TSTP Solution File: SWC091-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC091-1 : 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 : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:19:44 EDT 2023

% Result   : Unsatisfiable 4.24s 4.30s
% Output   : CNFRefutation 4.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :  134
% Syntax   : Number of formulae    :  290 (  62 unt;  72 typ;   0 def)
%            Number of atoms       :  598 ( 163 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  741 ( 361   ~; 380   |;   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    :   53 (  53 usr;   7 con; 0-2 aty)
%            Number of variables   :  295 (  40 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 ).

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

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

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

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(co1_8,negated_conjecture,
    frontsegP(sk4,sk3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

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

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

cnf(clause173,axiom,
    ( segmentP(X4,X2)
    | app(app(X1,X2),X3) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).

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

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

cnf(clause168,axiom,
    ( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause168) ).

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

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(clause49,axiom,
    ssList(skaf47(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause49) ).

cnf(clause48,axiom,
    ssList(skaf48(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause48) ).

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

cnf(co1_10,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(X1,nil)
    | ~ segmentP(sk2,X1)
    | ~ segmentP(sk1,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).

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

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

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

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(clause100,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).

cnf(clause171,axiom,
    ( X4 = X2
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).

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

cnf(clause12,axiom,
    ssItem(skaf83(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).

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

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

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

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(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(clause57,axiom,
    ( segmentP(X1,X1)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).

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

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_7,negated_conjecture,
    neq(sk2,nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

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

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

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

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

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

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(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(clause150,axiom,
    ( X2 = X3
    | app(X1,X2) != app(X1,X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause150) ).

cnf(clause178,axiom,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause178) ).

cnf(co1_11,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(sk3,X1)
    | ~ frontsegP(sk4,X1)
    | ~ segmentP(X1,sk3)
    | ~ totalorderedP(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

cnf(clause56,axiom,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).

cnf(clause67,axiom,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause67) ).

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(clause102,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssItem(X1)
    | ~ ssItem(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause102) ).

cnf(clause79,axiom,
    ( segmentP(nil,X1)
    | nil != X1
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).

cnf(c_0_62,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_63,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_64,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_65,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_66,axiom,
    ( frontsegP(app(X1,X3),X2)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause137 ).

cnf(c_0_67,axiom,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    clause60 ).

cnf(c_0_68,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_69,axiom,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause132 ).

cnf(c_0_70,negated_conjecture,
    frontsegP(sk4,sk3),
    co1_8 ).

cnf(c_0_71,negated_conjecture,
    ssList(sk3),
    inference(rw,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_72,negated_conjecture,
    ssList(sk4),
    inference(rw,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_73,plain,
    ( frontsegP(app(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).

cnf(c_0_74,negated_conjecture,
    app(sk3,skaf45(sk4,sk3)) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72])]) ).

cnf(c_0_75,axiom,
    ssList(skaf45(X1,X2)),
    clause51 ).

cnf(c_0_76,negated_conjecture,
    frontsegP(sk4,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_71])]) ).

cnf(c_0_77,axiom,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    clause74 ).

cnf(c_0_78,negated_conjecture,
    app(nil,skaf45(sk4,nil)) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_76]),c_0_68]),c_0_72])]) ).

cnf(c_0_79,axiom,
    ( segmentP(X4,X2)
    | app(app(X1,X2),X3) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X4) ),
    clause173 ).

cnf(c_0_80,negated_conjecture,
    skaf45(sk4,nil) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_75])]) ).

cnf(c_0_81,plain,
    ( segmentP(app(app(X1,X2),X3),X2)
    | ~ ssList(app(app(X1,X2),X3))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_79]) ).

cnf(c_0_82,negated_conjecture,
    app(nil,sk4) = sk4,
    inference(rw,[status(thm)],[c_0_78,c_0_80]) ).

cnf(c_0_83,axiom,
    ( rearsegP(app(X3,X1),X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause136 ).

cnf(c_0_84,axiom,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    clause58 ).

cnf(c_0_85,negated_conjecture,
    ( segmentP(app(sk4,X1),sk4)
    | ~ ssList(app(sk4,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_72]),c_0_68])]) ).

