%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC088-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 5 05:18:13 PM UTC 2026
% Result : Unsatisfiable 168.04s 84.85s
% Output : CNFRefutation 168.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 60
% Syntax : Number of clauses : 341 ( 67 unt; 72 nHn; 289 RR)
% Number of literals : 998 ( 376 equ; 625 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 492 ( 68 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(clause133,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(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(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
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(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(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(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(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(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
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(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
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(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_9,negated_conjecture,
( app(X2,cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(clause119,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
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(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(co1_8,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_7,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause175,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause175) ).
cnf(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(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(clause58,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause58) ).
cnf(clause151,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause151) ).
cnf(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(co1_10,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(clause161,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(clause57,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
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(clause80,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause176,axiom,
( X1 = X3
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause176) ).
cnf(clause177,axiom,
( nil = X2
| X1 = X2
| nil = X1
| tl(X1) != tl(X2)
| hd(X1) != hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause177) ).
cnf(c_0_60,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_61,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_62,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_63,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_64,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_65,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_60]) ).
cnf(c_0_66,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_67,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_68,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_69,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64]) ).
cnf(c_0_70,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_71,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_72,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_73,plain,
( ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,cons(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_74,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_75,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_76,axiom,
ssList(nil),
clause8 ).
cnf(c_0_77,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_78,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_69,c_0_70]),c_0_71]),c_0_72]) ).
cnf(c_0_79,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_80,plain,
( ~ memberP(X1,skaf44(X2))
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ duplicatefreeP(app(X1,X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76])]),c_0_71]) ).
cnf(c_0_81,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_77]) ).
cnf(c_0_82,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_83,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
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_78,c_0_79]),c_0_76])]),c_0_63]) ).
cnf(c_0_85,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_87,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_88,plain,
( ~ singletonP(X1)
| ~ ssList(cons(skaf44(X1),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ duplicatefreeP(app(cons(skaf44(X1),X2),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_75])]) ).
cnf(c_0_89,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_90,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_91,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_92,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_82]),c_0_71]) ).
cnf(c_0_93,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_83])]),c_0_76])]) ).
cnf(c_0_94,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_85]),c_0_86]),c_0_87]) ).
cnf(c_0_95,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_96,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_74]),c_0_76])]) ).
cnf(c_0_97,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_89]) ).
cnf(c_0_98,plain,
( ssItem(X1)
| duplicatefreeP(cons(X2,X3))
| ~ ssItem(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_90,c_0_86]) ).
cnf(c_0_99,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_100,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_101,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_102,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_91]),c_0_71]) ).
cnf(c_0_103,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_104,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_79,c_0_82]),c_0_76])]),c_0_71]) ).
cnf(c_0_105,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_76])]) ).
cnf(c_0_106,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_107,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_76])]) ).
cnf(c_0_108,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ duplicatefreeP(cons(X1,cons(X1,nil))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_95]),c_0_97]) ).
cnf(c_0_109,plain,
( ssItem(X1)
| duplicatefreeP(cons(skaf44(X2),X3))
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_98,c_0_75]) ).
cnf(c_0_110,plain,
( skaf45(app(X1,X2),X1) = X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101])])]),c_0_71]),c_0_102]) ).
cnf(c_0_111,plain,
( app(nil,X1) = app(X1,nil)
| ~ 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_76])]),c_0_105]) ).
cnf(c_0_112,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_113,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_95]),c_0_107]) ).
cnf(c_0_114,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(cons(skaf44(X1),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_74]),c_0_75])]) ).
cnf(c_0_115,plain,
( ssItem(X1)
| duplicatefreeP(cons(skaf44(X2),skaf45(X3,X4))) ),
inference(spm,[status(thm)],[c_0_109,c_0_101]) ).
cnf(c_0_116,plain,
( skaf45(app(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_76])]) ).
cnf(c_0_117,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_118,plain,
( hd(cons(X1,nil)) = X1
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_119,plain,
( ssItem(X1)
| ~ singletonP(skaf45(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_101])]) ).
