TSTP Solution File: SWC111-1 by E-SAT---3.1.00

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%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWC111-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n022.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 : Tue May 21 04:27:41 EDT 2024

% Result   : Unsatisfiable 13.21s 2.18s
% Output   : CNFRefutation 13.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   59
% Syntax   : Number of clauses     :  241 (  55 unt;  37 nHn; 207 RR)
%            Number of literals    :  711 ( 199 equ; 458 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   5 con; 0-2 aty)
%            Number of variables   :  371 (  43 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(co1_11,negated_conjecture,
    ( nil = sk2
    | ~ neq(sk1,nil)
    | ~ segmentP(sk2,sk1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).

cnf(co1_7,negated_conjecture,
    segmentP(sk4,sk3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

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

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

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

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

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

cnf(clause80,axiom,
    ( nil = X1
    | ~ segmentP(nil,X1)
    | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).

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

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

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

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

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

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

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

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

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

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

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

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

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(clause170,axiom,
    ( X1 = X3
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause170) ).

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

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

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(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(co1_9,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(sk3,X1)
    | ~ segmentP(sk4,X1)
    | ~ segmentP(X1,sk3)
    | ~ totalorderedP(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

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

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(clause117,axiom,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause117) ).

cnf(co1_12,negated_conjecture,
    ( neq(sk2,nil)
    | nil != sk1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).

cnf(c_0_59,negated_conjecture,
    ( nil = sk2
    | ~ neq(sk1,nil)
    | ~ segmentP(sk2,sk1) ),
    inference(fof_simplification,[status(thm)],[co1_11]) ).

cnf(c_0_60,negated_conjecture,
    segmentP(sk4,sk3),
    co1_7 ).

cnf(c_0_61,negated_conjecture,
    sk2 = sk4,
    co1_5 ).

cnf(c_0_62,negated_conjecture,
    sk1 = sk3,
    co1_6 ).

cnf(c_0_63,negated_conjecture,
    ( nil = sk2
    | ~ neq(sk1,nil)
    | ~ segmentP(sk2,sk1) ),
    c_0_59 ).

cnf(c_0_64,negated_conjecture,
    segmentP(sk2,sk1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).

cnf(c_0_65,plain,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause100]) ).

cnf(c_0_66,negated_conjecture,
    ( sk2 = nil
    | ~ neq(sk1,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).

cnf(c_0_67,plain,
    ( neq(X2,X1)
    | X2 = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    c_0_65 ).

cnf(c_0_68,negated_conjecture,
    ssList(sk1),
    co1_1 ).

cnf(c_0_69,axiom,
    ssList(nil),
    clause8 ).

cnf(c_0_70,plain,
    ( nil = X1
    | ~ segmentP(nil,X1)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause80]) ).

cnf(c_0_71,negated_conjecture,
    ( sk1 = nil
    | sk2 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69])]) ).

cnf(c_0_72,plain,
    ( nil = X1
    | ~ segmentP(nil,X1)
    | ~ ssList(X1) ),
    c_0_70 ).

cnf(c_0_73,negated_conjecture,
    ( sk1 = nil
    | segmentP(nil,sk1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_71]) ).

cnf(c_0_74,plain,
    ( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause168]) ).

cnf(c_0_75,negated_conjecture,
    sk1 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_68])]) ).

cnf(c_0_76,plain,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(fof_simplification,[status(thm)],[clause138]) ).

cnf(c_0_77,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause136]) ).

cnf(c_0_78,plain,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause58]) ).

cnf(c_0_79,plain,
    ( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    c_0_74 ).

cnf(c_0_80,negated_conjecture,
    segmentP(sk2,nil),
    inference(rw,[status(thm)],[c_0_64,c_0_75]) ).

cnf(c_0_81,negated_conjecture,
    ssList(sk2),
    co1_2 ).

cnf(c_0_82,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause73]) ).

cnf(c_0_83,plain,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    inference(fof_simplification,[status(thm)],[clause179]) ).