cnf(c_0_86,axiom,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    clause73 ).

cnf(c_0_87,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_68])]) ).

cnf(c_0_88,axiom,
    ( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause168 ).

cnf(c_0_89,negated_conjecture,
    segmentP(sk4,sk4),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_72]),c_0_68])]) ).

cnf(c_0_90,axiom,
    ( app(skaf46(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause131 ).

cnf(c_0_91,negated_conjecture,
    rearsegP(sk4,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_74]),c_0_71]),c_0_75])]) ).

cnf(c_0_92,axiom,
    ( frontsegP(X3,X1)
    | app(X1,X2) != X3
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    clause144 ).

cnf(c_0_93,axiom,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause85 ).

cnf(c_0_94,axiom,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause149 ).

cnf(c_0_95,negated_conjecture,
    app(app(skaf47(sk4,sk4),sk4),skaf48(sk4,sk4)) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_72])]) ).

cnf(c_0_96,axiom,
    ssList(skaf47(X1,X2)),
    clause49 ).

cnf(c_0_97,axiom,
    ssList(skaf48(X1,X2)),
    clause48 ).

cnf(c_0_98,negated_conjecture,
    app(skaf46(sk4,nil),nil) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_68]),c_0_72])]) ).

cnf(c_0_99,axiom,
    ssList(skaf46(X1,X2)),
    clause50 ).

cnf(c_0_100,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_92]),c_0_93]) ).

cnf(c_0_101,negated_conjecture,
    app(skaf47(sk4,sk4),app(sk4,skaf48(sk4,sk4))) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_72]),c_0_97])]) ).

cnf(c_0_102,negated_conjecture,
    skaf46(sk4,nil) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_98]),c_0_99])]) ).

cnf(c_0_103,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(X1,nil)
    | ~ segmentP(sk2,X1)
    | ~ segmentP(sk1,X1) ),
    co1_10 ).

cnf(c_0_104,negated_conjecture,
    ( frontsegP(sk4,skaf47(sk4,sk4))
    | ~ ssList(app(sk4,skaf48(sk4,sk4))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_96])]) ).

cnf(c_0_105,axiom,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause104 ).

cnf(c_0_106,axiom,
    ( nil = X2
    | hd(app(X2,X1)) = hd(X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause123 ).

cnf(c_0_107,axiom,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause118 ).

cnf(c_0_108,axiom,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause75 ).

cnf(c_0_109,axiom,
    ( nil = X2
    | tl(app(X2,X1)) = app(tl(X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause133 ).

cnf(c_0_110,negated_conjecture,
    app(sk4,nil) = sk4,
    inference(rw,[status(thm)],[c_0_98,c_0_102]) ).

cnf(c_0_111,negated_conjecture,
    ( ~ neq(X1,nil)
    | ~ segmentP(sk3,X1)
    | ~ segmentP(sk4,X1)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_63]),c_0_65]) ).

cnf(c_0_112,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    clause100 ).

cnf(c_0_113,negated_conjecture,
    frontsegP(sk4,skaf47(sk4,sk4)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_93]),c_0_72]),c_0_97])]) ).

cnf(c_0_114,axiom,
    ( X4 = X2
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    clause171 ).

cnf(c_0_115,axiom,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    clause109 ).

cnf(c_0_116,axiom,
    ssItem(skaf83(X1)),
    clause12 ).

cnf(c_0_117,axiom,
    ssList(skaf82(X1)),
    clause13 ).

cnf(c_0_118,axiom,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause86 ).

cnf(c_0_119,axiom,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause98 ).

cnf(c_0_120,plain,
    ( cons(hd(X1),tl(app(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_105,c_0_106]),c_0_93]),c_0_107]) ).

cnf(c_0_121,plain,
    ( nil = X1
    | ssList(app(tl(X1),X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_93]),c_0_107]) ).

cnf(c_0_122,negated_conjecture,
    ( app(tl(sk4),nil) = tl(sk4)
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_72]),c_0_68])]) ).

cnf(c_0_123,axiom,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    clause138 ).

