TSTP Solution File: SWC087-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC087-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 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 : Thu Aug 31 20:19:42 EDT 2023
% Result : Unsatisfiable 5.33s 5.40s
% Output : CNFRefutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 119
% Syntax : Number of formulae : 267 ( 32 unt; 72 typ; 0 def)
% Number of atoms : 595 ( 191 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 746 ( 346 ~; 400 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 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 : 237 ( 28 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_7,negated_conjecture,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_12,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk4) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk4) != X4
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause133,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause120,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause144,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(clause123,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).
cnf(clause138,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause173,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause169,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause132,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(clause157,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause127,axiom,
( X2 = X1
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause176,axiom,
( X1 = X3
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause176) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(co1_11,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause61,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause61) ).
cnf(clause117,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause117) ).
cnf(c_0_47,negated_conjecture,
neq(sk2,nil),
inference(fof_simplification,[status(thm)],[co1_7]) ).
cnf(c_0_48,negated_conjecture,
( sk3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(sk4) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(sk4) != X4
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
co1_12 ).
cnf(c_0_49,negated_conjecture,
neq(sk2,nil),
c_0_47 ).
cnf(c_0_50,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_51,negated_conjecture,
( sk3 = X1
| tl(sk4) != X2
| hd(sk4) != X4
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(cn,[status(thm)],[c_0_48]) ).
cnf(c_0_52,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_53,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_55,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_56,negated_conjecture,
( app(tl(sk4),cons(hd(sk4),nil)) = sk1
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53])])])])])]),c_0_54]) ).
cnf(c_0_57,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_58,axiom,
ssList(nil),
clause8 ).
cnf(c_0_59,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_60,negated_conjecture,
( app(tl(sk4),cons(hd(sk4),nil)) = sk1
| sk4 = nil
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_61,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_62,negated_conjecture,
( app(tl(sk4),cons(hd(sk4),nil)) = sk1
| sk4 = nil
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_59])]) ).
cnf(c_0_63,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_64,negated_conjecture,
( app(tl(sk4),cons(hd(sk4),nil)) = sk1
| sk4 = nil
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_59])]) ).
cnf(c_0_65,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_66,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_67,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_68,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_69,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_70,negated_conjecture,
( app(tl(sk4),cons(hd(sk4),nil)) = sk1
| sk4 = nil
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_58])]) ).
cnf(c_0_71,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
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_66,c_0_67]),c_0_63]),c_0_61]) ).
cnf(c_0_73,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_67,c_0_68]),c_0_54]),c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( app(tl(sk4),cons(hd(sk4),nil)) = sk1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_61]),c_0_59])]) ).
cnf(c_0_75,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_76,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_77,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_78,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_71]) ).
cnf(c_0_79,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_68]),c_0_54]),c_0_69]) ).
cnf(c_0_80,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_81,negated_conjecture,
( cons(hd(app(sk4,cons(hd(sk4),nil))),sk1) = app(sk4,cons(hd(sk4),nil))
| sk4 = nil
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_59])]) ).
cnf(c_0_82,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_75,c_0_76]),c_0_77]),c_0_58])]) ).
cnf(c_0_83,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_65]),c_0_58])]) ).
cnf(c_0_84,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_79,c_0_80]),c_0_58])]),c_0_63]) ).
cnf(c_0_85,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_86,negated_conjecture,
( cons(hd(app(sk4,cons(hd(sk4),nil))),sk1) = app(sk4,cons(hd(sk4),nil))
| sk4 = nil
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_65]),c_0_58])]) ).
cnf(c_0_87,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,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_84,c_0_75]),c_0_65]),c_0_85]) ).
cnf(c_0_89,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_90,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_91,negated_conjecture,
( cons(hd(app(sk4,cons(hd(sk4),nil))),sk1) = app(sk4,cons(hd(sk4),nil))
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_61]),c_0_59])]) ).
cnf(c_0_92,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_93,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_65]),c_0_58])]) ).
cnf(c_0_94,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_58])]) ).
cnf(c_0_95,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_96,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_90]),c_0_54]) ).
cnf(c_0_97,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_98,negated_conjecture,
( app(sk4,cons(hd(sk4),nil)) = cons(hd(sk4),sk1)
| sk4 = nil
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_59])]) ).
cnf(c_0_99,plain,
( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_93]),c_0_94]) ).
cnf(c_0_100,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_101,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( sk4 = nil
| frontsegP(sk1,tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4)) ),
inference(spm,[status(thm)],[c_0_96,c_0_74]) ).
cnf(c_0_103,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_97]) ).
cnf(c_0_104,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_105,negated_conjecture,
( app(sk4,cons(hd(sk4),nil)) = cons(hd(sk4),sk1)
| sk4 = nil
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_65]),c_0_58])]) ).
cnf(c_0_106,plain,
( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_65]),c_0_58])]) ).
cnf(c_0_107,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_100]) ).