cnf(c_0_84,plain,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    c_0_76 ).

cnf(c_0_85,plain,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause101]) ).

cnf(c_0_86,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ rearsegP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    c_0_77 ).

cnf(c_0_87,plain,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    c_0_78 ).

cnf(c_0_88,negated_conjecture,
    app(app(skaf47(sk2,nil),nil),skaf48(nil,sk2)) = sk2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_69]),c_0_81])]) ).

cnf(c_0_89,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    c_0_82 ).

cnf(c_0_90,axiom,
    ssList(skaf47(X1,X2)),
    clause49 ).

cnf(c_0_91,plain,
    ( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ duplicatefreeP(X5)
    | ~ ssList(X5) ),
    c_0_83 ).

cnf(c_0_92,plain,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause169]) ).

cnf(c_0_93,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_84]) ).

cnf(c_0_94,plain,
    ( cons(skaf44(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    c_0_85 ).

cnf(c_0_95,axiom,
    ssItem(skaf44(X1)),
    clause47 ).

cnf(c_0_96,plain,
    ( app(skaf46(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause131]) ).

cnf(c_0_97,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_69])]) ).

cnf(c_0_98,negated_conjecture,
    app(skaf47(sk2,nil),skaf48(nil,sk2)) = sk2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).

cnf(c_0_99,axiom,
    ssList(skaf48(X1,X2)),
    clause48 ).

cnf(c_0_100,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_91]) ).

cnf(c_0_101,plain,
    ( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
    | ~ memberP(X1,X2)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    c_0_92 ).

cnf(c_0_102,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_93,c_0_94]),c_0_95]),c_0_69])]) ).

cnf(c_0_103,plain,
    ( app(skaf46(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    c_0_96 ).

cnf(c_0_104,negated_conjecture,
    rearsegP(sk2,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_90]),c_0_99])]) ).

cnf(c_0_105,plain,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause116]) ).

cnf(c_0_106,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_100,c_0_94]),c_0_95]),c_0_69])]) ).

cnf(c_0_107,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_101,c_0_102]),c_0_95])]) ).

cnf(c_0_108,axiom,
    ssList(skaf43(X1,X2)),
    clause52 ).

cnf(c_0_109,axiom,
    ssList(skaf42(X1,X2)),
    clause53 ).

cnf(c_0_110,plain,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause72]) ).

cnf(c_0_111,plain,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause85]) ).

cnf(c_0_112,plain,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(fof_simplification,[status(thm)],[clause157]) ).

cnf(c_0_113,plain,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause86]) ).

cnf(c_0_114,plain,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause145]) ).

cnf(c_0_115,plain,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause99]) ).

cnf(c_0_116,plain,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause104]) ).

cnf(c_0_117,plain,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause75]) ).

cnf(c_0_118,plain,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause76]) ).

cnf(c_0_119,negated_conjecture,
    app(skaf46(sk2,nil),nil) = sk2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_69]),c_0_81])]) ).

cnf(c_0_120,axiom,
    ssList(skaf46(X1,X2)),
    clause50 ).

cnf(c_0_121,plain,
    ( tl(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause96]) ).

cnf(c_0_122,plain,
    ( singletonP(X2)
    | cons(X1,nil) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    c_0_105 ).

cnf(c_0_123,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_106,c_0_107]),c_0_108]),c_0_109])]) ).

cnf(c_0_124,plain,
    ( duplicatefreeP(X1)
    | ssItem(X2)
    | ~ ssList(X1) ),
    c_0_110 ).

cnf(c_0_125,plain,
    ( ssList(app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    c_0_111 ).

cnf(c_0_126,plain,
    ( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    c_0_112 ).

cnf(c_0_127,plain,
    ( ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    c_0_113 ).

cnf(c_0_128,plain,
    ( app(X1,X2) = nil
    | nil != X1
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    c_0_114 ).