cnf(c_0_124,axiom,
    ( X1 = X3
    | app(X1,X2) != app(X3,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause151 ).

cnf(c_0_125,negated_conjecture,
    ( nil = X1
    | ~ segmentP(sk3,X1)
    | ~ segmentP(sk4,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_68])]) ).

cnf(c_0_126,axiom,
    ( segmentP(X1,X1)
    | ~ ssList(X1) ),
    clause57 ).

cnf(c_0_127,plain,
    ( segmentP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_77]),c_0_68])]),c_0_93]) ).

cnf(c_0_128,negated_conjecture,
    app(skaf47(sk4,sk4),skaf45(sk4,skaf47(sk4,sk4))) = sk4,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_113]),c_0_96]),c_0_72])]) ).

cnf(c_0_129,plain,
    ( skaf82(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),c_0_117])])]),c_0_118]),c_0_119]) ).

cnf(c_0_130,negated_conjecture,
    ( cons(hd(sk4),tl(sk4)) = sk4
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_110]),c_0_72]),c_0_68])]) ).

cnf(c_0_131,negated_conjecture,
    ( sk4 = nil
    | ssList(tl(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_72]),c_0_68])]) ).

cnf(c_0_132,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_133,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_123]) ).

cnf(c_0_134,axiom,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    clause101 ).

cnf(c_0_135,axiom,
    ssItem(skaf44(X1)),
    clause47 ).

cnf(c_0_136,negated_conjecture,
    ( sk3 = X1
    | app(X1,skaf45(sk4,sk3)) != sk4
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_74]),c_0_75]),c_0_71])]) ).

cnf(c_0_137,negated_conjecture,
    ( sk3 = nil
    | ~ segmentP(sk4,sk3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_71])]) ).

cnf(c_0_138,negated_conjecture,
    segmentP(sk4,sk3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_74]),c_0_75]),c_0_71])]) ).

cnf(c_0_139,axiom,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    clause76 ).

cnf(c_0_140,negated_conjecture,
    ( hd(skaf47(sk4,sk4)) = hd(sk4)
    | skaf47(sk4,sk4) = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_128]),c_0_96]),c_0_75])]) ).

cnf(c_0_141,negated_conjecture,
    ( skaf82(sk4) = tl(sk4)
    | sk4 = nil
    | ~ ssItem(hd(sk4)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).

cnf(c_0_142,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_132]) ).

cnf(c_0_143,axiom,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    clause169 ).

cnf(c_0_144,plain,
    ( memberP(X1,skaf44(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_68])]) ).

cnf(c_0_145,negated_conjecture,
    ( app(X1,X2) = sk3
    | app(X1,app(X2,skaf45(sk4,sk3))) != sk4
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_94]),c_0_75])]),c_0_93]) ).

cnf(c_0_146,negated_conjecture,
    sk3 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138])]) ).

cnf(c_0_147,negated_conjecture,
    ( skaf47(sk4,sk4) = nil
    | ssItem(hd(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_96])]) ).

cnf(c_0_148,negated_conjecture,
    ( skaf82(sk4) = tl(sk4)
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_139]),c_0_72])]) ).

cnf(c_0_149,negated_conjecture,
    neq(sk2,nil),
    co1_7 ).

cnf(c_0_150,plain,
    ( ~ singletonP(X1)
    | ~ ssList(app(app(X2,cons(skaf44(X1),X3)),X1))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(app(X2,cons(skaf44(X1),X3)),X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_134]),c_0_135]),c_0_68])]) ).

cnf(c_0_151,plain,
    ( app(skaf42(X1,skaf44(X1)),cons(skaf44(X1),skaf43(skaf44(X1),X1))) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_135])]) ).

cnf(c_0_152,axiom,
    ssList(skaf43(X1,X2)),
    clause52 ).

cnf(c_0_153,axiom,
    ssList(skaf42(X1,X2)),
    clause53 ).

cnf(c_0_154,negated_conjecture,
    ( app(X1,X2) = nil
    | app(X1,app(X2,sk4)) != sk4
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146]),c_0_146]),c_0_80]) ).

cnf(c_0_155,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_94,c_0_77]),c_0_68])]) ).

