%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC061-1 : 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 : n015.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 05:18:06 PM UTC 2026
% Result : Unsatisfiable 2.22s 1.99s
% Output : CNFRefutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 37
% Syntax : Number of clauses : 163 ( 29 unt; 34 nHn; 151 RR)
% Number of literals : 425 ( 171 equ; 245 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 : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 149 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_11,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_14,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_9,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(co1_8,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_10,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(co1_12,negated_conjecture,
( nil = sk2
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(co1_7,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause120,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
cnf(clause157,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause179,axiom,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
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(clause133,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).
cnf(clause177,axiom,
( nil = X2
| X1 = X2
| nil = X1
| tl(X1) != tl(X2)
| hd(X1) != hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause177) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
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(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(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(co1_13,negated_conjecture,
( nil = sk2
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause57,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(c_0_37,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk3
| ~ neq(sk4,nil) ),
co1_11 ).
cnf(c_0_38,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_39,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
co1_14 ).
cnf(c_0_40,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_41,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk1
| ~ neq(sk4,nil) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( neq(sk4,nil)
| sk1 != nil ),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ssList(sk6)
| ~ neq(sk4,nil) ),
co1_9 ).
cnf(c_0_44,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_45,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk1
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( ssList(sk6)
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
co1_8 ).
cnf(c_0_48,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| ~ neq(sk4,nil) ),
co1_10 ).
cnf(c_0_49,negated_conjecture,
( sk6 = nil
| sk1 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_50,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_51,axiom,
ssList(nil),
clause8 ).
cnf(c_0_52,negated_conjecture,
( ssItem(sk5)
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_53,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_54,negated_conjecture,
( sk6 = nil
| sk1 != nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),c_0_52]) ).
cnf(c_0_55,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_56,negated_conjecture,
( app(cons(sk5,nil),nil) = sk4
| sk1 != nil ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( nil = sk2
| neq(sk2,nil) ),
co1_12 ).
cnf(c_0_58,negated_conjecture,
( cons(sk5,nil) = sk4
| sk1 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( nil = sk3
| nil != sk4 ),
co1_7 ).
cnf(c_0_60,negated_conjecture,
( sk4 = nil
| neq(sk4,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_40]),c_0_40]) ).
cnf(c_0_61,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_62,negated_conjecture,
( cons(sk5,nil) = sk4
| sk1 != nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_50]),c_0_51])]),c_0_52]) ).
cnf(c_0_63,negated_conjecture,
( sk1 = nil
| sk4 != nil ),
inference(rw,[status(thm)],[c_0_59,c_0_38]) ).
cnf(c_0_64,negated_conjecture,
( app(cons(sk5,nil),sk6) = sk4
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_48,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
sk4 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_51])]),c_0_52]),c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( sk4 = nil
| ssItem(sk5) ),
inference(spm,[status(thm)],[c_0_47,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( sk4 = nil
| ssList(sk6) ),
inference(spm,[status(thm)],[c_0_43,c_0_60]) ).
cnf(c_0_68,negated_conjecture,
app(cons(sk5,nil),sk6) = sk4,
inference(sr,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_70,negated_conjecture,
ssItem(sk5),
inference(sr,[status(thm)],[c_0_66,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
ssList(sk6),
inference(sr,[status(thm)],[c_0_67,c_0_65]) ).
cnf(c_0_72,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_73,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_74,negated_conjecture,
cons(sk5,sk6) = sk4,
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_75,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_76,negated_conjecture,
( app(sk6,cons(sk5,nil)) = sk1
| sk4 = nil ),
inference(spm,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_77,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_78,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_79,negated_conjecture,
cons(sk5,app(nil,sk6)) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_72]),c_0_70]),c_0_71]),c_0_51])]) ).
cnf(c_0_80,negated_conjecture,
tl(sk4) = sk6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_70]),c_0_71])]) ).
cnf(c_0_81,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_75]) ).
cnf(c_0_82,negated_conjecture,
app(sk6,cons(sk5,nil)) = sk1,
inference(sr,[status(thm)],[c_0_76,c_0_65]) ).
cnf(c_0_83,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_85,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_86,negated_conjecture,
( app(nil,sk6) = sk6
| ~ ssList(app(nil,sk6)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_79]),c_0_80]),c_0_70])]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(app(sk1,cons(sk5,X1)))
| ~ ssList(X1)
| ~ duplicatefreeP(app(sk1,cons(sk5,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_70]),c_0_51]),c_0_71])]) ).
