TSTP Solution File: SWC056-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC056-1 : 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 : n017.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 20:19:26 EDT 2023
% Result : Timeout 294.21s 294.10s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 209
% Syntax : Number of formulae : 366 ( 46 unt; 149 typ; 0 def)
% Number of atoms : 659 ( 202 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 864 ( 422 ~; 440 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 65 >; 17 *; 0 +; 0 <<)
% Number of predicates : 97 ( 95 usr; 77 prp; 0-2 aty)
% Number of functors : 54 ( 54 usr; 8 con; 0-2 aty)
% Number of variables : 309 ( 26 sgn; 2 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
nil: $i ).
tff(decl_23,type,
equalelemsP: $i > $o ).
tff(decl_24,type,
duplicatefreeP: $i > $o ).
tff(decl_25,type,
strictorderedP: $i > $o ).
tff(decl_26,type,
totalorderedP: $i > $o ).
tff(decl_27,type,
strictorderP: $i > $o ).
tff(decl_28,type,
totalorderP: $i > $o ).
tff(decl_29,type,
cyclefreeP: $i > $o ).
tff(decl_30,type,
ssList: $i > $o ).
tff(decl_31,type,
skac3: $i ).
tff(decl_32,type,
ssItem: $i > $o ).
tff(decl_33,type,
skac2: $i ).
tff(decl_34,type,
singletonP: $i > $o ).
tff(decl_35,type,
skaf83: $i > $i ).
tff(decl_36,type,
skaf82: $i > $i ).
tff(decl_37,type,
skaf81: $i > $i ).
tff(decl_38,type,
skaf80: $i > $i ).
tff(decl_39,type,
skaf79: $i > $i ).
tff(decl_40,type,
skaf78: $i > $i ).
tff(decl_41,type,
skaf77: $i > $i ).
tff(decl_42,type,
skaf76: $i > $i ).
tff(decl_43,type,
skaf75: $i > $i ).
tff(decl_44,type,
skaf74: $i > $i ).
tff(decl_45,type,
skaf73: $i > $i ).
tff(decl_46,type,
skaf72: $i > $i ).
tff(decl_47,type,
skaf71: $i > $i ).
tff(decl_48,type,
skaf70: $i > $i ).
tff(decl_49,type,
skaf69: $i > $i ).
tff(decl_50,type,
skaf68: $i > $i ).
tff(decl_51,type,
skaf67: $i > $i ).
tff(decl_52,type,
skaf66: $i > $i ).
tff(decl_53,type,
skaf65: $i > $i ).
tff(decl_54,type,
skaf64: $i > $i ).
tff(decl_55,type,
skaf63: $i > $i ).
tff(decl_56,type,
skaf62: $i > $i ).
tff(decl_57,type,
skaf61: $i > $i ).
tff(decl_58,type,
skaf60: $i > $i ).
tff(decl_59,type,
skaf59: $i > $i ).
tff(decl_60,type,
skaf58: $i > $i ).
tff(decl_61,type,
skaf57: $i > $i ).
tff(decl_62,type,
skaf56: $i > $i ).
tff(decl_63,type,
skaf55: $i > $i ).
tff(decl_64,type,
skaf54: $i > $i ).
tff(decl_65,type,
skaf53: $i > $i ).
tff(decl_66,type,
skaf52: $i > $i ).
tff(decl_67,type,
skaf51: $i > $i ).
tff(decl_68,type,
skaf50: $i > $i ).
tff(decl_69,type,
skaf49: $i > $i ).
tff(decl_70,type,
skaf44: $i > $i ).
tff(decl_71,type,
skaf48: ( $i * $i ) > $i ).
tff(decl_72,type,
skaf47: ( $i * $i ) > $i ).
tff(decl_73,type,
skaf46: ( $i * $i ) > $i ).
tff(decl_74,type,
skaf45: ( $i * $i ) > $i ).
tff(decl_75,type,
skaf43: ( $i * $i ) > $i ).
tff(decl_76,type,
skaf42: ( $i * $i ) > $i ).
tff(decl_77,type,
geq: ( $i * $i ) > $o ).
