X3))) = app(tl(cons(X1,X2)),X3)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_147]),c_0_103]),c_0_148]) ).

cnf(c_0_162,negated_conjecture,
    ( app(nil,sk3) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151])]) ).

cnf(c_0_163,negated_conjecture,
    ( sk4 = nil
    | ssList(app(X1,sk3))
    | ~ 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_151]),c_0_121])]) ).

cnf(c_0_164,negated_conjecture,
    ( sk4 = nil
    | app(X1,sk3) != nil
    | ~ ssList(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_115]),c_0_116]),c_0_109])]),c_0_99]) ).

cnf(c_0_165,axiom,
    ( memberP(X4,X2)
    | app(X1,cons(X2,X3)) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ ssList(X4) ),
    clause175 ).

cnf(c_0_166,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | sk4 = nil
    | ~ ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_66])]),c_0_60])]) ).

cnf(c_0_167,plain,
    ( app(X1,cons(X2,X3)) != nil
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_101]),c_0_116])]),c_0_155]) ).

cnf(c_0_168,axiom,
    ( memberP(X2,X3)
    | X3 = X1
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    clause161 ).

cnf(c_0_169,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_95])]) ).

cnf(c_0_170,axiom,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    clause71 ).

cnf(c_0_171,plain,
    ( cons(X1,app(X2,nil)) != nil
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_147]),c_0_79])]),c_0_103]),c_0_148]) ).

cnf(c_0_172,plain,
    ( cons(hd(app(cons(X1,X2),X3)),app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_103]),c_0_148]) ).

cnf(c_0_173,plain,
    ( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_160]),c_0_103]),c_0_148]) ).

cnf(c_0_174,negated_conjecture,
    ( tl(cons(X1,sk3)) = app(nil,sk3)
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_98]),c_0_121]),c_0_79])]) ).

cnf(c_0_175,negated_conjecture,
    ( sk4 = nil
    | ssList(cons(X1,sk3)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_101]),c_0_116]),c_0_121])]) ).

cnf(c_0_176,negated_conjecture,
    ( sk4 = nil
    | cons(X1,sk3) != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_101]),c_0_116]),c_0_121])]) ).

cnf(c_0_177,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssItem(X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_165]) ).

cnf(c_0_178,negated_conjecture,
    ( app(tl(sk4),cons(hd(sk4),nil)) = sk3
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_67]),c_0_60])]) ).

cnf(c_0_179,negated_conjecture,
    sk4 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_62]),c_0_63]),c_0_64])]) ).

cnf(c_0_180,axiom,
    ( nil = X2
    | hd(app(X2,X1)) = hd(X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause123 ).

cnf(c_0_181,plain,
    ( X1 = X2
    | memberP(X3,X2)
    | ~ memberP(cons(X1,X3),X2)
    | ~ ssList(X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_95]),c_0_95])]) ).

cnf(c_0_182,plain,
    memberP(cons(X1,nil),hd(cons(X1,nil))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_110]),c_0_79])]) ).

cnf(c_0_183,plain,
    ~ memberP(nil,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_95])]) ).

cnf(c_0_184,plain,
    ( app(cons(X1,X2),nil) != nil
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_79])]) ).

cnf(c_0_185,negated_conjecture,
    ( cons(X1,app(nil,sk3)) = cons(X1,sk3)
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_121])]) ).

cnf(c_0_186,negated_conjecture,
    ( sk4 = nil
    | ssList(app(nil,sk3)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_174]),c_0_175]),c_0_176]) ).

cnf(c_0_187,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_95])]) ).

cnf(c_0_188,axiom,
    ( memberP(app(X1,X3),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    clause140 ).

cnf(c_0_189,plain,
    ( cons(hd(X1),app(tl(X1),X2)) = app(X1,X2)
    | nil = X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_66]),c_0_67]) ).

cnf(c_0_190,negated_conjecture,
    app(tl(sk4),cons(hd(sk4),nil)) = sk3,
    inference(sr,[status(thm)],[c_0_178,c_0_179]) ).

