%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC409-1 : 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 : n006.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 05:19:33 PM UTC 2026
% Result : Unsatisfiable 24.58s 14.85s
% Output : CNFRefutation 24.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 58
% Syntax : Number of clauses : 239 ( 60 unt; 44 nHn; 193 RR)
% Number of literals : 677 ( 194 equ; 417 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-2 aty)
% Number of variables : 368 ( 53 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(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
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(co1_8,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
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(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(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(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(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
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(co1_11,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
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(co1_7,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_7) ).
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(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(clause168,axiom,
( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause168) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause49,axiom,
ssList(skaf47(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause49) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(clause48,axiom,
ssList(skaf48(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause48) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
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(clause149,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause145,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).
cnf(clause150,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause150) ).
cnf(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(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(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(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(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(co1_9,negated_conjecture,
memberP(sk2,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
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(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(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(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(clause140,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause140) ).
cnf(co1_10,negated_conjecture,
~ memberP(sk1,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(c_0_58,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_59,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_60,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_61,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_58]) ).
cnf(c_0_62,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_63,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_64,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_65,plain,
( ssItem(X1)
| duplicatefreeP(cons(X2,X3))
| ~ ssItem(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
ssItem(sk5),
co1_8 ).
cnf(c_0_67,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_68,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_69,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_70,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_71,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_61,c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_72,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_73,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_74,axiom,
ssList(nil),
clause8 ).
cnf(c_0_75,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(cons(sk5,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_77,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_78,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_79,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_80,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_68]) ).
cnf(c_0_81,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_82,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_71,c_0_72]),c_0_73]),c_0_74])]),c_0_68]) ).
cnf(c_0_83,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(cons(sk5,cons(X2,X3)))
| ~ ssItem(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_75,c_0_60]) ).
cnf(c_0_84,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_85,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_86,plain,
( nil = X1
| ~ memberP(X2,skaf83(X1))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X2,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_76]),c_0_77]),c_0_78])]),c_0_68]) ).
cnf(c_0_87,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_79,c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_88,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk4,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,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_82,c_0_79]),c_0_73])]) ).
cnf(c_0_90,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_91,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(cons(sk5,cons(sk5,X2)))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_66]) ).
cnf(c_0_92,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_93,plain,
( nil = X1
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk4,sk4)) ),
inference(spm,[status(thm)],[c_0_88,c_0_81]) ).
cnf(c_0_95,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_72]),c_0_74])]) ).
cnf(c_0_96,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_97,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_90]) ).
cnf(c_0_98,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(cons(sk5,cons(sk5,sk3))) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( nil = sk3
| nil != sk4 ),
co1_11 ).
cnf(c_0_100,negated_conjecture,
( sk4 = nil
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_81])]) ).
cnf(c_0_101,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ duplicatefreeP(cons(X1,cons(X1,nil))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(cons(sk5,cons(sk5,nil))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_103,negated_conjecture,
( ssItem(X1)
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_66])]) ).
cnf(c_0_104,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
clause175 ).
cnf(c_0_105,negated_conjecture,
( app(X2,cons(X1,nil)) = sk3
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != sk4 ),
co1_7 ).
cnf(c_0_106,negated_conjecture,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_60]),c_0_66]),c_0_74])]) ).
cnf(c_0_107,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_104]) ).
cnf(c_0_108,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| app(cons(X2,nil),X1) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).
cnf(c_0_109,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_106])]) ).
cnf(c_0_110,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_111,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_112,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_113,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_114,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_106])]) ).
cnf(c_0_115,negated_conjecture,
( app(X1,cons(X2,nil)) = sk3
| cons(X2,X1) != sk4
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_117,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_118,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_113]) ).
cnf(c_0_119,negated_conjecture,
( memberP(sk3,X1)
| cons(X1,X2) != sk4
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_92]),c_0_74])]) ).
cnf(c_0_120,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_111,c_0_116]),c_0_68]),c_0_117]) ).