tff(decl_78,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_79,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_80,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_81,type,
leq: ( $i * $i ) > $o ).
tff(decl_82,type,
lt: ( $i * $i ) > $o ).
tff(decl_83,type,
cons: ( $i * $i ) > $i ).
tff(decl_84,type,
memberP: ( $i * $i ) > $o ).
tff(decl_85,type,
app: ( $i * $i ) > $i ).
tff(decl_86,type,
tl: $i > $i ).
tff(decl_87,type,
hd: $i > $i ).
tff(decl_88,type,
neq: ( $i * $i ) > $o ).
tff(decl_89,type,
gt: ( $i * $i ) > $o ).
tff(decl_90,type,
sk1: $i ).
tff(decl_91,type,
sk2: $i ).
tff(decl_92,type,
sk3: $i ).
tff(decl_93,type,
sk4: $i ).
tff(decl_94,type,
sk5: $i ).
tff(decl_95,type,
epred1_0: $o ).
tff(decl_96,type,
epred2_0: $o ).
tff(decl_97,type,
epred3_0: $o ).
tff(decl_98,type,
epred4_0: $o ).
tff(decl_99,type,
epred5_0: $o ).
tff(decl_100,type,
epred6_0: $o ).
tff(decl_101,type,
epred7_0: $o ).
tff(decl_102,type,
epred8_0: $o ).
tff(decl_103,type,
epred9_0: $o ).
tff(decl_104,type,
epred10_0: $o ).
tff(decl_105,type,
epred11_0: $o ).
tff(decl_106,type,
epred12_0: $o ).
tff(decl_107,type,
epred13_0: $o ).
tff(decl_108,type,
epred14_0: $o ).
tff(decl_109,type,
epred15_0: $o ).
tff(decl_110,type,
epred16_0: $o ).
tff(decl_111,type,
epred17_0: $o ).
tff(decl_112,type,
epred18_0: $o ).
tff(decl_113,type,
epred19_0: $o ).
tff(decl_114,type,
epred20_0: $o ).
tff(decl_115,type,
epred21_0: $o ).
tff(decl_116,type,
epred22_0: $o ).
tff(decl_117,type,
epred23_0: $o ).
tff(decl_118,type,
epred24_0: $o ).
tff(decl_119,type,
epred25_0: $o ).
tff(decl_120,type,
epred26_0: $o ).
tff(decl_121,type,
epred27_0: $o ).
tff(decl_122,type,
epred28_0: $o ).
tff(decl_123,type,
epred29_0: $o ).
tff(decl_124,type,
epred30_0: $o ).
tff(decl_125,type,
epred31_0: $o ).
tff(decl_126,type,
epred32_0: $o ).
tff(decl_127,type,
epred33_0: $o ).
tff(decl_128,type,
epred34_0: $o ).
tff(decl_129,type,
epred35_0: $o ).
tff(decl_130,type,
epred36_0: $o ).
tff(decl_131,type,
epred37_0: $o ).
tff(decl_132,type,
epred38_0: $o ).
tff(decl_133,type,
epred39_0: $o ).
tff(decl_134,type,
epred40_0: $o ).
tff(decl_135,type,
epred41_0: $o ).
tff(decl_136,type,
epred42_0: $o ).
tff(decl_137,type,
epred43_0: $o ).
tff(decl_138,type,
epred44_0: $o ).
tff(decl_139,type,
epred45_0: $o ).
tff(decl_140,type,
epred46_0: $o ).
tff(decl_141,type,
epred47_0: $o ).
tff(decl_142,type,
epred48_0: $o ).
tff(decl_143,type,
epred49_0: $o ).
tff(decl_144,type,
epred50_0: $o ).
tff(decl_145,type,
epred51_0: $o ).
tff(decl_146,type,
epred52_0: $o ).
tff(decl_147,type,
epred53_0: $o ).
tff(decl_148,type,
epred54_0: $o ).
tff(decl_149,type,
epred55_0: $o ).
tff(decl_150,type,
epred56_0: $o ).
tff(decl_151,type,
epred57_0: $o ).
tff(decl_152,type,
epred58_0: $o ).
tff(decl_153,type,
epred59_0: $o ).
