%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC057-1 : 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 : n031.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 05:18:05 PM UTC 2026
% Result : Unsatisfiable 123.88s 70.56s
% Output : CNFRefutation 124.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 56
% Syntax : Number of clauses : 214 ( 32 unt; 47 nHn; 192 RR)
% Number of literals : 671 ( 177 equ; 425 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 302 ( 34 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(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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause169,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/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(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(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(clause129,axiom,
( X2 = X1
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause129) ).
cnf(clause137,axiom,
( frontsegP(app(X1,X3),X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause137) ).
cnf(co1_12,negated_conjecture,
( nil = sk4
| frontsegP(sk4,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
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(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
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(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(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(co1_14,negated_conjecture,
( nil = sk3
| frontsegP(sk4,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
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(clause154,axiom,
( frontsegP(X1,X3)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause154) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
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(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(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(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(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(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
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(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(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(clause48,axiom,
ssList(skaf48(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause48) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
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(clause84,axiom,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause84) ).
cnf(clause58,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause58) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(co1_10,negated_conjecture,
( nil != sk1
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_9,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
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(co1_8,negated_conjecture,
( nil = sk2
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_11,negated_conjecture,
( nil = sk4
| neq(sk3,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause172,axiom,
( segmentP(app(app(X4,X1),X3),X2)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
cnf(clause57,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause83,axiom,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause83) ).
cnf(c_0_56,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_57,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_58,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_59,axiom,
ssList(nil),
clause8 ).
cnf(c_0_60,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_61,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_62,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_56]) ).
cnf(c_0_63,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_64,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_65,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_66,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_67,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_68,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_69,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_70,axiom,
( X2 = X1
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause129 ).
cnf(c_0_71,axiom,
( frontsegP(app(X1,X3),X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause137 ).
cnf(c_0_72,negated_conjecture,
( nil = sk4
| frontsegP(sk4,sk3) ),
co1_12 ).
cnf(c_0_73,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_74,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_75,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_57,c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_76,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_58,c_0_61]),c_0_59])]) ).
cnf(c_0_77,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_78,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_79,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_80,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_81,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_82,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_83,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_84,negated_conjecture,
( nil = sk3
| frontsegP(sk4,sk3) ),
co1_14 ).
cnf(c_0_85,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_62,c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_86,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_87,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_88,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_89,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_66]) ).
cnf(c_0_90,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_60]) ).
cnf(c_0_91,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_92,plain,
( X1 = app(X2,X3)
| ~ frontsegP(X1,app(X2,X3))
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_60]) ).
cnf(c_0_93,axiom,
( frontsegP(X1,X3)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause154 ).
cnf(c_0_94,negated_conjecture,
( sk2 = nil
| frontsegP(sk2,sk3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_73]) ).
cnf(c_0_95,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_96,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_74]),c_0_60]) ).
cnf(c_0_97,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_59])]) ).
cnf(c_0_98,axiom,
( rearsegP(X3,X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause143 ).
cnf(c_0_99,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_77,c_0_78]),c_0_79]),c_0_80]) ).
cnf(c_0_100,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_81,c_0_82]),c_0_83])]) ).
cnf(c_0_101,negated_conjecture,
( sk3 = nil
| frontsegP(sk2,sk3) ),
inference(rw,[status(thm)],[c_0_84,c_0_73]) ).
cnf(c_0_102,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_85,c_0_86]),c_0_87]),c_0_88])]),c_0_60]) ).
cnf(c_0_103,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_89,c_0_86]),c_0_87]),c_0_88])]) ).
cnf(c_0_104,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk3,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_105,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_106,plain,
( X1 = X2
| ~ frontsegP(nil,X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_61]),c_0_59])]) ).
cnf(c_0_107,negated_conjecture,
( sk2 = nil
| frontsegP(X1,sk3)
| ~ frontsegP(X1,sk2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_91]),c_0_95])]) ).
cnf(c_0_108,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_109,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_110,plain,
( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_58]),c_0_60]) ).
cnf(c_0_111,plain,
( app(nil,app(X1,nil)) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_97]),c_0_59])]) ).
cnf(c_0_112,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_113,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_98]),c_0_60]) ).
cnf(c_0_114,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_99,c_0_86]),c_0_87]),c_0_88])]) ).