cnf(c_0_129,plain,
    ( cons(X1,X2) != X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    c_0_115 ).

cnf(c_0_130,plain,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    c_0_116 ).

cnf(c_0_131,plain,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    c_0_117 ).

cnf(c_0_132,plain,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    c_0_118 ).

cnf(c_0_133,plain,
    ( nil = X2
    | tl(app(X2,X1)) = app(tl(X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause133]) ).

cnf(c_0_134,plain,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause118]) ).

cnf(c_0_135,plain,
    ( nil = X2
    | hd(app(X2,X1)) = hd(X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause123]) ).

cnf(c_0_136,negated_conjecture,
    skaf46(sk2,nil) = sk2,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_119]),c_0_120])]) ).

cnf(c_0_137,plain,
    ( tl(cons(X1,X2)) = X2
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    c_0_121 ).

cnf(c_0_138,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(er,[status(thm)],[c_0_122]) ).

cnf(c_0_139,plain,
    ( ssItem(X1)
    | ~ singletonP(X2)
    | ~ ssList(app(X2,X2))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_123,c_0_124]) ).

cnf(c_0_140,plain,
    ( ssList(cons(X1,app(X2,X3)))
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).

cnf(c_0_141,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_128])]),c_0_69])]) ).

cnf(c_0_142,plain,
    ( X1 = X3
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause170]) ).

cnf(c_0_143,plain,
    ( nil = X1
    | tl(X1) != X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_132]) ).

cnf(c_0_144,plain,
    ( nil = X2
    | tl(app(X2,X1)) = app(tl(X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    c_0_133 ).

cnf(c_0_145,plain,
    ( nil = X1
    | app(X1,X2) != nil
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    c_0_134 ).

cnf(c_0_146,plain,
    ( X4 = X2
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause171]) ).

cnf(c_0_147,plain,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause109]) ).

cnf(c_0_148,plain,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause98]) ).

cnf(c_0_149,plain,
    ( nil = X2
    | hd(app(X2,X1)) = hd(X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    c_0_135 ).

cnf(c_0_150,negated_conjecture,
    app(sk2,nil) = sk2,
    inference(rw,[status(thm)],[c_0_119,c_0_136]) ).

cnf(c_0_151,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_137,c_0_94]),c_0_95]),c_0_69])]) ).

cnf(c_0_152,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_127]),c_0_69])]) ).

cnf(c_0_153,plain,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause120]) ).

cnf(c_0_154,plain,
    ( ssItem(X1)
    | ~ singletonP(X2)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[c_0_139,c_0_125]) ).

cnf(c_0_155,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_69])]) ).

cnf(c_0_156,plain,
    ( X1 = X3
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    c_0_142 ).

cnf(c_0_157,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_143,c_0_144]),c_0_125]),c_0_145]) ).

cnf(c_0_158,plain,
    ( X4 = X2
    | cons(X1,X2) != cons(X3,X4)
    | ~ ssItem(X3)
    | ~ ssItem(X1)
    | ~ ssList(X4)
    | ~ ssList(X2) ),
    c_0_146 ).

cnf(c_0_159,plain,
    ( cons(skaf83(X1),skaf82(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    c_0_147 ).

cnf(c_0_160,axiom,
    ssItem(skaf83(X1)),
    clause12 ).

cnf(c_0_161,axiom,
    ssList(skaf82(X1)),
    clause13 ).

cnf(c_0_162,plain,
    ( cons(X1,X2) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    c_0_148 ).

cnf(c_0_163,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_130,c_0_149]),c_0_125]),c_0_145]) ).

cnf(c_0_164,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_131,c_0_144]),c_0_125]),c_0_145]) ).

cnf(c_0_165,negated_conjecture,
    ( app(tl(sk2),nil) = tl(sk2)
    | sk2 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_150]),c_0_81]),c_0_69])]) ).

cnf(c_0_166,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[c_0_151,c_0_152]) ).