cnf(c_0_120,plain,
( skaf45(app(nil,X1),nil) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_111]) ).
cnf(c_0_121,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_117]),c_0_86]) ).
cnf(c_0_122,plain,
( hd(cons(X1,nil)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_86]),c_0_76])]) ).
cnf(c_0_123,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_124,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_125,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_126,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_93]),c_0_76])]) ).
cnf(c_0_127,plain,
( hd(cons(skaf44(X1),nil)) = skaf44(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_75]) ).
cnf(c_0_128,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_129,plain,
( ssItem(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_97]),c_0_126]) ).
cnf(c_0_130,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_79]),c_0_76])]) ).
cnf(c_0_131,negated_conjecture,
hd(cons(skaf44(X1),nil)) = skaf44(X1),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_132,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_95,c_0_74]),c_0_75])]) ).
cnf(c_0_133,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_129,c_0_75]) ).
cnf(c_0_134,plain,
( X1 = nil
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_95]) ).
cnf(c_0_135,negated_conjecture,
( app(X2,cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != sk4 ),
co1_9 ).
cnf(c_0_136,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_112,c_0_74]),c_0_75]),c_0_76])]) ).
cnf(c_0_137,negated_conjecture,
( skaf44(X1) = hd(app(X1,nil))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_76])]) ).
cnf(c_0_138,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_133])]) ).
cnf(c_0_139,plain,
( hd(cons(X1,nil)) = X1
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_133])]) ).
cnf(c_0_140,plain,
( X1 = nil
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_86]),c_0_76])]) ).
cnf(c_0_141,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| cons(X2,app(nil,X1)) != sk4
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_117]),c_0_76])]) ).
cnf(c_0_142,negated_conjecture,
( hd(app(X1,nil)) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,plain,
singletonP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_133])]),c_0_138])]) ).
cnf(c_0_144,negated_conjecture,
hd(cons(X1,nil)) = X1,
inference(spm,[status(thm)],[c_0_139,c_0_128]) ).
cnf(c_0_145,plain,
( tl(X1) = nil
| nil = X1
| cons(hd(X1),nil) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_62]),c_0_63]),c_0_64]) ).
cnf(c_0_146,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_133])]) ).
cnf(c_0_147,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| cons(X2,X1) != sk4
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_135,c_0_95]) ).
cnf(c_0_148,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_149,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| cons(X2,app(nil,X1)) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_133])]) ).
cnf(c_0_150,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_62,c_0_70]),c_0_71]),c_0_72]) ).
cnf(c_0_151,negated_conjecture,
hd(app(cons(X1,nil),nil)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]),c_0_138])]) ).
cnf(c_0_152,negated_conjecture,
tl(cons(X1,nil)) = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_144]),c_0_138])]),c_0_146]) ).
cnf(c_0_153,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_82,c_0_103]),c_0_76])]) ).
cnf(c_0_154,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| cons(X2,X1) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_133])]) ).
cnf(c_0_155,plain,
( cons(hd(cons(X1,X2)),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_85]),c_0_86]),c_0_87]) ).
cnf(c_0_156,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_157,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_158,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_159,negated_conjecture,
( cons(X1,app(nil,X2)) != sk4
| sk3 != nil
| ~ ssList(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_138])]),c_0_146]) ).
cnf(c_0_160,negated_conjecture,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]),c_0_93]),c_0_138]),c_0_76])]),c_0_146]) ).
cnf(c_0_161,negated_conjecture,
( app(nil,sk3) = sk3
| cons(X1,X2) != sk4
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_138])]) ).
cnf(c_0_162,plain,
( cons(hd(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_163,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_164,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_165,negated_conjecture,
( cons(X1,app(X2,nil)) != sk4
| sk3 != nil
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_159,c_0_111]) ).
cnf(c_0_166,plain,
( cons(skaf83(X1),app(skaf82(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_167,plain,
( app(X1,app(X2,skaf45(X3,app(X1,X2)))) = X3
| ~ frontsegP(X3,app(X1,X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_82]),c_0_101])]),c_0_71]) ).