cnf(c_0_156,negated_conjecture,
    ( app(sk4,skaf48(sk4,sk4)) = sk4
    | ssItem(hd(sk4)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_147]),c_0_82]) ).

cnf(c_0_157,axiom,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause97 ).

cnf(c_0_158,negated_conjecture,
    ( cons(skaf83(sk4),tl(sk4)) = sk4
    | sk4 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_148]),c_0_72])]) ).

cnf(c_0_159,negated_conjecture,
    neq(sk4,nil),
    inference(rw,[status(thm)],[c_0_149,c_0_65]) ).

cnf(c_0_160,axiom,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause99 ).

cnf(c_0_161,axiom,
    ( tl(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause96 ).

cnf(c_0_162,plain,
    ( ~ singletonP(X1)
    | ~ ssList(app(X1,X1))
    | ~ ssList(X1)
    | ~ duplicatefreeP(app(X1,X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]),c_0_153])]) ).

cnf(c_0_163,axiom,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    clause72 ).

cnf(c_0_164,axiom,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause116 ).

cnf(c_0_165,axiom,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    clause157 ).

cnf(c_0_166,axiom,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    clause145 ).

cnf(c_0_167,negated_conjecture,
    ( app(nil,X1) = nil
    | app(X1,sk4) != sk4
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_68]),c_0_72])]) ).

cnf(c_0_168,negated_conjecture,
    ( app(skaf47(sk4,sk4),sk4) = sk4
    | ssItem(hd(sk4)) ),
    inference(spm,[status(thm)],[c_0_101,c_0_156]) ).

cnf(c_0_169,axiom,
    ( X2 = X3
    | app(X1,X2) != app(X1,X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    clause150 ).

cnf(c_0_170,negated_conjecture,
    ( skaf83(sk4) = hd(sk4)
    | sk4 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_116])]),c_0_131]) ).

cnf(c_0_171,negated_conjecture,
    ( ~ segmentP(sk3,sk4)
    | ~ segmentP(sk4,sk4) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_159]),c_0_72])]) ).

cnf(c_0_172,plain,
    ( nil = X1
    | skaf82(X1) != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_115]),c_0_116]),c_0_117])]) ).

cnf(c_0_173,plain,
    ( skaf82(X1) = tl(X1)
    | nil = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_115]),c_0_116]),c_0_117])]) ).

cnf(c_0_174,axiom,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    clause178 ).

cnf(c_0_175,plain,
    ( ssItem(X1)
    | ~ singletonP(X2)
    | ~ ssList(app(X2,X2))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_162,c_0_163]) ).

cnf(c_0_176,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(er,[status(thm)],[c_0_164]) ).

cnf(c_0_177,plain,
    ( ssList(cons(X1,app(X2,X3)))
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_165]),c_0_118]) ).

cnf(c_0_178,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_166])]),c_0_68])]) ).

cnf(c_0_179,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_81,c_0_86]),c_0_68])]),c_0_93]) ).

cnf(c_0_180,negated_conjecture,
    ( app(nil,skaf47(sk4,sk4)) = nil
    | ssItem(hd(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_96])]) ).

cnf(c_0_181,negated_conjecture,
    ( sk4 = X1
    | app(nil,X1) != sk4
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_82]),c_0_72]),c_0_68])]) ).

cnf(c_0_182,negated_conjecture,
    ( sk4 = nil
    | ssItem(hd(sk4)) ),
    inference(spm,[status(thm)],[c_0_116,c_0_170]) ).

cnf(c_0_183,negated_conjecture,
    ~ segmentP(sk3,sk4),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_89])]) ).

cnf(c_0_184,plain,
    ( nil = X1
    | tl(X1) != X1
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_172,c_0_173]) ).

cnf(c_0_185,plain,
    ( frontsegP(cons(X1,X2),cons(X1,X3))
    | ~ frontsegP(X2,X3)
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_174]) ).

cnf(c_0_186,plain,
    ( ssItem(X1)
    | ~ singletonP(X2)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_175,c_0_93]) ).

cnf(c_0_187,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_118]),c_0_68])]) ).

