%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC045-1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/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 05:18:02 PM UTC 2026
% Result : Unsatisfiable 197.33s 87.60s
% Output : CNFRefutation 198.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 43
% Syntax : Number of clauses : 165 ( 42 unt; 24 nHn; 137 RR)
% Number of literals : 484 ( 134 equ; 312 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 261 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause120,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause123,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).
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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_7,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause169,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause169) ).
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(clause138,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause138) ).
cnf(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(co1_8,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause157,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause145,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause150) ).
cnf(clause149,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(co1_6,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
nil = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(clause173,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
cnf(co1_11,negated_conjecture,
( segmentP(sk4,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)))
| ~ ssItem(X1)
| ~ memberP(sk3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(clause152,axiom,
( segmentP(X1,X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause152) ).
cnf(co1_10,negated_conjecture,
( ssList(sk5(X1))
| ~ ssItem(X1)
| ~ memberP(sk3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(clause175,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
cnf(clause127,axiom,
( X2 = X1
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
cnf(c_0_43,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_44,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_45,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_46,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_47,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_48,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_49,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_50,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_51,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_47,c_0_48]),c_0_49]),c_0_50]) ).
cnf(c_0_52,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_53,axiom,
ssList(nil),
clause8 ).
cnf(c_0_54,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_51,c_0_52]),c_0_53])]),c_0_45]) ).
cnf(c_0_55,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_56,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_57,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_58,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_54,c_0_55]),c_0_56]),c_0_57]) ).
cnf(c_0_59,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_60,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_61,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_53])]) ).
cnf(c_0_62,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_63,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_64,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_65,negated_conjecture,
sk1 = sk3,
co1_7 ).
cnf(c_0_66,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_67,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_59]),c_0_61]) ).
cnf(c_0_68,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_62]) ).
cnf(c_0_69,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_70,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_71,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_72,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_49]) ).
cnf(c_0_73,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_75,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_76,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_77,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_78,plain,
( hd(cons(X1,nil)) = X1
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_79,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_68,c_0_69]),c_0_70]),c_0_71])]) ).
cnf(c_0_80,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk3,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_81,negated_conjecture,
nil != sk1,
co1_8 ).
cnf(c_0_82,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_83,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_84,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_85,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_86,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_55,c_0_75]),c_0_76]),c_0_53])]) ).
cnf(c_0_87,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_77]) ).
cnf(c_0_88,plain,
( hd(cons(X1,nil)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_56]),c_0_53])]) ).
cnf(c_0_89,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_90,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_91,plain,
( nil = X1
| ~ memberP(X2,hd(X1))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X2,X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_44]),c_0_45]),c_0_49]),c_0_46]) ).
cnf(c_0_92,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk3,sk3)) ),
inference(spm,[status(thm)],[c_0_80,c_0_73]) ).
cnf(c_0_93,negated_conjecture,
sk3 != nil,
inference(rw,[status(thm)],[c_0_81,c_0_65]) ).
cnf(c_0_94,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_82,c_0_83]),c_0_84]),c_0_85])]) ).
cnf(c_0_95,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_66,c_0_83]),c_0_84]),c_0_85])]) ).
cnf(c_0_96,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_97,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_45,c_0_48]),c_0_49]),c_0_50]) ).
cnf(c_0_98,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_99,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_100,plain,
( hd(cons(skaf44(X1),nil)) = skaf44(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_76]) ).
cnf(c_0_101,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_89]),c_0_56]) ).
cnf(c_0_102,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_90])]),c_0_53])]) ).
cnf(c_0_103,negated_conjecture,
( ssItem(X1)
| ~ memberP(sk3,hd(sk3)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_73])]),c_0_93]) ).
cnf(c_0_104,plain,
( nil = X1
| memberP(X1,hd(X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_105,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_96,c_0_52]),c_0_53])]) ).
cnf(c_0_106,plain,
( ssList(app(nil,X1))
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_61]) ).
cnf(c_0_107,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_108,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_52,c_0_99]),c_0_53])]),c_0_49]) ).
cnf(c_0_109,negated_conjecture,
hd(cons(skaf44(X1),nil)) = skaf44(X1),
inference(spm,[status(thm)],[c_0_100,c_0_73]) ).
cnf(c_0_110,plain,
( cons(skaf44(X1),X2) = app(X1,X2)
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_75]),c_0_76])]) ).
cnf(c_0_111,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_53])]) ).
cnf(c_0_112,negated_conjecture,
ssItem(X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_73])]),c_0_93]) ).
cnf(c_0_113,plain,
( X1 = nil
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_59]) ).
cnf(c_0_114,plain,
( ssList(app(nil,X1))
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_56]),c_0_53])]) ).
cnf(c_0_115,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_53])]) ).
cnf(c_0_116,plain,
( skaf44(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_75]),c_0_76]),c_0_53])]) ).
cnf(c_0_117,negated_conjecture,
( skaf44(X1) = hd(app(X1,nil))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_53])]) ).
cnf(c_0_118,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112])]) ).
cnf(c_0_119,plain,
( hd(cons(X1,nil)) = X1
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_112])]) ).
cnf(c_0_120,plain,
( X1 = nil
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_56]),c_0_53])]) ).
cnf(c_0_121,plain,
( app(nil,app(nil,X1)) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_102]),c_0_53])]) ).
cnf(c_0_122,plain,
( ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_76]) ).