cnf(c_0_168,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_169,plain,
( X1 = nil
| app(X2,app(X3,X1)) != app(X2,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_82]),c_0_71]) ).
cnf(c_0_170,negated_conjecture,
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_153,c_0_160]),c_0_138]),c_0_76])]) ).
cnf(c_0_171,plain,
( skaf45(app(nil,X1),X1) = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_76])]) ).
cnf(c_0_172,negated_conjecture,
( app(nil,sk3) = sk3
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_158])])]),c_0_128])]) ).
cnf(c_0_173,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_174,plain,
( frontsegP(app(nil,X1),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_111]),c_0_76])]) ).
cnf(c_0_175,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
co1_8 ).
cnf(c_0_176,negated_conjecture,
neq(sk2,nil),
co1_7 ).
cnf(c_0_177,negated_conjecture,
( nil = X1
| app(X1,nil) != sk4
| sk3 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_158]),c_0_76])]) ).
cnf(c_0_178,plain,
( app(nil,app(nil,skaf45(X1,nil))) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_93]),c_0_76])]),c_0_168]) ).
cnf(c_0_179,plain,
( skaf45(X1,nil) = 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_103,c_0_100]),c_0_101]),c_0_76])]),c_0_168]) ).
cnf(c_0_180,negated_conjecture,
( app(X1,cons(X2,nil)) != app(X1,nil)
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_138]),c_0_76])]),c_0_146]) ).
cnf(c_0_181,plain,
( cons(X1,app(X2,X3)) != nil
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_117]),c_0_86]),c_0_87]) ).
cnf(c_0_182,negated_conjecture,
( skaf45(sk3,sk3) = nil
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173])]) ).
cnf(c_0_183,negated_conjecture,
( sk4 = nil
| frontsegP(sk3,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_172]),c_0_173])]) ).
cnf(c_0_184,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
clause175 ).
cnf(c_0_185,negated_conjecture,
( ~ neq(X1,nil)
| ~ segmentP(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_164]),c_0_124]) ).
cnf(c_0_186,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_176,c_0_124]) ).
cnf(c_0_187,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_188,negated_conjecture,
( nil = X1
| app(nil,X1) != sk4
| sk3 != nil
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_177,c_0_111]) ).
cnf(c_0_189,plain,
( app(nil,app(nil,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_190,negated_conjecture,
( app(X1,nil) != sk3
| cons(X2,X1) != sk4
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_180,c_0_154]) ).
cnf(c_0_191,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_192,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_193,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
clause58 ).
cnf(c_0_194,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_195,plain,
( cons(X1,app(nil,X2)) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_111]),c_0_76])]) ).
cnf(c_0_196,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause170 ).
cnf(c_0_197,negated_conjecture,
( app(sk3,nil) = sk3
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_182]),c_0_173])]),c_0_183]) ).
cnf(c_0_198,negated_conjecture,
( nil = sk3
| nil != sk4 ),
co1_10 ).
cnf(c_0_199,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssItem(X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_184]) ).
cnf(c_0_200,negated_conjecture,
( ~ segmentP(sk3,sk4)
| ~ segmentP(sk4,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_128])]) ).
cnf(c_0_201,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_187]) ).
cnf(c_0_202,negated_conjecture,
( app(nil,sk4) = nil
| sk3 != nil
| ~ ssList(app(nil,sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189])]),c_0_128])]) ).
cnf(c_0_203,negated_conjecture,
( app(nil,X1) != sk3
| cons(X2,X1) != sk4
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_190,c_0_111]) ).
cnf(c_0_204,plain,
( app(nil,skaf46(X1,nil)) = 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_191,c_0_111]),c_0_76]),c_0_192])]),c_0_193]) ).
cnf(c_0_205,plain,
( X1 = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_93]),c_0_76])]) ).
cnf(c_0_206,plain,
( cons(X1,app(nil,X2)) != nil
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_133])]) ).
cnf(c_0_207,plain,
( skaf83(cons(X1,X2)) = X1
| ~ 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_196,c_0_156]),c_0_157]),c_0_158])])]),c_0_86]),c_0_87]) ).