tff(decl_154,type,
epred60_0: $o ).
tff(decl_155,type,
epred61_0: $o ).
tff(decl_156,type,
epred62_0: $o ).
tff(decl_157,type,
epred63_0: $o ).
tff(decl_158,type,
epred64_0: $o ).
tff(decl_159,type,
epred65_0: $o ).
tff(decl_160,type,
epred66_0: $o ).
tff(decl_161,type,
epred67_0: $o ).
tff(decl_162,type,
epred68_0: $o ).
tff(decl_163,type,
epred69_0: $o ).
tff(decl_164,type,
epred70_0: $o ).
tff(decl_165,type,
epred71_0: $o ).
tff(decl_166,type,
epred72_0: $o ).
tff(decl_167,type,
epred73_0: $o ).
tff(decl_168,type,
epred74_0: $o ).
tff(decl_169,type,
epred75_0: $o ).
tff(decl_170,type,
epred76_0: $o ).
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(clause161,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).
cnf(co1_12,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(co1_8,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
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(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(clause172,axiom,
( segmentP(app(app(X4,X1),X3),X2)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(co1_18,negated_conjecture,
( nil != sk1
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_17,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause79,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(co1_9,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_7,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
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(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause57,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
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(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(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(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(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(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
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(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause179,axiom,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause169,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(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(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/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/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(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(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
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(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(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause143,axiom,
( rearsegP(X3,X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause143) ).
cnf(clause141,axiom,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause141) ).
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(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(clause81,axiom,
( rearsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause81) ).
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(co1_13,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_16,negated_conjecture,
( nil = sk2
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(c_0_58,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_59,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
clause161 ).
cnf(c_0_60,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk3 ),
co1_12 ).
cnf(c_0_61,axiom,
ssList(nil),
clause8 ).
cnf(c_0_62,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
co1_8 ).
cnf(c_0_63,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_64,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_65,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_66,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_67,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_68,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_69,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_70,negated_conjecture,
( sk3 = nil
| sk5 = X1
| ~ memberP(sk3,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]),c_0_62]),c_0_63]) ).
cnf(c_0_71,plain,
( nil = X1
| memberP(X1,skaf83(X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67])]) ).
cnf(c_0_72,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( skaf83(sk3) = sk5
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_66]),c_0_72])]) ).
cnf(c_0_74,axiom,
( segmentP(app(app(X4,X1),X3),X2)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause172 ).
cnf(c_0_75,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_76,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_77,negated_conjecture,
( cons(sk5,skaf82(sk3)) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_73]),c_0_72])]) ).
cnf(c_0_78,negated_conjecture,
( nil != sk1
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
co1_18 ).
cnf(c_0_79,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_80,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
co1_17 ).
cnf(c_0_81,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_82,plain,
( segmentP(app(X1,X2),X3)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_61])]) ).
cnf(c_0_83,negated_conjecture,
( skaf82(sk3) = tl(sk3)
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_67])]),c_0_62]) ).
cnf(c_0_84,negated_conjecture,
( sk3 != nil
| ~ neq(X1,nil)
| ~ segmentP(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_69]),c_0_69]),c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( neq(sk4,nil)
| sk3 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_79]),c_0_69]) ).
cnf(c_0_86,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_81,c_0_79]) ).
cnf(c_0_87,plain,
( segmentP(X1,X2)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_75]),c_0_61])]) ).
cnf(c_0_88,axiom,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause79 ).
cnf(c_0_89,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_90,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
co1_9 ).
cnf(c_0_91,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
co1_7 ).
cnf(c_0_92,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_93,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_94,negated_conjecture,
( cons(skaf83(sk3),tl(sk3)) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_83]),c_0_72])]) ).
cnf(c_0_95,negated_conjecture,
( tl(sk3) = nil
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_60]),c_0_61])]),c_0_62]) ).
cnf(c_0_96,negated_conjecture,
( sk3 != nil
| ~ segmentP(sk3,sk4)
| ~ segmentP(sk4,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
cnf(c_0_97,plain,
( segmentP(X1,X2)
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_98,negated_conjecture,
( sk4 = nil
| sk3 != nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_61])]),c_0_91]) ).