cnf(c_0_167,plain,
    ( app(cons(X1,nil),X2) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    c_0_153 ).

cnf(c_0_168,plain,
    ( ssItem(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_152]),c_0_155]) ).

cnf(c_0_169,plain,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(fof_simplification,[status(thm)],[clause97]) ).

cnf(c_0_170,plain,
    ( skaf44(cons(X1,X2)) = X1
    | ~ singletonP(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    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_156,c_0_94]),c_0_95]),c_0_69])])]),c_0_127]) ).

cnf(c_0_171,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_157,c_0_89]),c_0_69])]),c_0_131]) ).

cnf(c_0_172,plain,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    inference(fof_simplification,[status(thm)],[clause178]) ).

cnf(c_0_173,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_158,c_0_159]),c_0_160]),c_0_161])])]),c_0_127]),c_0_162]) ).

cnf(c_0_174,negated_conjecture,
    ( cons(hd(sk2),tl(sk2)) = sk2
    | sk2 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_150]),c_0_81]),c_0_69])]) ).

cnf(c_0_175,negated_conjecture,
    ( sk2 = nil
    | ssList(tl(sk2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_81]),c_0_69])]) ).

cnf(c_0_176,plain,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause132]) ).

cnf(c_0_177,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause60]) ).

cnf(c_0_178,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_127]),c_0_69])]) ).

cnf(c_0_179,plain,
    ( cons(skaf44(X1),X2) = app(X1,X2)
    | ~ singletonP(X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_94]),c_0_95])]) ).

cnf(c_0_180,plain,
    ssItem(X1),
    inference(spm,[status(thm)],[c_0_168,c_0_95]) ).

cnf(c_0_181,plain,
    ( hd(cons(X1,X2)) = X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    c_0_169 ).

cnf(c_0_182,plain,
    ( skaf44(cons(X1,nil)) = X1
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_152]),c_0_69])]) ).

cnf(c_0_183,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_171,c_0_137]),c_0_127]),c_0_162]) ).

cnf(c_0_184,plain,
    ( frontsegP(cons(X3,X1),cons(X4,X2))
    | ~ frontsegP(X1,X2)
    | X3 != X4
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3) ),
    c_0_172 ).

cnf(c_0_185,negated_conjecture,
    ( skaf82(sk2) = tl(sk2)
    | sk2 = nil
    | ~ ssItem(hd(sk2)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]) ).

cnf(c_0_186,plain,
    ( X2 = X3
    | app(X1,X2) != app(X1,X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    inference(fof_simplification,[status(thm)],[clause150]) ).

cnf(c_0_187,plain,
    ( app(X2,skaf45(X1,X2)) = X1
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    c_0_176 ).

cnf(c_0_188,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    c_0_177 ).

cnf(c_0_189,plain,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(fof_simplification,[status(thm)],[clause149]) ).

cnf(c_0_190,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause74]) ).

cnf(c_0_191,plain,
    ( tl(app(X1,nil)) = nil
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_95]),c_0_69])]) ).

cnf(c_0_192,plain,
    singletonP(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_180])]) ).

cnf(c_0_193,plain,
    ssList(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_180])]) ).

cnf(c_0_194,plain,
    ( skaf44(X1) = hd(X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_94]),c_0_95]),c_0_69])]) ).

cnf(c_0_195,plain,
    skaf44(cons(X1,nil)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_180])]) ).

cnf(c_0_196,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_167]),c_0_69])]) ).

cnf(c_0_197,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(sk3,X1)
    | ~ segmentP(sk4,X1)
    | ~ segmentP(X1,sk3)
    | ~ totalorderedP(X1) ),
    inference(fof_simplification,[status(thm)],[co1_9]) ).

cnf(c_0_198,plain,
    ( segmentP(X4,X2)
    | app(app(X1,X2),X3) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X4) ),
    inference(fof_simplification,[status(thm)],[clause173]) ).