cnf(c_0_115,negated_conjecture,
( hd(sk3) = hd(sk2)
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_91]),c_0_95])]) ).
cnf(c_0_116,plain,
( nil = X1
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_117,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk3,sk3)) ),
inference(spm,[status(thm)],[c_0_104,c_0_91]) ).
cnf(c_0_118,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_105,c_0_57]),c_0_59])]) ).
cnf(c_0_119,negated_conjecture,
( sk2 = nil
| sk3 = X1
| ~ frontsegP(nil,sk2)
| ~ frontsegP(sk3,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_91]),c_0_59])]) ).
cnf(c_0_120,plain,
( frontsegP(X1,skaf46(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_108]),c_0_109])]) ).
cnf(c_0_121,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_59])]) ).
cnf(c_0_122,plain,
( skaf46(app(X1,X2),X2) = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
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_112,c_0_108]),c_0_109])])]),c_0_60]),c_0_113]) ).
cnf(c_0_123,negated_conjecture,
( cons(hd(sk2),skaf82(sk3)) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_91])]) ).
cnf(c_0_124,negated_conjecture,
( sk3 = nil
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_91])]) ).
cnf(c_0_125,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_126,plain,
( X1 = nil
| skaf46(X2,X1) != X2
| ~ rearsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_108]),c_0_109])]) ).
cnf(c_0_127,negated_conjecture,
( skaf46(sk3,X1) = sk3
| sk2 = nil
| ~ frontsegP(nil,sk2)
| ~ rearsegP(sk3,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_109]),c_0_91])]) ).
cnf(c_0_128,plain,
( frontsegP(X1,app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_57]) ).
cnf(c_0_129,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_130,plain,
( skaf46(app(nil,X1),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_97]),c_0_59])]) ).
cnf(c_0_131,negated_conjecture,
( skaf82(sk3) = tl(sk3)
| sk3 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_123]),c_0_88])]),c_0_124]) ).
cnf(c_0_132,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_125])]),c_0_59])]) ).
cnf(c_0_133,negated_conjecture,
( sk2 = nil
| X1 = nil
| ~ frontsegP(nil,sk2)
| ~ rearsegP(sk3,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_91])]) ).
cnf(c_0_134,plain,
( rearsegP(X1,skaf45(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_82]),c_0_83])]) ).
cnf(c_0_135,axiom,
( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause168 ).
cnf(c_0_136,axiom,
ssList(skaf47(X1,X2)),
clause49 ).
cnf(c_0_137,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_138,negated_conjecture,
( sk3 = nil
| frontsegP(X1,sk3)
| ~ frontsegP(X1,sk2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_101]),c_0_91]),c_0_95])]) ).
cnf(c_0_139,plain,
( frontsegP(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_128,c_0_82]),c_0_83]),c_0_59])]),c_0_129]) ).
cnf(c_0_140,plain,
( skaf45(X1,nil) = skaf46(X1,nil)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_82]),c_0_83]),c_0_59])]),c_0_129]) ).
cnf(c_0_141,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
clause140 ).
cnf(c_0_142,negated_conjecture,
( cons(skaf83(sk3),tl(sk3)) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_131]),c_0_91])]) ).
cnf(c_0_143,negated_conjecture,
( sk3 = nil
| ssList(tl(sk3)) ),
inference(spm,[status(thm)],[c_0_88,c_0_131]) ).
cnf(c_0_144,plain,
( X1 = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_132]),c_0_59])]) ).
cnf(c_0_145,negated_conjecture,
( skaf45(sk3,X1) = nil
| sk2 = nil
| ~ frontsegP(nil,sk2)
| ~ frontsegP(sk3,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_83]),c_0_91])]) ).
cnf(c_0_146,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_135,c_0_57]),c_0_59]),c_0_136])]),c_0_137]) ).
cnf(c_0_147,axiom,
ssList(skaf48(X1,X2)),
clause48 ).
cnf(c_0_148,negated_conjecture,
( sk3 = nil
| frontsegP(X1,sk3)
| ~ frontsegP(X2,sk2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_138]),c_0_91])]) ).
cnf(c_0_149,plain,
( frontsegP(skaf46(X1,nil),X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_150,plain,
( memberP(X1,X2)
| ~ memberP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_82]),c_0_83])]) ).