cnf(c_0_121,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_116]),c_0_68]),c_0_117]) ).
cnf(c_0_122,axiom,
( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause168 ).
cnf(c_0_123,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_124,axiom,
ssList(skaf47(X1,X2)),
clause49 ).
cnf(c_0_125,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_126,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_118,c_0_116]),c_0_68]),c_0_117]) ).
cnf(c_0_127,negated_conjecture,
( nil = X1
| memberP(sk3,hd(app(X1,X2)))
| app(X1,X2) != sk4
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]) ).
cnf(c_0_128,plain,
( app(skaf47(X1,nil),skaf48(nil,X1)) = 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_122,c_0_123]),c_0_74]),c_0_124])]),c_0_125]) ).
cnf(c_0_129,axiom,
ssList(skaf48(X1,X2)),
clause48 ).
cnf(c_0_130,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_131,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_132,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_126,c_0_123]),c_0_74])]),c_0_112]) ).
cnf(c_0_133,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_134,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_135,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_136,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_137,negated_conjecture,
( skaf47(sk4,nil) = 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_124]),c_0_129])])]),c_0_81])]) ).
cnf(c_0_138,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_106])]) ).
cnf(c_0_139,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_131,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_140,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_132,c_0_131]),c_0_60]),c_0_133]) ).
cnf(c_0_141,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_142,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_143,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_144,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_145,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_134]),c_0_68]) ).
cnf(c_0_146,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_123,c_0_135]),c_0_74])]),c_0_68]) ).
cnf(c_0_147,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_135,c_0_136]),c_0_74])]) ).
cnf(c_0_148,negated_conjecture,
( skaf47(sk4,nil) = nil
| sk4 != nil ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_99]),c_0_138]) ).
cnf(c_0_149,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_139,c_0_97]) ).
cnf(c_0_150,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_96]),c_0_74])]) ).
cnf(c_0_151,axiom,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
clause141 ).
cnf(c_0_152,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_153,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_141])]),c_0_74])]) ).
cnf(c_0_154,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_142,c_0_143]),c_0_144])])]),c_0_68]),c_0_145]) ).
cnf(c_0_155,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_74])]) ).
cnf(c_0_156,negated_conjecture,
( app(nil,skaf48(nil,sk4)) = sk4
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_148]),c_0_81])]) ).
cnf(c_0_157,plain,
( tl(cons(X1,nil)) = nil
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_106])]) ).
cnf(c_0_158,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_106])]) ).
cnf(c_0_159,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_160,plain,
( memberP(app(X1,X2),X3)
| ~ memberP(X2,X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_106])]) ).
cnf(c_0_161,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_162,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_163,negated_conjecture,
memberP(sk2,sk5),
co1_9 ).
cnf(c_0_164,plain,
( X1 = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_74])]) ).
cnf(c_0_165,plain,
( skaf45(app(nil,X1),X1) = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_74])]) ).
cnf(c_0_166,negated_conjecture,
( app(nil,sk4) = sk4
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_156]),c_0_74]),c_0_129])]) ).
cnf(c_0_167,plain,
( frontsegP(app(nil,X1),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_155]),c_0_74])]) ).
cnf(c_0_168,axiom,
( memberP(X2,X3)
| X3 = X1
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
clause161 ).
cnf(c_0_169,plain,
( memberP(cons(X1,X2),X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_106])]) ).
cnf(c_0_170,plain,
( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
| ~ ssList(cons(X1,nil)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_157]),c_0_158]) ).
cnf(c_0_171,plain,
( app(cons(X1,X2),X3) = cons(X1,app(X2,X3))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_106])]) ).
cnf(c_0_172,plain,
( ssList(cons(X1,X2))
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_106])]) ).
cnf(c_0_173,plain,
( memberP(X1,X2)
| ~ memberP(X3,X2)
| ~ rearsegP(X1,X3)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162])]) ).
cnf(c_0_174,negated_conjecture,
memberP(sk4,sk5),
inference(rw,[status(thm)],[c_0_163,c_0_70]) ).