cnf(c_0_108,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_109,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_101,c_0_76]),c_0_77]),c_0_58])]) ).
cnf(c_0_110,negated_conjecture,
( sk4 = nil
| frontsegP(sk1,tl(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_63]),c_0_59])]) ).
cnf(c_0_111,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_103,c_0_104]),c_0_58])]),c_0_54]) ).
cnf(c_0_112,negated_conjecture,
( app(sk4,cons(hd(sk4),nil)) = cons(hd(sk4),sk1)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_61]),c_0_59])]) ).
cnf(c_0_113,plain,
( ssList(cons(X1,nil))
| ~ ssItem(hd(cons(X1,nil)))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_106]),c_0_58])]) ).
cnf(c_0_114,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_115,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_107,c_0_76]),c_0_77]),c_0_58])]) ).
cnf(c_0_116,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_108,c_0_109]),c_0_77])]) ).
cnf(c_0_117,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_118,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_119,negated_conjecture,
( sk4 = nil
| frontsegP(sk1,tl(sk4))
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_65]),c_0_58])]) ).
cnf(c_0_120,negated_conjecture,
( sk4 = nil
| segmentP(cons(hd(sk4),sk1),sk4)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_59])]) ).
cnf(c_0_121,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_58])]) ).
cnf(c_0_122,negated_conjecture,
( sk4 = nil
| ssList(cons(hd(sk4),sk1))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_112]),c_0_59])]) ).
cnf(c_0_123,negated_conjecture,
( hd(cons(hd(sk4),sk1)) = hd(sk4)
| sk4 = nil
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_112]),c_0_59])]) ).
cnf(c_0_124,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_115,c_0_116]),c_0_117]),c_0_118])]) ).
cnf(c_0_125,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_126,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_127,negated_conjecture,
( sk4 = nil
| frontsegP(sk1,tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_61]),c_0_59])]) ).
cnf(c_0_128,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_129,negated_conjecture,
( sk4 = nil
| segmentP(cons(hd(sk4),sk1),sk4)
| ~ ssItem(hd(sk4)) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_130,negated_conjecture,
( sk4 = nil
| ssList(cons(hd(sk4),sk1))
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_65]),c_0_58])]) ).
cnf(c_0_131,negated_conjecture,
( hd(cons(hd(sk4),sk1)) = hd(sk4)
| sk4 = nil
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_65]),c_0_58])]) ).
cnf(c_0_132,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(app(X2,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_133,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_134,negated_conjecture,
( app(tl(sk4),skaf45(sk1,tl(sk4))) = sk1
| sk4 = nil
| ~ ssList(tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128])]) ).
cnf(c_0_135,axiom,
( X2 = X1
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause127 ).
cnf(c_0_136,negated_conjecture,
( sk4 = nil
| segmentP(cons(hd(sk4),sk1),sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_61]),c_0_59])]) ).
cnf(c_0_137,negated_conjecture,
( sk4 = nil
| ssList(cons(hd(sk4),sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_61]),c_0_59])]) ).
cnf(c_0_138,negated_conjecture,
( hd(cons(hd(sk4),sk1)) = hd(sk4)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_61]),c_0_59])]) ).
cnf(c_0_139,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_132,c_0_54]) ).
cnf(c_0_140,plain,
( cons(hd(X1),app(tl(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_67]),c_0_63]),c_0_61]) ).
cnf(c_0_141,negated_conjecture,
( app(tl(sk4),skaf45(sk1,tl(sk4))) = sk1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_63]),c_0_59])]) ).
cnf(c_0_142,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_143,negated_conjecture,
( cons(hd(sk4),sk1) = sk4
| sk4 = nil
| ~ segmentP(sk4,cons(hd(sk4),sk1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_59])]),c_0_137]) ).
cnf(c_0_144,negated_conjecture,
( cons(hd(sk4),sk1) = nil
| sk4 = nil
| ssItem(hd(sk4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_138]),c_0_137]) ).
cnf(c_0_145,plain,
( ssItem(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_83]),c_0_121]) ).
cnf(c_0_146,axiom,
( X1 = X3
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
clause176 ).
cnf(c_0_147,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_148,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_149,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_150,negated_conjecture,
( app(sk4,skaf45(sk1,tl(sk4))) = cons(hd(sk4),sk1)
| 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_142]),c_0_59])]) ).
cnf(c_0_151,negated_conjecture,
( sk4 = nil
| ssItem(hd(sk4))
| ~ segmentP(sk4,nil) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_152,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_153,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_103,c_0_80]),c_0_58])]),c_0_54]) ).
cnf(c_0_154,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_145,c_0_77]) ).
cnf(c_0_155,plain,
( X1 = skaf83(X2)
| nil = X2
| ~ frontsegP(cons(X1,X3),X2)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_149])]) ).
cnf(c_0_156,negated_conjecture,
( sk4 = nil
| frontsegP(cons(hd(sk4),sk1),sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_150]),c_0_142]),c_0_59])]) ).