cnf(c_0_208,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_62,c_0_106]),c_0_71]),c_0_72]) ).
cnf(c_0_209,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_63,c_0_70]),c_0_71]),c_0_72]) ).
cnf(c_0_210,negated_conjecture,
( app(tl(sk3),nil) = tl(sk3)
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_197]),c_0_173]),c_0_76])]),c_0_198]) ).
cnf(c_0_211,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
clause161 ).
cnf(c_0_212,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_213,plain,
( nil = X1
| memberP(app(X2,X1),hd(X1))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_62]),c_0_63]),c_0_71]),c_0_64]) ).
cnf(c_0_214,negated_conjecture,
( sk4 != nil
| ~ segmentP(nil,sk4)
| ~ segmentP(sk4,sk4) ),
inference(spm,[status(thm)],[c_0_200,c_0_198]) ).
cnf(c_0_215,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
clause57 ).
cnf(c_0_216,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_201,c_0_79]),c_0_76])]),c_0_71]) ).
cnf(c_0_217,negated_conjecture,
( app(nil,sk4) = nil
| sk3 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_71]),c_0_76]),c_0_128])]) ).
cnf(c_0_218,negated_conjecture,
cons(X1,skaf46(sk3,nil)) != sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_192])])]),c_0_173])]) ).
cnf(c_0_219,plain,
( app(X1,X2) = nil
| app(X1,app(X2,nil)) != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_82]),c_0_76])]),c_0_71]) ).
cnf(c_0_220,negated_conjecture,
( sk4 = nil
| cons(X1,sk3) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_172]),c_0_173])]) ).
cnf(c_0_221,plain,
( skaf83(cons(X1,X2)) = X1
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_133])]) ).
cnf(c_0_222,negated_conjecture,
( cons(hd(sk3),tl(sk3)) = sk3
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_197]),c_0_173]),c_0_76])]),c_0_198]) ).
cnf(c_0_223,negated_conjecture,
( sk3 = nil
| ssList(tl(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_173]),c_0_76])]) ).
cnf(c_0_224,plain,
( skaf44(X1) = X2
| ~ memberP(X1,X2)
| ~ singletonP(X1)
| ~ ssItem(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_211,c_0_74]),c_0_75]),c_0_76])]),c_0_212]) ).
cnf(c_0_225,negated_conjecture,
( memberP(sk3,X1)
| cons(X1,X2) != sk4
| ~ ssList(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_154]),c_0_144]),c_0_138])]),c_0_146]) ).
cnf(c_0_226,plain,
( tl(cons(X1,app(X2,X3))) = app(tl(cons(X1,X2)),X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_117]),c_0_86]),c_0_87]) ).
cnf(c_0_227,negated_conjecture,
( sk4 != nil
| ~ segmentP(nil,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_128])]) ).
cnf(c_0_228,negated_conjecture,
( segmentP(nil,sk4)
| sk3 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_128]),c_0_76])]) ).
cnf(c_0_229,plain,
( hd(cons(X1,app(X2,X3))) = hd(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_117]),c_0_86]),c_0_87]) ).
cnf(c_0_230,negated_conjecture,
( app(X1,skaf46(sk3,nil)) != sk4
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_132]),c_0_192])]) ).
cnf(c_0_231,plain,
( app(X1,skaf46(X2,nil)) = nil
| app(X1,X2) != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
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_191]),c_0_192]),c_0_76])]),c_0_193]) ).
cnf(c_0_232,negated_conjecture,
( sk4 = nil
| app(X1,sk3) != nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_132]),c_0_173])]) ).
cnf(c_0_233,plain,
( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_95]),c_0_107]) ).
cnf(c_0_234,negated_conjecture,
( skaf83(sk3) = hd(sk3)
| sk3 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_223]) ).
cnf(c_0_235,negated_conjecture,
( app(nil,cons(X1,nil)) = sk3
| cons(X1,nil) != sk4
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_79]),c_0_76])]) ).