cnf(c_0_199,plain,
    ( frontsegP(cons(X1,X2),cons(X1,X3))
    | ~ frontsegP(X2,X3)
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(er,[status(thm)],[c_0_184]) ).

cnf(c_0_200,negated_conjecture,
    ( skaf82(sk2) = tl(sk2)
    | sk2 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_132]),c_0_81])]) ).

cnf(c_0_201,plain,
    ( X2 = X3
    | app(X1,X2) != app(X1,X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    c_0_186 ).

cnf(c_0_202,plain,
    ( app(nil,skaf45(X1,nil)) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_69])]) ).

cnf(c_0_203,axiom,
    ssList(skaf45(X1,X2)),
    clause51 ).

cnf(c_0_204,plain,
    ( app(app(X3,X2),X1) = app(X3,app(X2,X1))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    c_0_189 ).

cnf(c_0_205,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    c_0_190 ).

cnf(c_0_206,plain,
    tl(app(cons(X1,nil),nil)) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_193])]) ).

cnf(c_0_207,plain,
    hd(cons(X1,nil)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_192]),c_0_193])]) ).

cnf(c_0_208,plain,
    cons(X1,nil) != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_180])]) ).

cnf(c_0_209,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(sk3,X1)
    | ~ segmentP(sk4,X1)
    | ~ segmentP(X1,sk3)
    | ~ totalorderedP(X1) ),
    c_0_197 ).

cnf(c_0_210,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(fof_simplification,[status(thm)],[clause56]) ).

cnf(c_0_211,plain,
    ( segmentP(X4,X2)
    | app(app(X1,X2),X3) != X4
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X4) ),
    c_0_198 ).

cnf(c_0_212,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_199,c_0_188]),c_0_69])]) ).

cnf(c_0_213,negated_conjecture,
    ( cons(skaf83(sk2),tl(sk2)) = sk2
    | sk2 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_200]),c_0_81])]) ).

cnf(c_0_214,plain,
    ( skaf45(app(nil,X1),nil) = X1
    | ~ ssList(app(nil,X1))
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_203]),c_0_69])])]) ).

cnf(c_0_215,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_204,c_0_205]),c_0_69])]) ).

cnf(c_0_216,plain,
    app(cons(X1,nil),nil) = cons(X1,nil),
    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_163,c_0_206]),c_0_207]),c_0_193]),c_0_69])]),c_0_208]) ).

cnf(c_0_217,negated_conjecture,
    ( ~ neq(sk1,X1)
    | ~ segmentP(X1,sk1)
    | ~ segmentP(sk2,X1)
    | ~ ssList(X1)
    | ~ totalorderedP(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_62]),c_0_61]),c_0_62]) ).

cnf(c_0_218,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    c_0_210 ).

cnf(c_0_219,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_211]) ).

cnf(c_0_220,negated_conjecture,
    ( sk2 = nil
    | frontsegP(sk2,cons(skaf83(sk2),nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_160])]),c_0_175]) ).

cnf(c_0_221,plain,
    ( skaf45(app(nil,X1),nil) = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_125]),c_0_69])]) ).

cnf(c_0_222,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_215,c_0_216]),c_0_193]),c_0_69])]) ).

cnf(c_0_223,plain,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(fof_simplification,[status(thm)],[clause67]) ).

cnf(c_0_224,plain,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(fof_simplification,[status(thm)],[clause117]) ).

cnf(c_0_225,negated_conjecture,
    ( neq(sk2,nil)
    | nil != sk1 ),
    inference(fof_simplification,[status(thm)],[co1_12]) ).

cnf(c_0_226,negated_conjecture,
    ( ~ neq(nil,X1)
    | ~ segmentP(sk2,X1)
    | ~ ssList(X1)
    | ~ totalorderedP(X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_217,c_0_75]),c_0_75]),c_0_218]) ).

cnf(c_0_227,plain,
    ( segmentP(app(X1,X2),skaf45(X1,nil))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_202]),c_0_203]),c_0_69])]),c_0_125]) ).