cnf(c_0_88,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk1,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_85,c_0_40]) ).
cnf(c_0_90,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_91,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_92,negated_conjecture,
app(nil,sk6) = sk6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_78]),c_0_51]),c_0_71])]) ).
cnf(c_0_93,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(app(sk1,sk4))
| ~ duplicatefreeP(app(sk1,sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_74]),c_0_71])]) ).
cnf(c_0_95,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk1,sk4)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,axiom,
( nil = X2
| X1 = X2
| nil = X1
| tl(X1) != tl(X2)
| hd(X1) != hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause177 ).
cnf(c_0_97,negated_conjecture,
hd(sk4) = sk5,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_74]),c_0_70]),c_0_71])]) ).
cnf(c_0_98,negated_conjecture,
( nil = X1
| app(X1,sk6) != sk6
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_71]),c_0_51])]) ).
cnf(c_0_99,negated_conjecture,
( app(tl(cons(sk5,nil)),sk6) = sk6
| cons(sk5,nil) = nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_68]),c_0_80]),c_0_71])]) ).
cnf(c_0_100,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_101,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_102,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_103,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_104,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_105,negated_conjecture,
( ssItem(X1)
| ~ ssList(app(sk1,sk4)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( X1 = sk4
| nil = X1
| tl(X1) != sk6
| hd(X1) != sk5
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_80]),c_0_97]),c_0_89])]),c_0_65]) ).
cnf(c_0_107,negated_conjecture,
( tl(cons(sk5,nil)) = nil
| cons(sk5,nil) = nil
| ~ ssList(cons(sk5,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_108,negated_conjecture,
( hd(cons(sk5,nil)) = sk5
| cons(sk5,nil) = nil
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_68]),c_0_97]),c_0_71])]) ).
cnf(c_0_109,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_90]),c_0_50]),c_0_103]) ).
cnf(c_0_110,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_111,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_112,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_104]) ).
cnf(c_0_113,negated_conjecture,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_78]),c_0_84]),c_0_89])]) ).
cnf(c_0_114,negated_conjecture,
( cons(sk5,app(sk6,X1)) = app(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_74]),c_0_70]),c_0_71])]) ).
cnf(c_0_115,negated_conjecture,
( cons(sk5,nil) = nil
| cons(sk5,nil) = sk4
| sk6 != nil
| ~ ssList(cons(sk5,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_116,plain,
( tl(cons(X1,X2)) != cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(tl(cons(X1,X2)))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_109]) ).
cnf(c_0_117,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_73,c_0_110]),c_0_111]),c_0_51])]) ).
cnf(c_0_118,plain,
( singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113])]) ).
cnf(c_0_119,negated_conjecture,
( app(sk4,cons(sk5,nil)) = cons(sk5,sk1)
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_114,c_0_82]) ).
cnf(c_0_120,negated_conjecture,
( cons(sk5,nil) = sk4
| cons(sk5,nil) = nil
| sk6 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_50]),c_0_70]),c_0_51])]) ).
cnf(c_0_121,plain,
( tl(cons(X1,X2)) != cons(X1,X2)
| ~ ssList(tl(cons(X1,X2)))
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_113])]) ).
cnf(c_0_122,plain,
( tl(cons(X1,nil)) = nil
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_123,negated_conjecture,
( app(sk4,sk4) = cons(sk5,sk1)
| cons(sk5,nil) = nil
| sk6 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_89])]) ).
cnf(c_0_124,plain,
( cons(X1,nil) != nil
| ~ ssList(cons(X1,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_125,plain,
( ssList(cons(X1,X2))
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_113])]) ).
cnf(c_0_126,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_113])]) ).
cnf(c_0_127,negated_conjecture,
( tl(cons(sk5,sk1)) = app(sk6,sk4)
| cons(sk5,nil) = nil
| sk6 != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_123]),c_0_80]),c_0_89])]),c_0_65]) ).
cnf(c_0_128,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_51])]) ).
cnf(c_0_129,negated_conjecture,
( cons(sk5,app(sk6,sk4)) = cons(sk5,sk1)
| sk6 != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_84])]),c_0_128]) ).
cnf(c_0_130,negated_conjecture,
( app(sk4,sk4) = cons(sk5,sk1)
| sk6 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_129]),c_0_89])]) ).