cnf(c_0_236,plain,
( skaf44(X1) = X2
| ~ memberP(X1,X2)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_224,c_0_133])]) ).
cnf(c_0_237,negated_conjecture,
( sk4 = nil
| memberP(sk3,skaf83(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_156]),c_0_158])])]),c_0_128])]) ).
cnf(c_0_238,plain,
( tl(cons(X1,app(X2,X3))) = app(tl(cons(X1,X2)),X3)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_226,c_0_133])]) ).
cnf(c_0_239,negated_conjecture,
sk4 != nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_198]) ).
cnf(c_0_240,plain,
( hd(cons(X1,app(X2,X3))) = hd(cons(X1,X2))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_229,c_0_133])]) ).
cnf(c_0_241,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_133])]) ).
cnf(c_0_242,negated_conjecture,
( app(X1,sk3) != nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_173])]),c_0_232]) ).
cnf(c_0_243,plain,
( tl(cons(X1,X2)) = app(nil,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_133])]),c_0_152]),c_0_138])]) ).
cnf(c_0_244,negated_conjecture,
( cons(hd(sk3),skaf82(sk3)) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_234]),c_0_173])]) ).
cnf(c_0_245,negated_conjecture,
( segmentP(app(sk3,X1),cons(X2,nil))
| cons(X2,nil) != sk4
| ~ ssItem(X2)
| ~ ssList(app(sk3,X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_235]),c_0_76])]),c_0_126]) ).
cnf(c_0_246,negated_conjecture,
( skaf44(sk3) = skaf83(sk4)
| sk4 = nil
| ~ singletonP(sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_237]),c_0_173])]) ).
cnf(c_0_247,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_248,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_117,c_0_62]),c_0_63]),c_0_64]) ).
cnf(c_0_249,negated_conjecture,
( tl(cons(X1,sk3)) = app(nil,sk3)
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_172]),c_0_152]),c_0_173]),c_0_76])]) ).
cnf(c_0_250,negated_conjecture,
app(nil,sk3) = sk3,
inference(sr,[status(thm)],[c_0_172,c_0_239]) ).
cnf(c_0_251,negated_conjecture,
( hd(cons(X1,sk3)) = X1
| sk4 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_172]),c_0_144]),c_0_173]),c_0_76])]) ).
cnf(c_0_252,negated_conjecture,
( sk4 = nil
| ssList(cons(X1,sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_197]),c_0_76]),c_0_173])]) ).
cnf(c_0_253,negated_conjecture,
app(cons(X1,nil),sk3) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_143]),c_0_138])]) ).
cnf(c_0_254,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_133])]) ).
cnf(c_0_255,plain,
( app(tl(X1),skaf45(X2,X1)) = tl(X2)
| nil = X1
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_100]),c_0_101])]) ).
cnf(c_0_256,negated_conjecture,
( frontsegP(sk3,X1)
| cons(X2,X1) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_154]),c_0_138])]) ).
cnf(c_0_257,negated_conjecture,
( app(nil,skaf82(sk3)) = tl(sk3)
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_158])]) ).
cnf(c_0_258,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
clause80 ).
cnf(c_0_259,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_260,negated_conjecture,
( segmentP(sk3,cons(X1,nil))
| cons(X1,nil) != sk4
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_79]),c_0_173]),c_0_76])]) ).
cnf(c_0_261,plain,
( skaf82(X1) = nil
| nil = X1
| cons(skaf83(X1),nil) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_262,negated_conjecture,
( cons(skaf83(sk4),nil) = sk3
| sk4 = nil
| ~ singletonP(sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_246]),c_0_173])]) ).
cnf(c_0_263,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_247]) ).
cnf(c_0_264,plain,
( app(cons(X1,nil),app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_95]),c_0_126]) ).
cnf(c_0_265,plain,
( cons(hd(X1),tl(X1)) = app(X1,nil)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_79]),c_0_76])]),c_0_63]) ).
cnf(c_0_266,negated_conjecture,
tl(cons(X1,sk3)) = sk3,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_249,c_0_239]),c_0_250]) ).