cnf(c_0_123,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_49]),c_0_53])]) ).
cnf(c_0_124,negated_conjecture,
sk2 = sk4,
co1_6 ).
cnf(c_0_125,negated_conjecture,
nil = sk2,
co1_5 ).
cnf(c_0_126,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_127,negated_conjecture,
( hd(app(X1,nil)) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_128,plain,
singletonP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_112])]),c_0_118])]) ).
cnf(c_0_129,negated_conjecture,
hd(cons(X1,nil)) = X1,
inference(spm,[status(thm)],[c_0_119,c_0_73]) ).
cnf(c_0_130,plain,
( tl(X1) = nil
| nil = X1
| cons(hd(X1),nil) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_131,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_112])]) ).
cnf(c_0_132,plain,
( app(nil,X1) = X2
| app(nil,X1) != app(nil,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_121]),c_0_53])]),c_0_122]) ).
cnf(c_0_133,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_123]),c_0_53])]) ).
cnf(c_0_134,negated_conjecture,
( segmentP(sk4,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)))
| ~ ssItem(X1)
| ~ memberP(sk3,X1) ),
co1_11 ).
cnf(c_0_135,negated_conjecture,
sk4 = nil,
inference(rw,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_136,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_126]) ).
cnf(c_0_137,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_44,c_0_48]),c_0_49]),c_0_50]) ).
cnf(c_0_138,negated_conjecture,
hd(app(cons(X1,nil),nil)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]),c_0_118])]) ).
cnf(c_0_139,negated_conjecture,
tl(cons(X1,nil)) = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_129]),c_0_118])]),c_0_131]) ).
cnf(c_0_140,plain,
( app(nil,X1) = app(X2,nil)
| app(nil,X1) != app(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_108]),c_0_53])]),c_0_133]) ).
cnf(c_0_141,axiom,
( segmentP(X1,X3)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause152 ).
cnf(c_0_142,negated_conjecture,
( segmentP(nil,app(app(cons(X1,nil),sk5(X1)),cons(X1,nil)))
| ~ memberP(sk3,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_143,negated_conjecture,
( ssList(sk5(X1))
| ~ ssItem(X1)
| ~ memberP(sk3,X1) ),
co1_10 ).
cnf(c_0_144,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_136,c_0_52]),c_0_53])]),c_0_49]) ).
cnf(c_0_145,negated_conjecture,
app(cons(X1,nil),nil) = cons(X1,nil),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]),c_0_102]),c_0_118]),c_0_53])]),c_0_131]) ).
cnf(c_0_146,axiom,
( memberP(X4,X2)
| app(X1,cons(X2,X3)) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X4) ),
clause175 ).
cnf(c_0_147,negated_conjecture,
( app(nil,sk3) = app(X1,nil)
| app(nil,sk3) != app(nil,X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_73]) ).
cnf(c_0_148,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,app(app(X3,X2),X4))
| ~ ssList(app(app(X3,X2),X4))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_141,c_0_136]) ).
cnf(c_0_149,negated_conjecture,
( segmentP(nil,app(cons(X1,sk5(X1)),cons(X1,nil)))
| ~ memberP(sk3,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_59]),c_0_143]) ).
cnf(c_0_150,axiom,
( X2 = X1
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause127 ).
cnf(c_0_151,negated_conjecture,
segmentP(cons(X1,nil),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_53]),c_0_118])]) ).
cnf(c_0_152,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_146]) ).
cnf(c_0_153,negated_conjecture,
app(sk3,nil) = app(nil,sk3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_147]),c_0_73])]) ).
cnf(c_0_154,plain,
( segmentP(X1,X2)
| ~ segmentP(X1,app(X3,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_52]),c_0_53])]),c_0_49]) ).
cnf(c_0_155,negated_conjecture,
( segmentP(nil,app(cons(X1,sk5(X1)),cons(X1,nil)))
| ~ memberP(sk3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_112])]) ).
cnf(c_0_156,negated_conjecture,
~ segmentP(nil,cons(X1,nil)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_118]),c_0_53])]),c_0_131]) ).
cnf(c_0_157,plain,
( nil = X1
| memberP(app(X2,X1),hd(X1))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_44]),c_0_45]),c_0_49]),c_0_46]) ).
cnf(c_0_158,negated_conjecture,
app(nil,sk3) = sk3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_153]),c_0_73])]) ).
cnf(c_0_159,negated_conjecture,
( ~ memberP(sk3,X1)
| ~ ssList(cons(X1,sk5(X1))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_118]),c_0_53])]),c_0_156]) ).
cnf(c_0_160,plain,
( ssList(cons(X1,X2))
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_112])]) ).
cnf(c_0_161,negated_conjecture,
( ssList(sk5(X1))
| ~ memberP(sk3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_112])]) ).
cnf(c_0_162,negated_conjecture,
memberP(sk3,hd(sk3)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_53]),c_0_73])]),c_0_93]) ).
cnf(c_0_163,negated_conjecture,
~ memberP(sk3,X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]) ).
cnf(c_0_164,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_162,c_0_163]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC045-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n006.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 04:19:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 197.33/87.60 % Version : CSE_E---1.7
% 197.33/87.60 % Problem : theBenchmark.p
% 197.33/87.60 % SZS status Unsatisfiable for theBenchmark.p
% 197.33/87.60 % SZS output start CNFRefutation
% See solution above
% 198.04/88.20 % Total time : 65.890s
%------------------------------------------------------------------------------