cnf(c_0_131,negated_conjecture,
( cons(sk5,sk1) != nil
| ~ ssList(cons(sk5,nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_119]),c_0_89])]),c_0_65]) ).
cnf(c_0_132,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_102,c_0_73]),c_0_50]),c_0_103]) ).
cnf(c_0_133,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_134,plain,
( app(tl(X1),nil) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_55]),c_0_51])]) ).
cnf(c_0_135,negated_conjecture,
( tl(cons(sk5,sk1)) = app(sk6,sk4)
| sk6 != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_130]),c_0_80]),c_0_89])]),c_0_65]) ).
cnf(c_0_136,negated_conjecture,
cons(sk5,sk1) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_50]),c_0_70]),c_0_51])]) ).
cnf(c_0_137,negated_conjecture,
( ssList(cons(sk5,sk1))
| sk6 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_130]),c_0_89])]) ).
cnf(c_0_138,plain,
( cons(hd(cons(X1,X2)),X2) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_113])]) ).
cnf(c_0_139,negated_conjecture,
( nil = sk2
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
co1_13 ).
cnf(c_0_140,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_133]) ).
cnf(c_0_141,negated_conjecture,
( app(app(sk6,sk4),nil) = app(sk6,sk4)
| sk6 != nil ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_137]) ).
cnf(c_0_142,negated_conjecture,
( ssList(app(sk6,sk4))
| sk6 != nil ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_135]),c_0_136]),c_0_137]) ).
cnf(c_0_143,negated_conjecture,
( cons(sk5,nil) = sk4
| sk6 != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_120]),c_0_97]),c_0_51])]),c_0_128]) ).
cnf(c_0_144,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_100,c_0_93]),c_0_78]),c_0_44]) ).
cnf(c_0_145,negated_conjecture,
( sk4 = nil
| ~ neq(X1,nil)
| ~ segmentP(sk1,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_40]),c_0_40]) ).
cnf(c_0_146,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_147,negated_conjecture,
( segmentP(app(sk6,sk4),sk4)
| sk6 != nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_51]),c_0_89]),c_0_71])]),c_0_142]) ).
cnf(c_0_148,negated_conjecture,
( app(sk6,sk4) = sk1
| sk6 != nil ),
inference(spm,[status(thm)],[c_0_82,c_0_143]) ).
cnf(c_0_149,negated_conjecture,
( ssList(app(sk4,X1))
| ~ ssList(app(sk6,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_114]),c_0_70])]) ).
cnf(c_0_150,negated_conjecture,
( ssList(app(sk6,X1))
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_80]),c_0_89])]),c_0_65]) ).
cnf(c_0_151,negated_conjecture,
( nil = X1
| ~ segmentP(sk1,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_51])]),c_0_65]) ).
cnf(c_0_152,negated_conjecture,
( segmentP(sk1,sk4)
| sk6 != nil ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_153,negated_conjecture,
( ssList(app(sk4,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_78]),c_0_71])]) ).
cnf(c_0_154,negated_conjecture,
( segmentP(app(sk6,X1),sk6)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_92]),c_0_71]),c_0_51])]),c_0_150]) ).
cnf(c_0_155,negated_conjecture,
( sk6 != nil
| ~ segmentP(sk4,sk4) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_89])]),c_0_65]) ).
cnf(c_0_156,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
clause57 ).
cnf(c_0_157,negated_conjecture,
( segmentP(app(sk4,X1),sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_68]),c_0_71])]),c_0_153]) ).
cnf(c_0_158,negated_conjecture,
( segmentP(sk1,sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(spm,[status(thm)],[c_0_154,c_0_82]) ).
cnf(c_0_159,negated_conjecture,
sk6 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_89])]) ).
cnf(c_0_160,negated_conjecture,
( segmentP(sk4,sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_55]),c_0_51]),c_0_89])]) ).
cnf(c_0_161,negated_conjecture,
~ ssList(cons(sk5,nil)),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_158]),c_0_71])]),c_0_159]),c_0_160]) ).
cnf(c_0_162,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_125]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC061-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:21:16 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.22/1.99 % Version : CSE_E---1.7
% 2.22/1.99 % Problem : theBenchmark.p
% 2.22/1.99 % SZS status Unsatisfiable for theBenchmark.p
% 2.22/1.99 % SZS output start CNFRefutation
% See solution above
% 2.22/1.99 % Total time : 1.373s
%------------------------------------------------------------------------------