%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC066-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:42:51 PM UTC 2026
% Result : Unsatisfiable 105.19s 15.85s
% Output : CNFRefutation 105.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 38
% Syntax : Number of clauses : 156 ( 30 unt; 26 nHn; 135 RR)
% Number of literals : 475 ( 102 equ; 317 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 : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 236 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause152,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| segmentP(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause152) ).
cnf(co1_7,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(clause80,axiom,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause80) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_13,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_12,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause79,axiom,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause79) ).
cnf(clause57,axiom,
( ~ ssList(X1)
| segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(clause76,axiom,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause75,axiom,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause179,axiom,
( ~ ssList(X5)
| ~ duplicatefreeP(X5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause74,axiom,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause86,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause104,axiom,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause72,axiom,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause85,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause173,axiom,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(clause100,axiom,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause131,axiom,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(co1_11,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(clause157,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(co1_9,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,sk3)
| ~ segmentP(sk4,X1)
| ~ neq(sk3,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause149,axiom,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause120,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause58,axiom,
( ~ ssList(X1)
| rearsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause58) ).
cnf(clause56,axiom,
( ~ ssList(X1)
| segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(clause102,axiom,
( ~ ssItem(X2)
| ~ ssItem(X1)
| X2 = X1
| neq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause102) ).
cnf(clause113,axiom,
( ~ ssItem(X2)
| ~ ssList(X1)
| nil != X1
| totalorderedP(cons(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause113) ).
cnf(clause98,axiom,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause169,axiom,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause138,axiom,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| segmentP(X1,X3) ),
inference(fof_simplification,[status(thm)],[clause152]) ).
cnf(c_0_39,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_40,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_41,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_42,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
inference(fof_simplification,[status(thm)],[clause80]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| segmentP(X1,X3) ),
c_0_38 ).
cnf(c_0_44,negated_conjecture,
segmentP(sk2,sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_45,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_46,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_47,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil != sk1 ),
inference(fof_simplification,[status(thm)],[co1_13]) ).
cnf(c_0_48,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
c_0_42 ).
cnf(c_0_50,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(X1,sk2)
| segmentP(X1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_51,axiom,
ssList(nil),
clause8 ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(fof_simplification,[status(thm)],[clause79]) ).
cnf(c_0_53,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil != sk1 ),
c_0_47 ).
cnf(c_0_54,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
c_0_48 ).
cnf(c_0_55,negated_conjecture,
( ~ segmentP(nil,sk2)
| sk1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_45]),c_0_51])]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
c_0_52 ).
cnf(c_0_57,negated_conjecture,
( ~ segmentP(sk2,sk2)
| ~ segmentP(sk1,sk2)
| sk1 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_46])]) ).
cnf(c_0_58,negated_conjecture,
( sk2 != nil
| sk1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_46])]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_simplification,[status(thm)],[clause57]) ).
cnf(c_0_60,negated_conjecture,
( ~ segmentP(sk2,sk2)
| ~ segmentP(nil,sk2)
| sk2 != nil ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
c_0_59 ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_64,plain,
( ~ ssList(X5)
| ~ duplicatefreeP(X5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5 ),
inference(fof_simplification,[status(thm)],[clause179]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_68,negated_conjecture,
( ~ segmentP(nil,sk2)
| sk2 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_46])]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(hd(X1)) ),
c_0_62 ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| nil = X1
| ssList(tl(X1)) ),
c_0_63 ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_72,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_73,plain,
( ~ ssList(X5)
| ~ duplicatefreeP(X5)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5 ),
c_0_64 ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
c_0_65 ).
cnf(c_0_75,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| ssList(cons(X1,X2)) ),
c_0_66 ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = X1 ),
c_0_67 ).
cnf(c_0_77,negated_conjecture,
sk2 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_56]),c_0_46])]) ).
cnf(c_0_78,negated_conjecture,
( ssItem(hd(sk2))
| sk2 = nil ),
inference(spm,[status(thm)],[c_0_69,c_0_46]) ).
cnf(c_0_79,negated_conjecture,
( ssList(tl(sk2))
| sk2 = nil ),
inference(spm,[status(thm)],[c_0_70,c_0_46]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| ssItem(X2)
| duplicatefreeP(X1) ),
c_0_71 ).
cnf(c_0_81,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X2,X1)) ),
c_0_72 ).
cnf(c_0_82,plain,
( ~ duplicatefreeP(X4)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssItem(X1)
| app(cons(X1,X2),cons(X1,X3)) != X4 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_51])]),c_0_75]) ).
