%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC342-1 : 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 : n005.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 05:19:15 PM UTC 2026
% Result : Unsatisfiable 42.08s 24.56s
% Output : CNFRefutation 42.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 55
% Syntax : Number of clauses : 183 ( 37 unt; 42 nHn; 154 RR)
% Number of literals : 507 ( 151 equ; 304 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 257 ( 48 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(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(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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
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(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
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(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
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(clause151,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause151) ).
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(clause140,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
cnf(clause131,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(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(clause58,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause58) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
cnf(co1_8,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
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(co1_11,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
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(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_7,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_12,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
cnf(clause171,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause171) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(co1_9,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(co1_13,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause4) ).
cnf(clause170,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause170) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
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(clause67,axiom,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause67) ).
cnf(co1_10,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(c_0_55,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_56,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_55]) ).
cnf(c_0_57,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_58,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_59,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_60,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_56,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_61,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_62,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_63,axiom,
ssList(nil),
clause8 ).
cnf(c_0_64,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_65,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_66,plain,
( ~ memberP(X1,skaf44(X2))
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ duplicatefreeP(app(X1,X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63])]),c_0_64]) ).
cnf(c_0_67,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_68,plain,
( ~ singletonP(X1)
| ~ ssList(cons(skaf44(X1),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ duplicatefreeP(app(cons(skaf44(X1),X2),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_62])]) ).
cnf(c_0_69,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_70,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_71,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_72,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_61]),c_0_63])]) ).
cnf(c_0_73,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_74,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_75,plain,
( ssItem(X1)
| duplicatefreeP(cons(X2,X3))
| ~ ssItem(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ duplicatefreeP(cons(X1,cons(X1,nil))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_77,plain,
( ssItem(X1)
| duplicatefreeP(cons(skaf44(X2),X3))
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_75,c_0_62]) ).
cnf(c_0_78,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_79,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(cons(skaf44(X1),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_61]),c_0_62])]) ).
cnf(c_0_80,plain,
( ssItem(X1)
| duplicatefreeP(cons(skaf44(X2),skaf45(X3,X4))) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_82,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_83,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_84,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_85,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_86,plain,
( ssItem(X1)
| ~ singletonP(skaf45(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_78])]) ).
cnf(c_0_87,plain,
( 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_81,c_0_82]),c_0_78]),c_0_63])]),c_0_83]) ).
cnf(c_0_88,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_84]),c_0_71]) ).
cnf(c_0_89,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_85])]),c_0_63])]) ).
cnf(c_0_90,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_63])]) ).
cnf(c_0_92,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_93,plain,
( ssItem(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_74]),c_0_91]) ).
cnf(c_0_94,plain,
( X1 = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_89]),c_0_63])]) ).
cnf(c_0_95,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_96,axiom,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
clause140 ).
cnf(c_0_97,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_93,c_0_62]) ).
cnf(c_0_98,plain,
( app(X1,X2) = nil
| app(X1,app(X2,nil)) != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_63])]),c_0_64]) ).
cnf(c_0_99,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_100,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_101,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
clause58 ).
cnf(c_0_102,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_103,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_104,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_95]),c_0_64]) ).
cnf(c_0_105,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_106,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_107,negated_conjecture,
( ssItem(sk5)
| nil = sk3 ),
co1_8 ).
cnf(c_0_108,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_109,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_110,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_111,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_112,plain,
( memberP(app(X1,X2),X3)
| ~ memberP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]) ).
cnf(c_0_113,plain,
( app(X1,skaf46(X2,nil)) = nil
| app(X1,X2) != nil
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]),c_0_63])]),c_0_101]) ).
cnf(c_0_114,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_97])]) ).
cnf(c_0_115,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_103,c_0_95]),c_0_63])]),c_0_64]) ).
cnf(c_0_116,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_89]),c_0_63])]) ).
cnf(c_0_117,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk3 ),
co1_11 ).
cnf(c_0_118,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_119,negated_conjecture,
( sk3 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_107]) ).
cnf(c_0_120,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),c_0_111]) ).
cnf(c_0_121,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_122,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_123,plain,
( app(X1,X2) != nil
| ~ memberP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_100])]),c_0_114]) ).
cnf(c_0_124,plain,
( app(nil,X1) = app(X1,nil)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_115]),c_0_63])]),c_0_116]) ).
cnf(c_0_125,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_126,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_127,negated_conjecture,
( sk3 = nil
| ~ duplicatefreeP(cons(sk5,sk3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_117]),c_0_118])]),c_0_107]) ).
cnf(c_0_128,negated_conjecture,
( sk3 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,sk3)) ),
inference(spm,[status(thm)],[c_0_119,c_0_118]) ).
cnf(c_0_129,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_120,c_0_121]),c_0_64]),c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( ssItem(sk5)
| nil = sk4 ),
co1_7 ).
cnf(c_0_131,plain,
( app(nil,X1) != nil
| ~ memberP(X1,X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_63])]) ).
cnf(c_0_132,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk3 ),
co1_12 ).
cnf(c_0_133,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_134,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_135,negated_conjecture,
( sk3 = nil
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_136,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_129,c_0_103]),c_0_63])]),c_0_110]) ).
cnf(c_0_137,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_138,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_139,negated_conjecture,
( cons(sk5,nil) = sk3
| nil = sk4 ),
co1_9 ).
cnf(c_0_140,negated_conjecture,
( sk4 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_130]) ).
cnf(c_0_141,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
co1_13 ).