cnf(c_0_157,negated_conjecture,
( sk4 = nil
| ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_59])]) ).
cnf(c_0_158,negated_conjecture,
( sk4 = nil
| segmentP(sk1,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4)) ),
inference(spm,[status(thm)],[c_0_153,c_0_74]) ).
cnf(c_0_159,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1)
| ~ neq(sk4,nil) ),
co1_11 ).
cnf(c_0_160,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_154])]) ).
cnf(c_0_161,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_154])]) ).
cnf(c_0_162,negated_conjecture,
( skaf83(sk4) = hd(sk4)
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_128]),c_0_59])]),c_0_157]) ).
cnf(c_0_163,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_164,negated_conjecture,
( sk4 = nil
| segmentP(sk1,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_63]),c_0_59])]) ).
cnf(c_0_165,negated_conjecture,
( ~ neq(X1,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_50]),c_0_53])]) ).
cnf(c_0_166,negated_conjecture,
( sk4 = nil
| segmentP(sk1,tl(sk4))
| ~ ssList(tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_141]),c_0_142])]) ).
cnf(c_0_167,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_160]),c_0_161])]) ).
cnf(c_0_168,negated_conjecture,
( cons(hd(sk4),skaf82(sk4)) = sk4
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_162]),c_0_59])]) ).
cnf(c_0_169,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_163]) ).
cnf(c_0_170,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
clause61 ).
cnf(c_0_171,negated_conjecture,
( sk4 = nil
| segmentP(sk1,cons(hd(sk4),nil))
| ~ ssItem(hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_65]),c_0_58])]) ).
cnf(c_0_172,negated_conjecture,
( nil = X1
| ~ segmentP(sk1,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_57]),c_0_58])]) ).
cnf(c_0_173,negated_conjecture,
( sk4 = nil
| segmentP(sk1,tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_63]),c_0_59])]) ).
cnf(c_0_174,negated_conjecture,
( sk4 = nil
| segmentP(sk4,skaf82(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_149])]) ).
cnf(c_0_175,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_75,c_0_147]),c_0_148]),c_0_149])]) ).
cnf(c_0_176,negated_conjecture,
( skaf82(sk4) = tl(sk4)
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_168]),c_0_149])]),c_0_157]) ).
cnf(c_0_177,plain,
( frontsegP(cons(X1,X2),cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_178,negated_conjecture,
( sk4 = nil
| segmentP(sk1,cons(hd(sk4),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_61]),c_0_59])]) ).
cnf(c_0_179,negated_conjecture,
( tl(sk4) = nil
| sk4 = nil
| ~ segmentP(sk4,tl(sk4))
| ~ ssList(tl(sk4)) ),
inference(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_180,negated_conjecture,
( sk4 = nil
| segmentP(sk4,tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_59])]) ).
cnf(c_0_181,negated_conjecture,
( sk4 = nil
| ssList(tl(sk4)) ),
inference(spm,[status(thm)],[c_0_149,c_0_176]) ).
cnf(c_0_182,negated_conjecture,
( sk4 = nil
| frontsegP(sk4,sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_168]),c_0_149])]),c_0_157]) ).
cnf(c_0_183,negated_conjecture,
( cons(hd(sk4),nil) = nil
| sk4 = nil
| ~ segmentP(sk4,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(spm,[status(thm)],[c_0_172,c_0_178]) ).
cnf(c_0_184,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_154])]) ).
cnf(c_0_185,negated_conjecture,
( tl(sk4) = nil
| sk4 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]) ).
cnf(c_0_186,negated_conjecture,
( app(sk4,skaf45(sk4,sk4)) = sk4
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_182]),c_0_59])]) ).
cnf(c_0_187,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause117 ).
cnf(c_0_188,negated_conjecture,
( sk4 = nil
| ~ segmentP(sk4,cons(hd(sk4),nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_161])]),c_0_184]) ).
cnf(c_0_189,negated_conjecture,
( cons(hd(sk4),nil) = sk4
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_185]),c_0_59])]) ).
cnf(c_0_190,negated_conjecture,
( sk4 = nil
| segmentP(sk4,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_186]),c_0_142]),c_0_59])]) ).
cnf(c_0_191,plain,
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_187]) ).
cnf(c_0_192,negated_conjecture,
sk4 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_190]) ).
cnf(c_0_193,plain,
~ neq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_154])]) ).
cnf(c_0_194,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_192]),c_0_193]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC087-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 17:15:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 5.33/5.40 % Version : CSE_E---1.5
% 5.33/5.40 % Problem : theBenchmark.p
% 5.33/5.40 % Proof found
% 5.33/5.40 % SZS status Theorem for theBenchmark.p
% 5.33/5.40 % SZS output start Proof
% See solution above
% 5.37/5.42 % Total time : 4.809000 s
% 5.37/5.42 % SZS output end Proof
% 5.37/5.42 % Total time : 4.815000 s
%------------------------------------------------------------------------------