cnf(c_0_83,negated_conjecture,
cons(hd(sk2),tl(sk2)) = sk2,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_46]),c_0_77]) ).
cnf(c_0_84,negated_conjecture,
ssItem(hd(sk2)),
inference(sr,[status(thm)],[c_0_78,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
ssList(tl(sk2)),
inference(sr,[status(thm)],[c_0_79,c_0_77]) ).
cnf(c_0_86,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| duplicatefreeP(app(X2,X3))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_87,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
inference(fof_simplification,[status(thm)],[clause173]) ).
cnf(c_0_88,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_89,negated_conjecture,
( ~ duplicatefreeP(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| app(sk2,cons(hd(sk2),X1)) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_85])]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X2)
| duplicatefreeP(app(sk2,X2))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_46]) ).
cnf(c_0_91,plain,
( ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(app(X1,X2),X3) != X4
| segmentP(X4,X2) ),
c_0_87 ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_93,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_88 ).
cnf(c_0_94,negated_conjecture,
( ~ duplicatefreeP(X1)
| ~ ssList(X1)
| app(sk2,sk2) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_83]),c_0_85])]) ).
cnf(c_0_95,negated_conjecture,
( duplicatefreeP(app(sk2,sk2))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_46]) ).
cnf(c_0_96,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| app(X2,X3) != X1
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_74]),c_0_51])]) ).
cnf(c_0_97,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X2),X2) = X1 ),
c_0_92 ).
cnf(c_0_98,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_99,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = sk2 ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_100,negated_conjecture,
( ~ ssList(X1)
| neq(sk1,X1)
| X1 = sk1 ),
inference(spm,[status(thm)],[c_0_93,c_0_45]) ).
cnf(c_0_101,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
inference(fof_simplification,[status(thm)],[clause157]) ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(app(sk2,sk2))
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_103,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X1,X2)
| segmentP(X1,skaf46(X1,X2)) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])])]) ).
cnf(c_0_104,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,sk3)
| ~ segmentP(sk4,X1)
| ~ neq(sk3,X1)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[co1_9]) ).
cnf(c_0_105,negated_conjecture,
( ~ segmentP(sk1,X1)
| ~ segmentP(sk2,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = sk2 ),
c_0_99 ).
cnf(c_0_106,negated_conjecture,
( neq(sk1,nil)
| sk1 = nil ),
inference(spm,[status(thm)],[c_0_100,c_0_51]) ).
cnf(c_0_107,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause149]) ).
cnf(c_0_108,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_109,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,app(X2,X3)) = app(cons(X1,X2),X3) ),
c_0_101 ).
cnf(c_0_110,negated_conjecture,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_81]),c_0_46])]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| skaf46(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_103]),c_0_98]),c_0_51])]) ).
cnf(c_0_112,plain,
( ~ ssList(X1)
| rearsegP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause58]) ).
cnf(c_0_113,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,sk3)
| ~ segmentP(sk4,X1)
| ~ neq(sk3,X1)
| ~ ssList(X1) ),
c_0_104 ).
cnf(c_0_114,negated_conjecture,
( ~ segmentP(sk1,sk1)
| sk1 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_44]),c_0_45])]),c_0_77]) ).
cnf(c_0_115,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_simplification,[status(thm)],[clause56]) ).
cnf(c_0_116,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| X2 = X1
| neq(X2,X1) ),
inference(fof_simplification,[status(thm)],[clause102]) ).
cnf(c_0_117,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X3,X2),X1) = app(X3,app(X2,X1)) ),
c_0_107 ).
cnf(c_0_118,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
c_0_108 ).
cnf(c_0_119,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| app(cons(X1,X2),X3) = cons(X1,app(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_120,plain,
( ~ ssList(X2)
| ssList(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_110])]) ).
cnf(c_0_121,plain,
( ~ ssList(X1)
| ~ rearsegP(nil,X1)
| app(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_111]),c_0_51])]) ).
cnf(c_0_122,plain,
( ~ ssList(X1)
| rearsegP(X1,nil) ),
c_0_112 ).
cnf(c_0_123,negated_conjecture,
( ~ totalorderedP(X1)
| ~ ssList(X1)
| ~ segmentP(sk2,X1)
| ~ segmentP(X1,sk1)
| ~ neq(sk1,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_41]),c_0_40]),c_0_41]) ).
cnf(c_0_124,negated_conjecture,
sk1 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_61]),c_0_45])]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
c_0_115 ).