cnf(c_0_99,plain,
( app(cons(X1,X2),nil) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_61])]) ).
cnf(c_0_100,negated_conjecture,
( cons(skaf83(sk3),nil) = sk3
| sk3 = nil ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
( sk3 != nil
| ~ segmentP(sk4,sk4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_72]),c_0_86])]),c_0_98]) ).
cnf(c_0_102,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
clause57 ).
cnf(c_0_103,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_104,negated_conjecture,
( app(sk3,nil) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_66]),c_0_61])]) ).
cnf(c_0_105,negated_conjecture,
sk3 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_86])]) ).
cnf(c_0_106,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_107,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_103,c_0_75]),c_0_61])]) ).
cnf(c_0_108,negated_conjecture,
app(sk3,nil) = sk3,
inference(sr,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_109,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_110,plain,
( app(cons(X1,X2),X3) = cons(X1,nil)
| nil != X3
| nil != X2
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
cons(sk5,nil) = sk3,
inference(sr,[status(thm)],[c_0_60,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
ssItem(sk5),
inference(sr,[status(thm)],[c_0_62,c_0_105]) ).
cnf(c_0_113,negated_conjecture,
app(nil,sk3) = sk3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_72]),c_0_61])]) ).
cnf(c_0_114,negated_conjecture,
( app(sk3,X1) = cons(sk5,X1)
| sk3 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_60]),c_0_62]) ).
cnf(c_0_115,negated_conjecture,
( app(sk3,X1) = sk3
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_111]),c_0_112]),c_0_61])]) ).
cnf(c_0_116,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_117,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_118,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_119,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_120,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_121,negated_conjecture,
( app(cons(X1,nil),sk3) = cons(X1,sk3)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_113]),c_0_72]),c_0_61])]) ).
cnf(c_0_122,negated_conjecture,
( cons(sk5,X1) = sk3
| nil != X1
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_105]) ).
cnf(c_0_123,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_103]),c_0_116]) ).
cnf(c_0_124,plain,
( X1 = skaf45(X2,X3)
| app(X3,X1) != X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119])]),c_0_120]) ).
cnf(c_0_125,negated_conjecture,
app(sk3,sk3) = cons(sk5,sk3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_112]),c_0_61])]) ).
cnf(c_0_126,negated_conjecture,
( ssList(app(X1,sk3))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_108]),c_0_61]),c_0_72])]) ).
cnf(c_0_127,plain,
( app(cons(X1,X2),skaf45(X3,X2)) = cons(X1,X3)
| ~ frontsegP(X3,X2)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_118]),c_0_119])]) ).
cnf(c_0_128,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_129,plain,
( skaf45(app(X1,X2),X1) = X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_124]),c_0_116]) ).
cnf(c_0_130,negated_conjecture,
app(nil,cons(sk5,sk3)) = cons(sk5,sk3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_125]),c_0_72])]) ).
cnf(c_0_131,negated_conjecture,
ssList(cons(sk5,sk3)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_114]),c_0_72])]),c_0_105]) ).
cnf(c_0_132,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_133,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_134,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_135,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_136,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_137,negated_conjecture,
( app(sk3,skaf45(X1,nil)) = cons(sk5,X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_111]),c_0_112]),c_0_61])]),c_0_128]) ).
cnf(c_0_138,negated_conjecture,
skaf45(cons(sk5,sk3),nil) = cons(sk5,sk3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_61])]) ).
cnf(c_0_139,negated_conjecture,
( sk3 = nil
| memberP(sk3,sk5) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_60]),c_0_61])]),c_0_62]) ).
cnf(c_0_140,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_141,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_142,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_143,negated_conjecture,
( hd(sk3) = sk5
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_60]),c_0_61])]),c_0_62]) ).
cnf(c_0_144,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_145,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_146,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_147,plain,
( app(X1,cons(X2,X3)) != X4
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ duplicatefreeP(X4) ),
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_136])]) ).
cnf(c_0_148,negated_conjecture,
app(sk3,cons(sk5,sk3)) = cons(sk5,cons(sk5,sk3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_131])]) ).