cnf(c_0_228,negated_conjecture,
    ( app(cons(skaf83(sk2),nil),skaf45(sk2,cons(skaf83(sk2),nil))) = sk2
    | sk2 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_220]),c_0_81])]),c_0_193])]) ).

cnf(c_0_229,plain,
    skaf45(cons(X1,nil),nil) = cons(X1,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_193])]) ).

cnf(c_0_230,plain,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    c_0_223 ).

cnf(c_0_231,plain,
    ( X1 != X2
    | ~ neq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    c_0_224 ).

cnf(c_0_232,negated_conjecture,
    ( neq(sk2,nil)
    | nil != sk1 ),
    c_0_225 ).

cnf(c_0_233,negated_conjecture,
    ( X1 = nil
    | ~ segmentP(sk2,X1)
    | ~ ssList(X1)
    | ~ totalorderedP(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_67]),c_0_69])]) ).

cnf(c_0_234,negated_conjecture,
    ( sk2 = nil
    | segmentP(sk2,cons(skaf83(sk2),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_229]),c_0_203]),c_0_193])]) ).

cnf(c_0_235,plain,
    totalorderedP(cons(X1,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_180])]) ).

cnf(c_0_236,plain,
    ( ~ neq(X1,X1)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_231]) ).

cnf(c_0_237,negated_conjecture,
    neq(sk2,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_75])]) ).

cnf(c_0_238,negated_conjecture,
    sk2 = nil,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_193]),c_0_235])]),c_0_208]) ).

cnf(c_0_239,plain,
    ~ neq(X1,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_180])]) ).