cnf(c_0_191,plain,
    ( hd(cons(X1,app(X2,X3))) = hd(cons(X1,X2))
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_147]),c_0_103]),c_0_148]) ).

cnf(c_0_192,plain,
    hd(cons(X1,nil)) = X1,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_79])]),c_0_183]) ).

cnf(c_0_193,negated_conjecture,
    ( sk4 = nil
    | app(cons(X1,sk3),nil) != nil ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]) ).

cnf(c_0_194,negated_conjecture,
    ( sk4 = nil
    | memberP(sk3,skaf83(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_115]),c_0_121]),c_0_79]),c_0_109])]) ).

cnf(c_0_195,plain,
    ( skaf83(X1) = hd(X1)
    | nil = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_108]),c_0_109])]) ).

cnf(c_0_196,negated_conjecture,
    ( memberP(app(sk4,X1),sk5)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_58]),c_0_59]),c_0_60])]) ).

cnf(c_0_197,negated_conjecture,
    app(sk4,cons(hd(sk4),nil)) = cons(hd(sk4),sk3),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_116]),c_0_60])]),c_0_179]) ).

cnf(c_0_198,negated_conjecture,
    ( hd(cons(X1,sk3)) = X1
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_162]),c_0_192]),c_0_121]),c_0_79])]) ).

cnf(c_0_199,negated_conjecture,
    app(nil,sk3) = sk3,
    inference(sr,[status(thm)],[c_0_162,c_0_179]) ).

cnf(c_0_200,negated_conjecture,
    ( sk4 = nil
    | cons(X1,app(sk3,nil)) != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_147]),c_0_79]),c_0_121])]) ).

cnf(c_0_201,negated_conjecture,
    app(sk3,nil) = sk3,
    inference(sr,[status(thm)],[c_0_133,c_0_179]) ).

cnf(c_0_202,negated_conjecture,
    ~ memberP(sk1,sk5),
    co1_10 ).

cnf(c_0_203,negated_conjecture,
    ( sk4 = nil
    | memberP(sk3,hd(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_60])]) ).

cnf(c_0_204,plain,
    ( hd(X1) = X2
    | nil = X1
    | memberP(tl(X1),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_66]),c_0_67]) ).

cnf(c_0_205,negated_conjecture,
    memberP(cons(hd(sk4),sk3),sk5),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_116])]) ).

cnf(c_0_206,negated_conjecture,
    hd(cons(X1,sk3)) = X1,
    inference(sr,[status(thm)],[c_0_198,c_0_179]) ).

cnf(c_0_207,negated_conjecture,
    tl(cons(X1,sk3)) = sk3,
    inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_174,c_0_179]),c_0_199]) ).

cnf(c_0_208,negated_conjecture,
    ssList(cons(X1,sk3)),
    inference(sr,[status(thm)],[c_0_175,c_0_179]) ).

cnf(c_0_209,negated_conjecture,
    cons(X1,sk3) != nil,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_201]),c_0_179]) ).

cnf(c_0_210,negated_conjecture,
    ~ memberP(sk3,sk5),
    inference(rw,[status(thm)],[c_0_202,c_0_118]) ).

cnf(c_0_211,negated_conjecture,
    memberP(sk3,hd(sk4)),
    inference(sr,[status(thm)],[c_0_203,c_0_179]) ).

cnf(c_0_212,negated_conjecture,
    hd(sk4) = sk5,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_206]),c_0_207]),c_0_208])]),c_0_209]),c_0_210]) ).

cnf(c_0_213,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212]),c_0_210]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWC409-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 18:36:51 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 9.44/9.54  % Version  : CSE_E---1.5
% 9.44/9.54  % Problem  : theBenchmark.p
% 9.44/9.54  % Proof found
% 9.44/9.54  % SZS status Theorem for theBenchmark.p
% 9.44/9.54  % SZS output start Proof
% See solution above
% 9.44/9.55  % Total time : 8.965000 s
% 9.44/9.55  % SZS output end Proof
% 9.44/9.55  % Total time : 8.972000 s
%------------------------------------------------------------------------------