cnf(c_0_149,negated_conjecture,
memberP(sk3,sk5),
inference(sr,[status(thm)],[c_0_139,c_0_105]) ).
fof(c_0_150,plain,
( ~ epred2_0
<=> ! [X1] :
( duplicatefreeP(X1)
| ~ ssList(X1) ) ),
introduced(definition) ).
cnf(c_0_151,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_140,c_0_141]),c_0_116]),c_0_142]) ).
cnf(c_0_152,negated_conjecture,
hd(sk3) = sk5,
inference(sr,[status(thm)],[c_0_143,c_0_105]) ).
cnf(c_0_153,negated_conjecture,
tl(sk3) = nil,
inference(sr,[status(thm)],[c_0_95,c_0_105]) ).
cnf(c_0_154,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_103]),c_0_61])]),c_0_116]) ).
cnf(c_0_155,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause170 ).
cnf(c_0_156,plain,
( X1 != nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_144]),c_0_145]),c_0_61])]) ).
cnf(c_0_157,negated_conjecture,
( singletonP(X1)
| sk3 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_111]),c_0_112])]) ).
cnf(c_0_158,negated_conjecture,
( cons(sk5,cons(sk5,sk3)) != X1
| ~ ssList(X1)
| ~ duplicatefreeP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]),c_0_112]),c_0_72])]) ).
cnf(c_0_159,plain,
( epred2_0
| duplicatefreeP(X1)
| ~ ssList(X1) ),
inference(split_equiv,[status(thm)],[c_0_150]) ).
cnf(c_0_160,negated_conjecture,
( ssList(app(X1,cons(sk5,sk3)))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_125]),c_0_72])]) ).
cnf(c_0_161,negated_conjecture,
( app(sk3,X1) = cons(sk5,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_111]),c_0_112])]) ).
cnf(c_0_162,negated_conjecture,
( cons(sk5,app(nil,X1)) = sk3
| nil != X1
| ~ ssList(X1) ),
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_151,c_0_115]),c_0_152]),c_0_153]),c_0_72])]),c_0_105]) ).
cnf(c_0_163,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_107]),c_0_61])]) ).
cnf(c_0_164,plain,
( X1 = skaf83(X2)
| nil = X2
| 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_155,c_0_65]),c_0_66]),c_0_67])]) ).
cnf(c_0_165,negated_conjecture,
( X1 != nil
| sk3 != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_166,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_167,axiom,
( rearsegP(app(X3,X1),X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause136 ).
fof(c_0_168,plain,
( ~ epred1_0
<=> ! [X2] : ssItem(X2) ),
introduced(definition) ).
cnf(c_0_169,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_170,negated_conjecture,
( epred2_0
| cons(sk5,cons(sk5,sk3)) != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_171,negated_conjecture,
ssList(cons(sk5,cons(sk5,sk3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_72]),c_0_131])]) ).
cnf(c_0_172,axiom,
( rearsegP(X3,X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause143 ).
cnf(c_0_173,negated_conjecture,
( cons(sk5,app(X1,nil)) = sk3
| nil != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_174,negated_conjecture,
( skaf83(X1) = sk5
| sk3 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_111]),c_0_112]),c_0_61])]),c_0_165]) ).
cnf(c_0_175,plain,
( X1 = skaf82(X2)
| nil = X2
| cons(X3,X1) != X2
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_65]),c_0_66]),c_0_67])]) ).
cnf(c_0_176,axiom,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
clause141 ).
cnf(c_0_177,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_178,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_179,plain,
( rearsegP(X1,X2)
| ~ rearsegP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_93]),c_0_61])]) ).
cnf(c_0_180,axiom,
( rearsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause81 ).
cnf(c_0_181,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_169,c_0_168]),c_0_150]) ).
cnf(c_0_182,negated_conjecture,
epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_170]),c_0_171])]) ).
cnf(c_0_183,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_184,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_172]),c_0_116]) ).
cnf(c_0_185,negated_conjecture,
( app(cons(sk5,X1),nil) = sk3
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_173]),c_0_112]),c_0_61])]) ).
cnf(c_0_186,negated_conjecture,
( cons(sk5,skaf82(X1)) = X1
| sk3 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_174]),c_0_165]) ).