cnf(c_0_240,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_237,c_0_238]),c_0_239]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWC111-1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n022.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun May 19 03:30:08 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.21/0.48  Running first-order model finding
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.21/2.18  # Version: 3.1.0
% 13.21/2.18  # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.21/2.18  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.21/2.18  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.21/2.18  # Starting new_bool_3 with 300s (1) cores
% 13.21/2.18  # Starting new_bool_1 with 300s (1) cores
% 13.21/2.18  # Starting sh5l with 300s (1) cores
% 13.21/2.18  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 10276 completed with status 0
% 13.21/2.18  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 13.21/2.18  # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.21/2.18  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.21/2.18  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.21/2.18  # No SInE strategy applied
% 13.21/2.18  # Search class: FGHSM-FSLM21-MFFFFFNN
% 13.21/2.18  # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 13.21/2.18  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2s with 406s (1) cores
% 13.21/2.18  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 13.21/2.18  # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 13.21/2.18  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 13.21/2.18  # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S0S with 136s (1) cores
% 13.21/2.18  # G-E--_208_C18_F1_SE_CS_SP_PS_S2s with pid 10282 completed with status 0
% 13.21/2.18  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2s
% 13.21/2.18  # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.21/2.18  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.21/2.18  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.21/2.18  # No SInE strategy applied
% 13.21/2.18  # Search class: FGHSM-FSLM21-MFFFFFNN
% 13.21/2.18  # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 13.21/2.18  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2s with 406s (1) cores
% 13.21/2.18  # Preprocessing time       : 0.003 s
% 13.21/2.18  # Presaturation interreduction done
% 13.21/2.18  
% 13.21/2.18  # Proof found!
% 13.21/2.18  # SZS status Unsatisfiable
% 13.21/2.18  # SZS output start CNFRefutation
% See solution above
% 13.21/2.18  # Parsed axioms                        : 198
% 13.21/2.18  # Removed by relevancy pruning/SinE    : 0
% 13.21/2.18  # Initial clauses                      : 198
% 13.21/2.18  # Removed in clause preprocessing      : 0
% 13.21/2.18  # Initial clauses in saturation        : 198
% 13.21/2.18  # Processed clauses                    : 15039
% 13.21/2.18  # ...of these trivial                  : 56
% 13.21/2.18  # ...subsumed                          : 12023
% 13.21/2.18  # ...remaining for further processing  : 2960
% 13.21/2.18  # Other redundant clauses eliminated   : 1014
% 13.21/2.18  # Clauses deleted for lack of memory   : 0
% 13.21/2.18  # Backward-subsumed                    : 65
% 13.21/2.18  # Backward-rewritten                   : 1251
% 13.21/2.18  # Generated clauses                    : 80145
% 13.21/2.18  # ...of the previous two non-redundant : 75467
% 13.21/2.18  # ...aggressively subsumed             : 0
% 13.21/2.18  # Contextual simplify-reflections      : 543
% 13.21/2.18  # Paramodulations                      : 79103
% 13.21/2.18  # Factorizations                       : 2
% 13.21/2.18  # NegExts                              : 0
% 13.21/2.18  # Equation resolutions                 : 1041
% 13.21/2.18  # Disequality decompositions           : 0
% 13.21/2.18  # Total rewrite steps                  : 87717
% 13.21/2.18  # ...of those cached                   : 86733
% 13.21/2.18  # Propositional unsat checks           : 0
% 13.21/2.18  #    Propositional check models        : 0
% 13.21/2.18  #    Propositional check unsatisfiable : 0
% 13.21/2.18  #    Propositional clauses             : 0
% 13.21/2.18  #    Propositional clauses after purity: 0
% 13.21/2.18  #    Propositional unsat core size     : 0
% 13.21/2.18  #    Propositional preprocessing time  : 0.000
% 13.21/2.18  #    Propositional encoding time       : 0.000
% 13.21/2.18  #    Propositional solver time         : 0.000
% 13.21/2.18  #    Success case prop preproc time    : 0.000
% 13.21/2.18  #    Success case prop encoding time   : 0.000
% 13.21/2.18  #    Success case prop solver time     : 0.000
% 13.21/2.18  # Current number of processed clauses  : 1431
% 13.21/2.18  #    Positive orientable unit clauses  : 101
% 13.21/2.18  #    Positive unorientable unit clauses: 0
% 13.21/2.18  #    Negative unit clauses             : 37
% 13.21/2.18  #    Non-unit-clauses                  : 1293
% 13.21/2.18  # Current number of unprocessed clauses: 58686
% 13.21/2.18  # ...number of literals in the above   : 331593
% 13.21/2.18  # Current number of archived formulas  : 0
% 13.21/2.18  # Current number of archived clauses   : 1506
% 13.21/2.18  # Clause-clause subsumption calls (NU) : 843067
% 13.21/2.18  # Rec. Clause-clause subsumption calls : 179430
% 13.21/2.18  # Non-unit clause-clause subsumptions  : 8805
% 13.21/2.18  # Unit Clause-clause subsumption calls : 5366
% 13.21/2.18  # Rewrite failures with RHS unbound    : 0
% 13.21/2.18  # BW rewrite match attempts            : 76
% 13.21/2.18  # BW rewrite match successes           : 57
% 13.21/2.18  # Condensation attempts                : 0
% 13.21/2.18  # Condensation successes               : 0
% 13.21/2.18  # Termbank termtop insertions          : 1698516
% 13.21/2.18  # Search garbage collected termcells   : 549
% 13.21/2.18  
% 13.21/2.18  # -------------------------------------------------
% 13.21/2.18  # User time                : 1.581 s
% 13.21/2.18  # System time              : 0.044 s
% 13.21/2.18  # Total time               : 1.625 s
% 13.21/2.18  # Maximum resident set size: 2144 pages
% 13.21/2.18  
% 13.21/2.18  # -------------------------------------------------
% 13.21/2.18  # User time                : 7.822 s
% 13.21/2.18  # System time              : 0.318 s
% 13.21/2.18  # Total time               : 8.139 s
% 13.21/2.18  # Maximum resident set size: 1876 pages
% 13.21/2.18  % E---3.1 exiting
%------------------------------------------------------------------------------