%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC031-1 : 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 : n020.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 05:17:58 PM UTC 2026
% Result : Unsatisfiable 6.50s 4.49s
% Output : CNFRefutation 6.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 48
% Syntax : Number of clauses : 165 ( 33 unt; 31 nHn; 138 RR)
% Number of literals : 473 ( 124 equ; 301 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 249 ( 29 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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(co1_10,negated_conjecture,
( nil = sk2
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
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(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_7,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
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(co1_13,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(clause84,axiom,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause144,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
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(co1_9,negated_conjecture,
( ~ ssList(X1)
| ~ neq(sk3,X1)
| ~ frontsegP(sk4,X1)
| ~ segmentP(X1,sk3)
| ~ totalorderedP(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
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(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(clause132,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
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(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause119,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
cnf(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(clause67,axiom,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause67) ).
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(clause178,axiom,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause137,axiom,
( frontsegP(app(X1,X3),X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause137) ).
cnf(clause63,axiom,
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause63) ).
cnf(clause134,axiom,
( lt(X1,hd(X2))
| nil = X2
| ~ strictorderedP(cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause134) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause66,axiom,
( strictorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause66) ).
cnf(c_0_48,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_49,negated_conjecture,
( nil = sk2
| nil = sk1 ),
co1_10 ).
cnf(c_0_50,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_51,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_52,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_48]) ).
cnf(c_0_53,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_54,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_55,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_56,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_57,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_58,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_59,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_60,negated_conjecture,
frontsegP(sk4,sk3),
co1_7 ).
cnf(c_0_61,negated_conjecture,
( sk4 = nil
| sk3 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_62,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_63,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_52,c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_64,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_65,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_66,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_67,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_68,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_59,c_0_51]) ).
cnf(c_0_70,negated_conjecture,
( nil != sk1
| nil != sk2 ),
co1_13 ).
cnf(c_0_71,axiom,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
clause84 ).
cnf(c_0_72,negated_conjecture,
( sk3 = nil
| frontsegP(nil,sk3) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_73,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_62,c_0_50]) ).
cnf(c_0_74,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_63,c_0_64]),c_0_65]),c_0_66])]),c_0_58]) ).
cnf(c_0_75,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_67,c_0_64]),c_0_65]),c_0_66])]) ).
cnf(c_0_76,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk4,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,negated_conjecture,
( sk3 != nil
| sk4 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_50]),c_0_51]) ).
cnf(c_0_78,negated_conjecture,
sk3 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_79,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_80,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_81,axiom,
ssList(nil),
clause8 ).
cnf(c_0_82,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_83,plain,
( nil = X1
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk4,sk4)) ),
inference(spm,[status(thm)],[c_0_76,c_0_69]) ).
cnf(c_0_85,negated_conjecture,
sk4 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_86,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_87,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_79,c_0_80]),c_0_81])]),c_0_58]) ).
cnf(c_0_88,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_80,c_0_82]),c_0_81])]) ).
cnf(c_0_89,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X1)
| ~ neq(sk3,X1)
| ~ frontsegP(sk4,X1)
| ~ segmentP(X1,sk3)
| ~ totalorderedP(X1) ),
co1_9 ).
cnf(c_0_91,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_92,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_93,negated_conjecture,
ssItem(X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_69])]),c_0_85]) ).
cnf(c_0_94,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_95,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_86]),c_0_58]) ).
cnf(c_0_96,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_81])]) ).
cnf(c_0_97,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_89])]),c_0_81])]) ).
cnf(c_0_98,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_99,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_100,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_101,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_102,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_103,negated_conjecture,
( ~ neq(nil,X1)
| ~ frontsegP(sk4,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_78]),c_0_78]),c_0_91]) ).
cnf(c_0_104,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_105,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_106,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_107,plain,
( app(cons(X1,X2),X3) = cons(X1,app(X2,X3))
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_93])]) ).
cnf(c_0_108,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_95,c_0_80]),c_0_58]) ).
cnf(c_0_109,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_88,c_0_96]),c_0_81])]) ).
cnf(c_0_110,axiom,
( nil = X2
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause119 ).
cnf(c_0_111,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_80,c_0_97]),c_0_81])]) ).
cnf(c_0_112,plain,
( app(X1,app(X2,skaf45(X3,app(X1,X2)))) = X3
| ~ frontsegP(X3,app(X1,X2))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_80]),c_0_99])]),c_0_58]) ).
cnf(c_0_113,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_114,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_101]),c_0_58]),c_0_102]) ).
cnf(c_0_115,plain,
( app(tl(X1),skaf45(X2,X1)) = tl(X2)
| nil = X1
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_98]),c_0_99])]) ).
cnf(c_0_116,plain,
( frontsegP(app(nil,X1),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_81])]) ).
cnf(c_0_117,negated_conjecture,
( X1 = nil
| ~ frontsegP(sk4,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_81])]) ).
cnf(c_0_118,axiom,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
clause67 ).
cnf(c_0_119,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_120,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_121,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_122,plain,
( cons(X1,X2) != X2
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_93])]) ).