cnf(c_0_175,axiom,
( rearsegP(X3,X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause143 ).
cnf(c_0_176,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_164,c_0_135]),c_0_74])]),c_0_68]) ).
cnf(c_0_177,negated_conjecture,
( skaf45(sk4,sk4) = nil
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_81])]) ).
cnf(c_0_178,negated_conjecture,
( frontsegP(sk4,sk4)
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_166]),c_0_81])]) ).
cnf(c_0_179,negated_conjecture,
( app(nil,sk3) = sk3
| cons(X1,X2) != sk4
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_147,c_0_115]) ).
cnf(c_0_180,plain,
( X1 = X2
| memberP(X3,X2)
| ~ memberP(cons(X1,X3),X2)
| ~ ssList(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_106]),c_0_106])]) ).
cnf(c_0_181,plain,
( memberP(cons(X1,nil),hd(cons(X1,nil)))
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_74])]) ).
cnf(c_0_182,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_171]),c_0_172]) ).
cnf(c_0_183,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_184,negated_conjecture,
( frontsegP(sk3,X1)
| cons(X2,X1) != sk4
| ~ ssList(cons(X2,nil))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_115]) ).
cnf(c_0_185,negated_conjecture,
( memberP(X1,sk5)
| ~ rearsegP(X1,sk4)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_81])]) ).
cnf(c_0_186,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_175]),c_0_68]) ).
cnf(c_0_187,plain,
( app(nil,X1) = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_147]),c_0_74])]) ).
cnf(c_0_188,negated_conjecture,
( app(sk4,nil) = sk4
| sk4 != nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_177]),c_0_81])]),c_0_178]) ).
cnf(c_0_189,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_190,plain,
( cons(X1,X2) != nil
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_106])]) ).
cnf(c_0_191,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_179,c_0_172]),c_0_74])]) ).
cnf(c_0_192,plain,
( hd(cons(X1,nil)) = X1
| ~ ssList(cons(X1,nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_74])]),c_0_138]) ).
cnf(c_0_193,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_153]),c_0_74])]) ).
cnf(c_0_194,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_183]) ).
cnf(c_0_195,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_184,c_0_172]),c_0_74])]) ).
cnf(c_0_196,negated_conjecture,
( memberP(app(X1,sk4),sk5)
| ~ ssList(app(X1,sk4))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_81])]) ).
cnf(c_0_197,negated_conjecture,
( app(nil,sk4) = nil
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_81])]) ).
cnf(c_0_198,plain,
( hd(cons(X1,app(X2,X3))) = hd(cons(X1,X2))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_171]),c_0_172]),c_0_190]) ).
cnf(c_0_199,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_191,c_0_76]),c_0_78])])]),c_0_81])]) ).
cnf(c_0_200,plain,
hd(cons(X1,nil)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_193])]) ).
cnf(c_0_201,plain,
( hd(X1) = hd(X2)
| nil = X2
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_143]),c_0_144])]) ).
cnf(c_0_202,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_106])]) ).
cnf(c_0_203,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_195,c_0_76]),c_0_78])])]),c_0_81])]) ).
cnf(c_0_204,negated_conjecture,
sk4 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_74])]),c_0_138]) ).
cnf(c_0_205,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_198,c_0_199]),c_0_200]),c_0_92]),c_0_74])]) ).
cnf(c_0_206,plain,
( hd(cons(X1,X2)) = hd(cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_172]),c_0_172]),c_0_190]) ).
cnf(c_0_207,negated_conjecture,
frontsegP(sk3,skaf82(sk4)),
inference(sr,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_208,negated_conjecture,
hd(cons(X1,sk3)) = X1,
inference(sr,[status(thm)],[c_0_205,c_0_204]) ).
cnf(c_0_209,negated_conjecture,
hd(cons(X1,skaf82(sk4))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_208]),c_0_78]),c_0_92])]) ).