cnf(c_0_267,negated_conjecture,
hd(cons(X1,sk3)) = X1,
inference(sr,[status(thm)],[c_0_251,c_0_239]) ).
cnf(c_0_268,negated_conjecture,
ssList(cons(X1,sk3)),
inference(sr,[status(thm)],[c_0_252,c_0_239]) ).
cnf(c_0_269,negated_conjecture,
cons(X1,sk3) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_254]),c_0_173])]) ).
cnf(c_0_270,plain,
( nil = X1
| ssList(tl(X2))
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_255]),c_0_101])]),c_0_63]) ).
cnf(c_0_271,negated_conjecture,
( sk4 = nil
| frontsegP(sk3,skaf82(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_162]),c_0_158])])]),c_0_128])]) ).
cnf(c_0_272,plain,
( cons(skaf44(X1),app(nil,X2)) = app(X1,X2)
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_74]),c_0_75]),c_0_76])]) ).
cnf(c_0_273,negated_conjecture,
( sk4 = nil
| memberP(sk3,hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_162]),c_0_158])])]),c_0_128])]) ).
cnf(c_0_274,negated_conjecture,
( skaf82(sk3) = nil
| sk3 = nil
| tl(sk3) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_257]),c_0_158]),c_0_76])]) ).
cnf(c_0_275,negated_conjecture,
sk3 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_228]),c_0_128])]),c_0_239]) ).
cnf(c_0_276,negated_conjecture,
( nil = X1
| ~ segmentP(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_259]),c_0_76])]) ).
cnf(c_0_277,negated_conjecture,
( segmentP(sk3,cons(X1,nil))
| cons(X1,nil) != sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_260,c_0_133])]) ).
cnf(c_0_278,negated_conjecture,
( skaf82(sk4) = nil
| sk4 = nil
| sk3 != sk4
| ~ singletonP(sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_262]),c_0_128])]) ).
cnf(c_0_279,axiom,
( X1 = X3
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
clause176 ).
cnf(c_0_280,plain,
( nil = X1
| frontsegP(cons(skaf83(X1),X2),X1)
| ~ frontsegP(X2,skaf82(X1))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_281,plain,
( skaf83(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_282,negated_conjecture,
( app(nil,app(cons(X1,nil),X2)) = app(sk3,X2)
| cons(X1,nil) != sk4
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_235]),c_0_76])]),c_0_126]) ).
cnf(c_0_283,plain,
( app(cons(X1,nil),app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_264,c_0_133])]) ).
cnf(c_0_284,negated_conjecture,
app(sk3,nil) = sk3,
inference(sr,[status(thm)],[c_0_197,c_0_239]) ).
cnf(c_0_285,negated_conjecture,
app(cons(X1,sk3),nil) = cons(X1,sk3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_266]),c_0_267]),c_0_268])]),c_0_269]) ).
cnf(c_0_286,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_85,c_0_74]),c_0_75]),c_0_76])]) ).
cnf(c_0_287,negated_conjecture,
( skaf82(sk4) = nil
| sk4 = nil
| ssList(tl(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_271]),c_0_158]),c_0_173])]) ).
cnf(c_0_288,plain,
( cons(skaf44(X1),nil) = app(X1,nil)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_79]),c_0_76])]) ).
cnf(c_0_289,negated_conjecture,
( skaf44(sk3) = hd(sk4)
| sk4 = nil
| ~ singletonP(sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_273]),c_0_173])]) ).
cnf(c_0_290,negated_conjecture,
( cons(skaf83(sk3),nil) = sk3
| sk3 = nil
| tl(sk3) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_274]),c_0_173])]) ).
cnf(c_0_291,negated_conjecture,
skaf83(sk3) = hd(sk3),
inference(sr,[status(thm)],[c_0_234,c_0_275]) ).
cnf(c_0_292,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_201,c_0_103]),c_0_76])]),c_0_71]) ).
cnf(c_0_293,negated_conjecture,
( cons(X1,nil) != sk4
| ~ segmentP(sk4,cons(X1,nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_276,c_0_277]),c_0_138])]),c_0_146]) ).