cnf(c_0_126,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| X2 = X1
| neq(X2,X1) ),
c_0_116 ).
cnf(c_0_127,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| nil != X1
| totalorderedP(cons(X2,X1)) ),
inference(fof_simplification,[status(thm)],[clause113]) ).
cnf(c_0_128,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_129,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X1)
| app(X3,app(X2,X4)) != X1
| segmentP(X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_117]) ).
cnf(c_0_130,plain,
( ~ ssList(X2)
| app(cons(X1,nil),X2) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_110])]) ).
cnf(c_0_131,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_119]),c_0_120]) ).
cnf(c_0_132,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_51])]) ).
cnf(c_0_133,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
inference(fof_simplification,[status(thm)],[clause169]) ).
cnf(c_0_134,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_135,negated_conjecture,
( ~ totalorderedP(X1)
| ~ ssList(X1)
| ~ segmentP(sk2,X1)
| ~ neq(nil,X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124]),c_0_124]),c_0_125]) ).
cnf(c_0_136,plain,
( neq(X2,X1)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_110]),c_0_110])]) ).
cnf(c_0_137,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| nil != X1
| totalorderedP(cons(X2,X1)) ),
c_0_127 ).
cnf(c_0_138,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| cons(X1,X2) != nil ),
c_0_128 ).
cnf(c_0_139,plain,
( ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X1)
| ~ ssList(cons(X2,nil))
| app(X3,cons(X2,X4)) != X1
| segmentP(X1,cons(X2,nil)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_140,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_51])]) ).
cnf(c_0_141,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
c_0_133 ).
cnf(c_0_142,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
c_0_134 ).
cnf(c_0_143,negated_conjecture,
( ~ totalorderedP(X1)
| ~ ssList(X1)
| ~ segmentP(sk2,X1)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_144,plain,
( ~ ssList(X2)
| nil != X2
| totalorderedP(cons(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_110])]) ).
cnf(c_0_145,plain,
( ~ ssList(X2)
| cons(X1,X2) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_110])]) ).
cnf(c_0_146,plain,
( ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X1)
| app(X3,cons(X2,X4)) != X1
| segmentP(X1,cons(X2,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140])]) ).
cnf(c_0_147,plain,
( ~ ssList(X1)
| ~ memberP(X1,X2)
| app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_110])]) ).
cnf(c_0_148,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_149,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_150,plain,
( ~ ssList(X2)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_142]) ).
cnf(c_0_151,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(sk2,cons(X2,X1))
| nil != X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_120]),c_0_145]) ).
cnf(c_0_152,plain,
( ~ ssList(X1)
| ~ memberP(X1,X2)
| segmentP(X1,cons(X2,nil)) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_149])])]) ).
cnf(c_0_153,negated_conjecture,
memberP(sk2,hd(sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_83]),c_0_84]),c_0_85])]) ).
cnf(c_0_154,negated_conjecture,
~ memberP(sk2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_51]),c_0_46])]) ).
cnf(c_0_155,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_153,c_0_154]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC066-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n016.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 07:57:52 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 105.19/15.85 % Version: 3.5.1
% 105.19/15.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 105.19/15.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 105.19/15.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 105.19/15.85 % Starting new_bool_3 with 300s (1) cores
% 105.19/15.85 % Starting new_bool_1 with 300s (1) cores
% 105.19/15.85 % Starting sh5l with 300s (1) cores
% 105.19/15.85 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1954886 completed with status 0
% 105.19/15.85 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 105.19/15.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 105.19/15.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 105.19/15.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 105.19/15.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 105.19/15.85 % No SInE strategy applied
% 105.19/15.85 % Search class: FGHSM-FSLM21-MFFFFFNN
% 105.19/15.85 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 105.19/15.85 % Starting SubtermCWHack with 136s (1) cores
% 105.19/15.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 105.19/15.85 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 105.19/15.85 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 105.19/15.85 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 105.19/15.85 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with pid 1954894 completed with status 0
% 105.19/15.85 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN
% 105.19/15.85 % Preprocessing class: FSLSSMSSSSSNFFN.
% 105.19/15.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 105.19/15.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 105.19/15.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 105.19/15.85 % No SInE strategy applied
% 105.19/15.85 % Search class: FGHSM-FSLM21-MFFFFFNN
% 105.19/15.85 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 105.19/15.85 % Starting SubtermCWHack with 136s (1) cores
% 105.19/15.85 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 105.19/15.85 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 105.19/15.85 % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 105.19/15.85 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 105.19/15.85 % Preprocessing time : 0.003 s
% 105.19/15.85
% 105.19/15.85 % Proof found!