cnf(c_0_142,negated_conjecture,
( sk3 = nil
| app(nil,sk4) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133])]) ).
cnf(c_0_143,negated_conjecture,
( sk3 = nil
| X1 = nil
| cons(X2,X1) != sk3
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_117]),c_0_63])]),c_0_135]),c_0_135]) ).
cnf(c_0_144,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_145,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_146,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_136,c_0_137]),c_0_71]),c_0_138]) ).
cnf(c_0_147,negated_conjecture,
( sk4 = nil
| ~ duplicatefreeP(cons(sk5,sk3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_139]),c_0_118])]),c_0_130]) ).
cnf(c_0_148,negated_conjecture,
( sk4 = nil
| ssItem(X1)
| duplicatefreeP(cons(sk5,sk3)) ),
inference(spm,[status(thm)],[c_0_140,c_0_118]) ).
cnf(c_0_149,negated_conjecture,
( ~ segmentP(sk4,sk3)
| ~ totalorderedP(sk3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_106]),c_0_126]),c_0_106]) ).
cnf(c_0_150,negated_conjecture,
( sk3 = nil
| sk4 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_81]),c_0_133])]) ).
cnf(c_0_151,axiom,
totalorderedP(nil),
clause4 ).
cnf(c_0_152,negated_conjecture,
( skaf82(sk3) = nil
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145])])]),c_0_118])]) ).
cnf(c_0_153,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause170 ).
cnf(c_0_154,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_155,plain,
( app(X1,nil) != nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_61]),c_0_62]),c_0_63])]) ).
cnf(c_0_156,negated_conjecture,
( sk4 = nil
| singletonP(sk3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_139]),c_0_118])]),c_0_130]) ).
cnf(c_0_157,negated_conjecture,
( sk4 = nil
| ssItem(X1) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_158,negated_conjecture,
( sk4 != nil
| ~ segmentP(sk4,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151])]) ).
cnf(c_0_159,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_160,negated_conjecture,
( cons(skaf83(sk3),nil) = sk3
| sk3 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_152]),c_0_118])]) ).
cnf(c_0_161,plain,
( skaf83(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_144]),c_0_154]),c_0_145])])]),c_0_71]),c_0_138]) ).
cnf(c_0_162,negated_conjecture,
( sk4 = nil
| app(sk3,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_118])]) ).
cnf(c_0_163,negated_conjecture,
( app(sk3,X1) = cons(sk5,X1)
| sk4 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_139]),c_0_157]) ).
cnf(c_0_164,negated_conjecture,
sk4 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_133])]) ).
cnf(c_0_165,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_166,negated_conjecture,
( cons(skaf83(sk3),X1) = app(sk3,X1)
| sk3 = nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_160]),c_0_154])]) ).
cnf(c_0_167,negated_conjecture,
( skaf83(sk3) = sk5
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_139]),c_0_63])]),c_0_157]) ).
cnf(c_0_168,negated_conjecture,
( sk4 = nil
| cons(sk5,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_63])]) ).
cnf(c_0_169,negated_conjecture,
cons(sk5,nil) = sk3,
inference(sr,[status(thm)],[c_0_139,c_0_164]) ).
cnf(c_0_170,axiom,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
clause67 ).
cnf(c_0_171,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_165]) ).
cnf(c_0_172,negated_conjecture,
( app(skaf42(X1,skaf83(sk3)),app(sk3,skaf43(skaf83(sk3),X1))) = X1
| sk3 = nil
| ~ memberP(X1,skaf83(sk3))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_166]),c_0_154]),c_0_58])]) ).
cnf(c_0_173,negated_conjecture,
skaf83(sk3) = sk5,
inference(sr,[status(thm)],[c_0_167,c_0_164]) ).
cnf(c_0_174,negated_conjecture,
sk3 != nil,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_169]),c_0_164]) ).
cnf(c_0_175,negated_conjecture,
( sk3 = nil
| totalorderedP(sk3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_117]),c_0_107]) ).
cnf(c_0_176,plain,
( segmentP(app(X1,app(X2,X3)),X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_95]),c_0_104]) ).
cnf(c_0_177,negated_conjecture,
( app(skaf42(X1,sk5),app(sk3,skaf43(sk5,X1))) = X1
| ~ memberP(X1,sk5)
| ~ ssList(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173]),c_0_173]),c_0_173]),c_0_174]) ).
cnf(c_0_178,negated_conjecture,
( memberP(sk4,sk5)
| nil = sk4 ),
co1_10 ).
cnf(c_0_179,negated_conjecture,
( sk3 = nil
| ~ segmentP(sk4,sk3) ),
inference(spm,[status(thm)],[c_0_149,c_0_175]) ).
cnf(c_0_180,negated_conjecture,
( segmentP(X1,sk3)
| ~ memberP(X1,sk5)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_58]),c_0_118]),c_0_59])]) ).
cnf(c_0_181,negated_conjecture,
memberP(sk4,sk5),
inference(sr,[status(thm)],[c_0_178,c_0_164]) ).
cnf(c_0_182,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]),c_0_133])]),c_0_174]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC342-1 : 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 : n005.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 04:44:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 42.08/24.56 % Version : CSE_E---1.7
% 42.08/24.56 % Problem : theBenchmark.p
% 42.08/24.56 % SZS status Unsatisfiable for theBenchmark.p
% 42.08/24.56 % SZS output start CNFRefutation
% See solution above
% 42.28/24.73 % Total time : 18.402s
%------------------------------------------------------------------------------