cnf(c_0_151,negated_conjecture,
( sk3 = nil
| memberP(sk3,skaf83(sk3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_142]),c_0_87])]),c_0_143]) ).
cnf(c_0_152,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_153,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_154,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_144,c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_155,negated_conjecture,
( app(X1,nil) = sk3
| sk2 = nil
| ~ frontsegP(nil,sk2)
| ~ frontsegP(sk3,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_145]),c_0_91])]) ).
cnf(c_0_156,plain,
( frontsegP(X1,skaf47(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_146]),c_0_147]),c_0_136])]) ).
cnf(c_0_157,axiom,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
clause84 ).
cnf(c_0_158,negated_conjecture,
( sk3 = nil
| frontsegP(X1,sk3)
| ~ frontsegP(X1,skaf46(sk2,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_109]),c_0_95])]) ).
cnf(c_0_159,plain,
( frontsegP(app(nil,X1),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_59])]) ).
cnf(c_0_160,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
clause58 ).
cnf(c_0_161,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_162,negated_conjecture,
( sk3 = nil
| memberP(X1,skaf83(sk3))
| ~ frontsegP(X1,sk3)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_87]),c_0_91])]) ).
cnf(c_0_163,plain,
( skaf46(nil,X1) = nil
| ~ rearsegP(nil,X1)
| ~ ssList(X1) ),
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_152,c_0_108]),c_0_109])])]),c_0_59])]) ).
cnf(c_0_164,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_153]) ).
cnf(c_0_165,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_154,c_0_76]),c_0_59])]) ).
cnf(c_0_166,negated_conjecture,
( app(skaf47(sk3,nil),nil) = sk3
| sk2 = nil
| ~ frontsegP(nil,sk2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_136]),c_0_91])]) ).
cnf(c_0_167,negated_conjecture,
( sk3 = nil
| ~ frontsegP(nil,sk2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_138]),c_0_91]),c_0_59])]) ).
cnf(c_0_168,negated_conjecture,
( nil != sk1
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
co1_10 ).
cnf(c_0_169,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
co1_9 ).
cnf(c_0_170,negated_conjecture,
( sk3 = nil
| frontsegP(app(nil,skaf46(sk2,nil)),sk3)
| ~ ssList(app(nil,skaf46(sk2,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_109])]) ).
cnf(c_0_171,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_154,c_0_108]),c_0_109]),c_0_59])]),c_0_160]) ).
cnf(c_0_172,negated_conjecture,
( sk3 = nil
| ~ frontsegP(nil,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_87]),c_0_59])]) ).
cnf(c_0_173,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_174,plain,
( app(nil,X1) = nil
| ~ rearsegP(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_163]),c_0_59])]) ).
cnf(c_0_175,negated_conjecture,
( nil = sk2
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
co1_8 ).
cnf(c_0_176,negated_conjecture,
( nil = sk4
| neq(sk3,nil) ),
co1_11 ).
cnf(c_0_177,axiom,
( segmentP(app(app(X4,X1),X3),X2)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause172 ).
cnf(c_0_178,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_164,c_0_57]),c_0_59])]),c_0_60]) ).
cnf(c_0_179,negated_conjecture,
( app(nil,skaf47(sk3,nil)) = nil
| sk2 = nil
| ~ frontsegP(nil,sk2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_136])]),c_0_167]) ).
cnf(c_0_180,negated_conjecture,
( sk3 != nil
| ~ neq(X1,nil)
| ~ segmentP(sk3,X1)
| ~ segmentP(sk2,X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_69]),c_0_69]) ).
cnf(c_0_181,negated_conjecture,
( neq(sk2,nil)
| sk3 != nil ),
inference(rw,[status(thm)],[c_0_169,c_0_69]) ).
cnf(c_0_182,negated_conjecture,
( sk3 = nil
| app(nil,sk2) != nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_59]),c_0_95])]),c_0_172]) ).
cnf(c_0_183,plain,
( skaf45(nil,X1) = nil
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
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_173,c_0_82]),c_0_83])])]),c_0_59])]) ).
cnf(c_0_184,plain,
( app(nil,skaf45(nil,X1)) = nil
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_134]),c_0_83]),c_0_59])]) ).