% 105.19/15.85 % SZS status Unsatisfiable
% 105.19/15.85 % SZS output start CNFRefutation
% See solution above
% 105.19/15.85 % Parsed axioms : 198
% 105.19/15.85 % Removed by relevancy pruning/SinE : 0
% 105.19/15.85 % Initial clauses : 198
% 105.19/15.85 % Removed in clause preprocessing : 0
% 105.19/15.85 % Initial clauses in saturation : 198
% 105.19/15.85 % Processed clauses : 25798
% 105.19/15.85 % ...of these trivial : 826
% 105.19/15.85 % ...subsumed : 15466
% 105.19/15.85 % ...remaining for further processing : 9506
% 105.19/15.85 % Other redundant clauses eliminated : 627
% 105.19/15.85 % Clauses deleted for lack of memory : 0
% 105.19/15.85 % Backward-subsumed : 929
% 105.19/15.85 % Backward-rewritten : 500
% 105.19/15.85 % Generated clauses : 695495
% 105.19/15.85 % ...of the previous two non-redundant : 672759
% 105.19/15.85 % ...aggressively subsumed : 0
% 105.19/15.85 % Contextual simplify-reflections : 712
% 105.19/15.85 % Paramodulations : 693325
% 105.19/15.85 % Factorizations : 365
% 105.19/15.85 % NegExts : 0
% 105.19/15.85 % Equation resolutions : 1366
% 105.19/15.85 % Disequality decompositions : 0
% 105.19/15.85 % Total rewrite steps : 240255
% 105.19/15.85 % ...of those cached : 236202
% 105.19/15.85 % Propositional unsat checks : 1
% 105.19/15.85 % Propositional check models : 0
% 105.19/15.85 % Propositional check unsatisfiable : 0
% 105.19/15.85 % Propositional clauses : 0
% 105.19/15.85 % Propositional clauses after purity: 0
% 105.19/15.85 % Propositional unsat core size : 0
% 105.19/15.85 % Propositional preprocessing time : 0.000
% 105.19/15.85 % Propositional encoding time : 0.879
% 105.19/15.85 % Propositional solver time : 0.389
% 105.19/15.85 % Success case prop preproc time : 0.000
% 105.19/15.85 % Success case prop encoding time : 0.000
% 105.19/15.85 % Success case prop solver time : 0.000
% 105.19/15.85 % Current number of processed clauses : 7633
% 105.19/15.85 % Positive orientable unit clauses : 201
% 105.19/15.85 % Positive unorientable unit clauses: 0
% 105.19/15.85 % Negative unit clauses : 64
% 105.19/15.85 % Non-unit-clauses : 7368
% 105.19/15.85 % Current number of unprocessed clauses: 642678
% 105.19/15.85 % ...number of literals in the above : 3899104
% 105.19/15.85 % Current number of archived formulas : 0
% 105.19/15.85 % Current number of archived clauses : 1868
% 105.19/15.85 % Clause-clause subsumption calls (NU) : 5283025
% 105.19/15.85 % Rec. Clause-clause subsumption calls : 1094231
% 105.19/15.85 % Non-unit clause-clause subsumptions : 11661
% 105.19/15.85 % Unit Clause-clause subsumption calls : 94741
% 105.19/15.85 % Rewrite failures with RHS unbound : 0
% 105.19/15.85 % BW rewrite match attempts : 366
% 105.19/15.85 % BW rewrite match successes : 88
% 105.19/15.85 % Condensation attempts : 0
% 105.19/15.85 % Condensation successes : 0
% 105.19/15.85 % Termbank termtop insertions : 26737243
% 105.19/15.85 % Search garbage collected termcells : 555
% 105.19/15.85
% 105.19/15.85 % -------------------------------------------------
% 105.19/15.85 % User time : 14.409 s
% 105.19/15.85 % System time : 0.515 s
% 105.19/15.85 % Total time : 14.924 s
% 105.19/15.85 % Maximum resident set size: 4068 pages
% 105.19/15.85
% 105.19/15.85 % -------------------------------------------------
% 105.19/15.85 % User time : 71.772 s
% 105.19/15.85 % System time : 2.605 s
% 105.19/15.85 % Total time : 74.377 s
% 105.19/15.85 % Maximum resident set size: 5120 pages
% 105.19/15.85 % E exiting
%------------------------------------------------------------------------------