cnf(c_0_188,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_68])]) ).

cnf(c_0_189,negated_conjecture,
    ( segmentP(nil,skaf47(sk4,sk4))
    | ssItem(hd(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_96]),c_0_68])]) ).

cnf(c_0_190,negated_conjecture,
    ( skaf47(sk4,sk4) = sk4
    | ssItem(hd(sk4)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_180]),c_0_96])]),c_0_182]) ).

cnf(c_0_191,negated_conjecture,
    ~ segmentP(nil,sk4),
    inference(rw,[status(thm)],[c_0_183,c_0_146]) ).

cnf(c_0_192,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_184,c_0_109]),c_0_93]),c_0_107]) ).

cnf(c_0_193,plain,
    ( frontsegP(cons(X1,X2),cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_67]),c_0_68])]) ).

cnf(c_0_194,plain,
    ( ssItem(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_188]) ).

cnf(c_0_195,negated_conjecture,
    ssItem(hd(sk4)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_191]) ).

cnf(c_0_196,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_192,c_0_86]),c_0_68])]),c_0_108]) ).

cnf(c_0_197,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(sk3,X1)
    | ~ frontsegP(sk4,X1)
    | ~ segmentP(X1,sk3)
    | ~ totalorderedP(X1) ),
    co1_11 ).

cnf(c_0_198,axiom,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    clause56 ).

cnf(c_0_199,negated_conjecture,
    ( sk4 = nil
    | frontsegP(sk4,cons(skaf83(sk4),nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_158]),c_0_116])]),c_0_131]) ).

cnf(c_0_200,plain,
    ( skaf83(X1) = hd(X1)
    | nil = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_115]),c_0_116]),c_0_117])]) ).

cnf(c_0_201,negated_conjecture,
    ssItem(X1),
    inference(spm,[status(thm)],[c_0_194,c_0_195]) ).

cnf(c_0_202,axiom,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    clause67 ).

cnf(c_0_203,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_196,c_0_161]),c_0_118]),c_0_119]) ).

cnf(c_0_204,axiom,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    clause120 ).

cnf(c_0_205,negated_conjecture,
    ( ~ neq(nil,X1)
    | ~ frontsegP(sk4,X1)
    | ~ ssList(X1)
    | ~ totalorderedP(X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_146]),c_0_146]),c_0_198]) ).

cnf(c_0_206,negated_conjecture,
    ( sk4 = nil
    | frontsegP(sk4,cons(hd(sk4),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_72])]) ).

cnf(c_0_207,plain,
    ssList(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_201])]) ).

cnf(c_0_208,plain,
    totalorderedP(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_202,c_0_201])]) ).

cnf(c_0_209,axiom,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssItem(X1)
    | ~ ssItem(X2) ),
    clause102 ).

cnf(c_0_210,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_68])]) ).

cnf(c_0_211,negated_conjecture,
    ( sk4 = nil
    | ~ neq(nil,cons(hd(sk4),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_207]),c_0_208])]) ).

cnf(c_0_212,plain,
    ( X1 = X2
    | neq(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_201]),c_0_201])]) ).

cnf(c_0_213,plain,
    cons(X1,nil) != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_201])]) ).

cnf(c_0_214,axiom,
    ( segmentP(nil,X1)
    | nil != X1
    | ~ ssList(X1) ),
    clause79 ).

cnf(c_0_215,negated_conjecture,
    sk4 = nil,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_213]) ).

cnf(c_0_216,plain,
    segmentP(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_214]),c_0_68])]) ).

cnf(c_0_217,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_215]),c_0_216])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC091-1 : 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
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 16:41:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 4.24/4.30  % Version  : CSE_E---1.5
% 4.24/4.30  % Problem  : theBenchmark.p
% 4.24/4.30  % Proof found
% 4.24/4.30  % SZS status Theorem for theBenchmark.p
% 4.24/4.30  % SZS output start Proof
% See solution above
% 4.24/4.32  % Total time : 3.722000 s
% 4.24/4.32  % SZS output end Proof
% 4.24/4.32  % Total time : 3.729000 s
%------------------------------------------------------------------------------