cnf(c_0_185,negated_conjecture,
( sk2 = nil
| ~ neq(X1,nil)
| ~ segmentP(sk3,X1)
| ~ segmentP(sk2,X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[c_0_175,c_0_69]) ).
cnf(c_0_186,negated_conjecture,
( sk2 = nil
| neq(sk3,nil) ),
inference(rw,[status(thm)],[c_0_176,c_0_73]) ).
cnf(c_0_187,plain,
( segmentP(app(nil,X1),X2)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_132]),c_0_59])]) ).
cnf(c_0_188,negated_conjecture,
( sk2 = nil
| segmentP(nil,skaf47(sk3,nil))
| ~ frontsegP(nil,sk2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_136]),c_0_59])]) ).
cnf(c_0_189,negated_conjecture,
( skaf47(sk3,nil) = sk3
| sk2 = nil
| ~ frontsegP(nil,sk2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_156]),c_0_136]),c_0_91])]) ).
cnf(c_0_190,negated_conjecture,
( sk3 != nil
| ~ segmentP(sk3,sk2)
| ~ segmentP(sk2,sk2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_95])]) ).
cnf(c_0_191,negated_conjecture,
( sk3 = nil
| sk2 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_61]),c_0_95])]) ).
cnf(c_0_192,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_164,c_0_61]),c_0_59])]),c_0_60]) ).
cnf(c_0_193,plain,
( app(X1,app(skaf45(X2,X1),X3)) = app(X2,X3)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_82]),c_0_83])]) ).
cnf(c_0_194,plain,
( app(X1,nil) = nil
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_183]),c_0_59])]) ).
cnf(c_0_195,plain,
( frontsegP(nil,skaf45(nil,X1))
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_184]),c_0_83])]) ).
cnf(c_0_196,negated_conjecture,
( sk2 = nil
| ~ segmentP(sk3,sk3)
| ~ segmentP(sk2,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_91])]) ).
cnf(c_0_197,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
clause57 ).
cnf(c_0_198,plain,
( segmentP(X1,X2)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_187,c_0_61]) ).
cnf(c_0_199,negated_conjecture,
( sk2 = nil
| segmentP(nil,sk3)
| ~ frontsegP(nil,sk2) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_200,negated_conjecture,
( sk2 != nil
| ~ segmentP(nil,sk2)
| ~ segmentP(sk2,sk2) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_201,plain,
( segmentP(app(X1,X2),X3)
| ~ frontsegP(X1,X3)
| ~ ssList(app(skaf45(X1,X3),X2))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_202,plain,
( app(skaf45(nil,X1),nil) = nil
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_83])]) ).
cnf(c_0_203,negated_conjecture,
( sk2 = nil
| ~ segmentP(sk2,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_91])]) ).
cnf(c_0_204,negated_conjecture,
( sk2 = nil
| segmentP(X1,sk3)
| ~ frontsegP(nil,sk2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_91])]) ).
cnf(c_0_205,negated_conjecture,
( sk2 != nil
| ~ segmentP(nil,sk2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_197]),c_0_95])]) ).
cnf(c_0_206,plain,
( segmentP(nil,X1)
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_132]),c_0_59])]) ).
cnf(c_0_207,negated_conjecture,
( sk2 = nil
| ~ frontsegP(nil,sk2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_95])]) ).
cnf(c_0_208,plain,
( segmentP(X1,X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_82]),c_0_83])]) ).
cnf(c_0_209,axiom,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause83 ).
cnf(c_0_210,negated_conjecture,
~ frontsegP(nil,sk2),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_95])]),c_0_207]) ).
cnf(c_0_211,negated_conjecture,
sk2 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_208]),c_0_91]),c_0_95])]),c_0_94]) ).
cnf(c_0_212,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_209]),c_0_59])]) ).
cnf(c_0_213,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_211]),c_0_212])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC057-1 : 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 : n031.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 04:22:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 123.88/70.56 % Version : CSE_E---1.7
% 123.88/70.56 % Problem : theBenchmark.p
% 123.88/70.56 % SZS status Unsatisfiable for theBenchmark.p
% 123.88/70.56 % SZS output start CNFRefutation
% See solution above
% 124.40/71.04 % Total time : 53.387s
%------------------------------------------------------------------------------