cnf(c_0_294,negated_conjecture,
( cons(skaf83(sk4),nil) = sk4
| sk4 = nil
| sk3 != sk4
| ~ singletonP(sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_278]),c_0_128])]) ).
cnf(c_0_295,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_279,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_296,plain,
( nil = X1
| frontsegP(cons(hd(X1),X2),X1)
| ~ frontsegP(X2,skaf82(X1))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_280,c_0_281]) ).
cnf(c_0_297,negated_conjecture,
frontsegP(sk3,skaf82(sk4)),
inference(sr,[status(thm)],[c_0_271,c_0_239]) ).
cnf(c_0_298,negated_conjecture,
( app(nil,app(cons(X1,nil),X2)) = app(sk3,X2)
| cons(X1,nil) != sk4
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_282,c_0_133])]) ).
cnf(c_0_299,negated_conjecture,
app(cons(X1,nil),sk3) = cons(X1,sk3),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284]),c_0_173]),c_0_76])]),c_0_285]) ).
cnf(c_0_300,negated_conjecture,
app(nil,cons(X1,sk3)) = cons(X1,sk3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_285]),c_0_268]),c_0_76])]) ).
cnf(c_0_301,axiom,
( nil = X2
| X1 = X2
| nil = X1
| tl(X1) != tl(X2)
| hd(X1) != hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause177 ).
cnf(c_0_302,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_286,c_0_97]) ).
cnf(c_0_303,negated_conjecture,
( cons(skaf83(sk4),nil) = sk4
| sk4 = nil
| ssList(tl(sk3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_287]),c_0_128])]) ).
cnf(c_0_304,negated_conjecture,
( cons(hd(sk4),nil) = app(sk3,nil)
| sk4 = nil
| ~ singletonP(sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_289]),c_0_173])]) ).
cnf(c_0_305,negated_conjecture,
( cons(hd(sk3),nil) = sk3
| tl(sk3) != nil ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_290,c_0_291]),c_0_275]) ).
cnf(c_0_306,negated_conjecture,
segmentP(cons(X1,nil),cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_160]),c_0_76]),c_0_138])]) ).
cnf(c_0_307,negated_conjecture,
( sk4 = nil
| sk3 != sk4
| ~ segmentP(sk4,sk4)
| ~ singletonP(sk3) ),
inference(spm,[status(thm)],[c_0_293,c_0_294]) ).
cnf(c_0_308,plain,
( X1 = skaf83(X2)
| nil = X2
| ~ frontsegP(cons(X1,X3),X2)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_295,c_0_133])]) ).
cnf(c_0_309,negated_conjecture,
frontsegP(cons(hd(sk4),sk3),sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297]),c_0_173]),c_0_128])]),c_0_239]) ).
cnf(c_0_310,negated_conjecture,
( segmentP(sk3,X1)
| cons(X2,X1) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_154]),c_0_138])]) ).
cnf(c_0_311,negated_conjecture,
( cons(X1,sk3) = app(sk3,sk3)
| cons(X1,nil) != sk4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_299]),c_0_300]),c_0_173])]) ).
cnf(c_0_312,plain,
( X1 = cons(X2,nil)
| nil = X1
| hd(X1) != hd(cons(X2,nil))
| tl(X1) != nil
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_302]),c_0_126]),c_0_107]) ).
cnf(c_0_313,negated_conjecture,
( sk4 = nil
| ssList(tl(sk3))
| ~ segmentP(sk4,sk4) ),
inference(spm,[status(thm)],[c_0_293,c_0_303]) ).
cnf(c_0_314,negated_conjecture,
( cons(hd(sk4),nil) = sk3
| ~ singletonP(sk3) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_304,c_0_284]),c_0_239]) ).
cnf(c_0_315,negated_conjecture,
( singletonP(sk3)
| tl(sk3) != nil ),
inference(spm,[status(thm)],[c_0_143,c_0_305]) ).
cnf(c_0_316,negated_conjecture,
( sk4 = nil
| sk3 != sk4
| ~ singletonP(sk3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_306,c_0_294]),c_0_307]) ).