cnf(c_0_123,plain,
( cons(X1,app(nil,X2)) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_81])]) ).
cnf(c_0_124,axiom,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
clause178 ).
cnf(c_0_125,plain,
( frontsegP(app(X1,nil),app(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_81])]) ).
cnf(c_0_126,plain,
( nil = X1
| app(X2,app(X3,X1)) != nil
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_80]),c_0_58]) ).
cnf(c_0_127,plain,
( app(nil,skaf45(X1,nil)) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_97]),c_0_97]),c_0_99]),c_0_97]),c_0_81])]),c_0_113]) ).
cnf(c_0_128,plain,
( nil = X1
| ssList(tl(X2))
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_99])]) ).
cnf(c_0_129,plain,
( frontsegP(X1,skaf45(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_116,c_0_98]),c_0_99]),c_0_81])]),c_0_113]) ).
cnf(c_0_130,negated_conjecture,
( cons(X1,nil) = nil
| ~ frontsegP(sk4,cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_131,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_132,plain,
( tl(cons(X1,X2)) = X2
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_93])]) ).
cnf(c_0_133,plain,
( ssList(cons(X1,X2))
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_93])]) ).
cnf(c_0_134,plain,
( cons(X1,X2) != nil
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_93])]) ).
cnf(c_0_135,plain,
( cons(X1,X2) != app(nil,X2)
| ~ ssList(app(nil,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_136,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_124]) ).
cnf(c_0_137,plain,
( frontsegP(X1,app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_79]) ).
cnf(c_0_138,plain,
( skaf45(X1,nil) = nil
| app(X2,X1) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_99]),c_0_81])]) ).
cnf(c_0_139,plain,
( cons(X1,skaf45(X2,nil)) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_127]),c_0_99])]) ).
cnf(c_0_140,plain,
( skaf45(X1,nil) = nil
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_99])]) ).
cnf(c_0_141,negated_conjecture,
( cons(X1,nil) = nil
| ~ frontsegP(sk4,cons(X1,nil))
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_93])]) ).
cnf(c_0_142,plain,
( cons(hd(cons(X1,X2)),X2) = cons(X1,X2)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]),c_0_134]) ).
cnf(c_0_143,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_79]),c_0_81])]) ).
cnf(c_0_144,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_93])]) ).
cnf(c_0_145,axiom,
( frontsegP(app(X1,X3),X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause137 ).
cnf(c_0_146,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_137,c_0_98]),c_0_99]),c_0_81])]),c_0_113]) ).
cnf(c_0_147,plain,
( skaf45(X1,nil) = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_96]),c_0_81])]) ).
cnf(c_0_148,axiom,
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
clause63 ).
cnf(c_0_149,axiom,
( lt(X1,hd(X2))
| nil = X2
| ~ strictorderedP(cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
clause134 ).
cnf(c_0_150,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_151,plain,
( cons(X1,nil) = cons(X1,X2)
| ssList(tl(X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_152,axiom,
( strictorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
clause66 ).
cnf(c_0_153,negated_conjecture,
( ~ frontsegP(sk4,cons(X1,nil))
| ~ ssList(cons(X1,nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_81])]),c_0_143]) ).
cnf(c_0_154,plain,
( nil = X1
| frontsegP(X1,cons(hd(X1),X2))
| ~ frontsegP(tl(X1),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_131]),c_0_100]) ).
cnf(c_0_155,plain,
( frontsegP(X1,X2)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_82]),c_0_81])]) ).
cnf(c_0_156,plain,
( frontsegP(nil,X1)
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_157,plain,
( nil = X1
| ~ ssList(X1)
| ~ strictorderedP(cons(hd(X1),X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150]) ).
cnf(c_0_158,negated_conjecture,
( cons(X1,sk4) = cons(X1,nil)
| ssList(tl(sk4)) ),
inference(spm,[status(thm)],[c_0_151,c_0_69]) ).
cnf(c_0_159,plain,
strictorderedP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_93])]) ).
cnf(c_0_160,negated_conjecture,
( ~ frontsegP(tl(sk4),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_81]),c_0_69])]),c_0_85]) ).
cnf(c_0_161,plain,
( frontsegP(X1,X2)
| app(X2,nil) != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_162,negated_conjecture,
ssList(tl(sk4)),
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_69]),c_0_159])]),c_0_85]) ).
cnf(c_0_163,negated_conjecture,
~ ssList(cons(hd(sk4),nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_97]),c_0_162]),c_0_81])]) ).
cnf(c_0_164,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_133]),c_0_81])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC031-1 : 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
% 0.16/0.33 % Computer : n020.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 04:16:20 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.50/4.49 % Version : CSE_E---1.7
% 6.50/4.49 % Problem : theBenchmark.p
% 6.50/4.49 % SZS status Unsatisfiable for theBenchmark.p
% 6.50/4.49 % SZS output start CNFRefutation
% See solution above
% 6.60/4.51 % Total time : 3.374s
%------------------------------------------------------------------------------