cnf(c_0_210,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_211,negated_conjecture,
skaf83(sk4) = hd(sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_76]),c_0_81])]),c_0_204]) ).
cnf(c_0_212,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_210,c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_213,plain,
( tl(cons(X1,X2)) = X2
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_106])]) ).
cnf(c_0_214,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_76,c_0_211]),c_0_81])]),c_0_204]) ).
cnf(c_0_215,plain,
( skaf82(X1) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_216,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
clause140 ).
cnf(c_0_217,negated_conjecture,
( skaf45(sk3,X1) = cons(X2,nil)
| cons(X2,X1) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_115]),c_0_193])]) ).
cnf(c_0_218,plain,
( cons(hd(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_212]) ).
cnf(c_0_219,negated_conjecture,
skaf82(sk4) = tl(sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_78])]) ).
cnf(c_0_220,negated_conjecture,
( sk4 = nil
| frontsegP(sk3,tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_215]),c_0_81])]) ).
cnf(c_0_221,plain,
( memberP(app(X1,X2),X3)
| ~ memberP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_106])]) ).
cnf(c_0_222,negated_conjecture,
skaf45(sk3,tl(sk4)) = cons(hd(sk4),nil),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[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_217,c_0_218]),c_0_78])])]),c_0_81])]),c_0_204]),c_0_219]) ).
cnf(c_0_223,negated_conjecture,
frontsegP(sk3,tl(sk4)),
inference(sr,[status(thm)],[c_0_220,c_0_204]) ).
cnf(c_0_224,negated_conjecture,
ssList(tl(sk4)),
inference(spm,[status(thm)],[c_0_78,c_0_219]) ).
cnf(c_0_225,plain,
( memberP(X1,X2)
| ~ memberP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_143]),c_0_144])]) ).
cnf(c_0_226,plain,
( cons(hd(X1),app(tl(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_111]),c_0_112]) ).
cnf(c_0_227,negated_conjecture,
app(tl(sk4),cons(hd(sk4),nil)) = sk3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_222]),c_0_223]),c_0_224]),c_0_92])]) ).
cnf(c_0_228,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_119,c_0_76]),c_0_78])])]),c_0_81])]) ).
cnf(c_0_229,negated_conjecture,
( memberP(X1,sk5)
| ~ frontsegP(X1,sk4)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_174]),c_0_81])]) ).
cnf(c_0_230,negated_conjecture,
app(sk4,cons(hd(sk4),nil)) = cons(hd(sk4),sk3),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_193]),c_0_81])]),c_0_204]) ).
cnf(c_0_231,negated_conjecture,
~ memberP(sk1,sk5),
co1_10 ).
cnf(c_0_232,negated_conjecture,
( sk4 = nil
| memberP(sk3,hd(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_212]),c_0_81])]) ).
cnf(c_0_233,negated_conjecture,
( X1 = sk5
| memberP(X2,sk5)
| ~ frontsegP(cons(X1,X2),sk4)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_229]),c_0_172]) ).
cnf(c_0_234,negated_conjecture,
frontsegP(cons(hd(sk4),sk3),sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_230]),c_0_193]),c_0_81])]) ).
cnf(c_0_235,negated_conjecture,
~ memberP(sk3,sk5),
inference(rw,[status(thm)],[c_0_231,c_0_85]) ).
cnf(c_0_236,negated_conjecture,
memberP(sk3,hd(sk4)),
inference(sr,[status(thm)],[c_0_232,c_0_204]) ).
cnf(c_0_237,negated_conjecture,
hd(sk4) = sk5,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_92])]),c_0_235]) ).
cnf(c_0_238,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_237]),c_0_235]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC409-1 : 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
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:48:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 24.58/14.85 % Version : CSE_E---1.7
% 24.58/14.85 % Problem : theBenchmark.p
% 24.58/14.85 % SZS status Unsatisfiable for theBenchmark.p
% 24.58/14.85 % SZS output start CNFRefutation
% See solution above
% 24.68/14.94 % Total time : 11.397s
%------------------------------------------------------------------------------