cnf(c_0_187,negated_conjecture,
( skaf82(X1) = nil
| sk3 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_111]),c_0_112]),c_0_61])]),c_0_165]) ).
cnf(c_0_188,plain,
( memberP(X1,X2)
| ~ memberP(X3,X2)
| ~ rearsegP(X1,X3)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_178])]) ).
cnf(c_0_189,plain,
( rearsegP(X1,X2)
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_190,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
co1_13 ).
cnf(c_0_191,plain,
( epred1_0
| ssItem(X1) ),
inference(split_equiv,[status(thm)],[c_0_168]) ).
cnf(c_0_192,plain,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_182])]) ).
cnf(c_0_193,negated_conjecture,
( nil = sk2
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
co1_16 ).
cnf(c_0_194,plain,
( segmentP(X1,X2)
| app(X3,X4) != X1
| ~ rearsegP(X3,X2)
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_177]),c_0_178])]) ).
cnf(c_0_195,plain,
( rearsegP(app(X1,nil),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_163]),c_0_61])]) ).
cnf(c_0_196,negated_conjecture,
( app(X1,nil) = sk3
| sk3 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_67])]),c_0_187]) ).
cnf(c_0_197,plain,
( memberP(X1,X2)
| nil != X3
| ~ memberP(X3,X2)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_198,negated_conjecture,
memberP(sk4,sk5),
inference(sr,[status(thm)],[c_0_190,c_0_105]) ).
cnf(c_0_199,plain,
( segmentP(app(X1,app(X2,X3)),X4)
| ~ segmentP(X2,X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_103]) ).
cnf(c_0_200,plain,
ssItem(X1),
inference(sr,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_201,negated_conjecture,
( sk4 = nil
| ~ neq(X1,nil)
| ~ segmentP(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_79]),c_0_69]),c_0_79]) ).
cnf(c_0_202,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_203,plain,
( segmentP(X1,X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_93]),c_0_61])])]) ).
cnf(c_0_204,negated_conjecture,
( rearsegP(sk3,X1)
| sk3 != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_205,negated_conjecture,
( memberP(X1,sk5)
| sk4 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_112]),c_0_86])]) ).
cnf(c_0_206,negated_conjecture,
( segmentP(app(X1,cons(sk5,X2)),X3)
| ~ segmentP(sk3,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_161]),c_0_72])]) ).
cnf(c_0_207,plain,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_200])]) ).
cnf(c_0_208,plain,
( segmentP(X1,X2)
| app(X2,X3) != X1
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_75]),c_0_61])]) ).
cnf(c_0_209,negated_conjecture,
( sk4 = nil
| nil = X1
| ~ segmentP(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_61])]) ).
cnf(c_0_210,negated_conjecture,
( segmentP(sk3,X1)
| sk3 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_72])]) ).
cnf(c_0_211,negated_conjecture,
sk4 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_205]),c_0_112]),c_0_61])]) ).
cnf(c_0_212,negated_conjecture,
( segmentP(X1,X2)
| ~ memberP(X1,sk5)
| ~ segmentP(sk3,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_136]),c_0_135])]) ).
cnf(c_0_213,negated_conjecture,
( segmentP(X1,sk3)
| sk3 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_108]),c_0_61]),c_0_72])]) ).
cnf(c_0_214,negated_conjecture,
( sk3 != X1
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_211]),c_0_165]) ).
cnf(c_0_215,negated_conjecture,
( segmentP(X1,sk3)
| ~ memberP(X1,sk5)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_72])]) ).
cnf(c_0_216,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_72]),c_0_198]),c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC056-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 16:52:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 294.21/294.10 % Version : CSE_E---1.5
% 294.21/294.10 % Problem : theBenchmark.p
% 294.21/294.10 % Proof found
% 294.21/294.10 % SZS status Theorem for theBenchmark.p
% 294.21/294.10 % SZS output start Proof
% See solution above
% 294.21/294.12 % Total time : 293.515000 s
% 294.21/294.12 % SZS output end Proof
% 294.21/294.12 % Total time : 293.533000 s
%------------------------------------------------------------------------------