cnf(c_0_317,negated_conjecture,
skaf83(sk4) = hd(sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_309]),c_0_173]),c_0_128])]),c_0_239]) ).
cnf(c_0_318,negated_conjecture,
( sk4 = nil
| segmentP(sk3,skaf82(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_310,c_0_162]),c_0_158])])]),c_0_128])]) ).
cnf(c_0_319,negated_conjecture,
( app(tl(sk3),sk3) = sk3
| cons(X1,nil) != sk4 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_311]),c_0_266]),c_0_173])]),c_0_275]) ).
cnf(c_0_320,plain,
( cons(hd(X1),nil) = X1
| nil = X1
| tl(X1) != nil
| ~ ssList(X1) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_312,c_0_133])]),c_0_144])]) ).
cnf(c_0_321,negated_conjecture,
( sk4 = nil
| ssList(tl(sk3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_306,c_0_303]),c_0_313]) ).
cnf(c_0_322,negated_conjecture,
( cons(hd(sk4),nil) = sk3
| tl(sk3) != nil ),
inference(spm,[status(thm)],[c_0_314,c_0_315]) ).
cnf(c_0_323,negated_conjecture,
( tl(sk3) != nil
| sk3 != sk4 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_315]),c_0_239]) ).
cnf(c_0_324,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_112]),c_0_86]),c_0_87]) ).
cnf(c_0_325,plain,
( tl(cons(X1,X2)) = X2
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_133])]) ).
cnf(c_0_326,negated_conjecture,
cons(hd(sk4),skaf82(sk4)) = sk4,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_317]),c_0_128])]),c_0_239]) ).
cnf(c_0_327,negated_conjecture,
segmentP(sk3,skaf82(sk4)),
inference(sr,[status(thm)],[c_0_318,c_0_239]) ).
cnf(c_0_328,plain,
( X1 = nil
| app(X1,X2) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_103]),c_0_76])]) ).
cnf(c_0_329,negated_conjecture,
( app(tl(sk3),sk3) = sk3
| tl(sk4) != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_320])]),c_0_128])]),c_0_239]) ).
cnf(c_0_330,negated_conjecture,
ssList(tl(sk3)),
inference(sr,[status(thm)],[c_0_321,c_0_239]) ).
cnf(c_0_331,negated_conjecture,
( tl(sk4) != nil
| tl(sk3) != nil ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_322]),c_0_128])]),c_0_239]),c_0_323]) ).
cnf(c_0_332,plain,
( cons(skaf83(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_156]),c_0_157]),c_0_158])]) ).
cnf(c_0_333,negated_conjecture,
skaf82(sk4) = tl(sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_326]),c_0_158])]) ).
cnf(c_0_334,negated_conjecture,
( skaf82(sk4) = nil
| ~ segmentP(sk4,skaf82(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_276,c_0_327]),c_0_158])]) ).
cnf(c_0_335,negated_conjecture,
tl(sk4) != nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_329]),c_0_173]),c_0_330])]),c_0_331]) ).
cnf(c_0_336,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_254]),c_0_138])]) ).
cnf(c_0_337,negated_conjecture,
cons(hd(sk4),tl(sk4)) = sk4,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_317]),c_0_128])]),c_0_239]) ).
cnf(c_0_338,negated_conjecture,
ssList(tl(sk4)),
inference(spm,[status(thm)],[c_0_158,c_0_333]) ).
cnf(c_0_339,negated_conjecture,
~ segmentP(sk4,tl(sk4)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_334,c_0_333]),c_0_333]),c_0_335]) ).
cnf(c_0_340,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_336,c_0_337]),c_0_338])]),c_0_339]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC088-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:24:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 168.04/84.85 % Version : CSE_E---1.7
% 168.04/84.85 % Problem : theBenchmark.p
% 168.04/84.85 % SZS status Unsatisfiable for theBenchmark.p
% 168.04/84.85 % SZS output start CNFRefutation
% See solution above
% 168.54/85.38 % Total time : 64.337s
%------------------------------------------------------------------------------