%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC081-1 : 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 : n021.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 05:18:11 PM UTC 2026
% Result : Unsatisfiable 107.85s 63.37s
% Output : CNFRefutation 108.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 54
% Syntax : Number of clauses : 179 ( 39 unt; 45 nHn; 152 RR)
% Number of literals : 520 ( 131 equ; 312 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 254 ( 39 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(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
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(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(clause10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause10) ).
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(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(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(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_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_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(clause154,axiom,
( frontsegP(X1,X3)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause154) ).
cnf(co1_13,negated_conjecture,
( frontsegP(sk3,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_9,negated_conjecture,
( ssList(sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
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(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(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(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(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(co1_12,negated_conjecture,
( frontsegP(sk4,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
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(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(clause61,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause61) ).
cnf(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(co1_8,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
cnf(co1_7,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
cnf(clause129,axiom,
( X2 = X1
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause129) ).
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(co1_14,negated_conjecture,
( neq(sk5,nil)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_10,negated_conjecture,
( ssList(sk5)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
cnf(clause117,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause117) ).
cnf(co1_16,negated_conjecture,
( frontsegP(sk3,sk5)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
cnf(clause57,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
cnf(co1_15,negated_conjecture,
( frontsegP(sk4,sk5)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
cnf(co1_11,negated_conjecture,
( neq(sk5,nil)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
cnf(clause83,axiom,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
cnf(c_0_54,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_55,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_54]) ).
cnf(c_0_56,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_57,axiom,
ssList(nil),
clause8 ).
cnf(c_0_58,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_59,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_60,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_61,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_62,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_63,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_64,plain,
( ~ ssItem(X1)
| ~ ssList(app(cons(X1,X2),cons(X1,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ duplicatefreeP(app(cons(X1,X2),cons(X1,X3))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]),c_0_58]) ).
cnf(c_0_65,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_66,plain,
( ssItem(X1)
| duplicatefreeP(cons(X2,X3))
| ~ ssItem(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_58]) ).
cnf(c_0_67,axiom,
ssItem(skac2),
clause10 ).
cnf(c_0_68,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_69,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_70,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_71,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_60]),c_0_61]) ).
cnf(c_0_72,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_62,c_0_63]),c_0_57])]),c_0_61]) ).
cnf(c_0_73,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_63,c_0_56]),c_0_57])]) ).
cnf(c_0_74,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,app(X2,cons(X1,X3))))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ duplicatefreeP(cons(X1,app(X2,cons(X1,X3)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_58]) ).
cnf(c_0_75,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_76,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_77,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_78,plain,
( ssItem(X1)
| duplicatefreeP(cons(skac2,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_79,plain,
( skaf45(app(X1,X2),X1) = X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])])]),c_0_61]),c_0_71]) ).
cnf(c_0_80,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_57])]) ).
cnf(c_0_81,plain,
( ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(cons(X2,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_77])]),c_0_58]) ).
cnf(c_0_82,plain,
( ssItem(X1)
| duplicatefreeP(cons(skac2,skaf45(X2,X3))) ),
inference(spm,[status(thm)],[c_0_78,c_0_70]) ).
cnf(c_0_83,plain,
( skaf45(app(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_57])]) ).
cnf(c_0_84,plain,
( ssItem(X1)
| ~ memberP(skaf45(X2,X3),skac2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_67]),c_0_70])]) ).
cnf(c_0_85,plain,
( skaf45(app(nil,X1),nil) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_80]) ).
cnf(c_0_86,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_87,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_88,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_89,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_90,plain,
( ssItem(X1)
| ~ memberP(X2,skac2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_92,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_65]),c_0_58]) ).
cnf(c_0_93,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_87])]),c_0_57])]) ).
cnf(c_0_94,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_95,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_96,axiom,
( frontsegP(X1,X3)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause154 ).
cnf(c_0_97,negated_conjecture,
( frontsegP(sk3,sk5)
| nil = sk4 ),
co1_13 ).
cnf(c_0_98,negated_conjecture,
ssList(sk3),
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_99,negated_conjecture,
( ssList(sk5)
| nil = sk4 ),
co1_9 ).
cnf(c_0_100,plain,
( ssItem(X1)
| ~ ssList(cons(skac2,X2))
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_67])]) ).
cnf(c_0_101,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_57])]) ).
cnf(c_0_102,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_103,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_104,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_105,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_106,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_55,c_0_75]),c_0_76]),c_0_77])]) ).
cnf(c_0_107,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_108,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_109,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_110,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_61]) ).
cnf(c_0_111,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_112,negated_conjecture,
( sk4 = nil
| frontsegP(X1,sk5)
| ~ frontsegP(X1,sk3)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]),c_0_99]) ).
cnf(c_0_113,axiom,
( frontsegP(app(X1,X3),X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause137 ).
cnf(c_0_114,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_115,plain,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_57]),c_0_67])]) ).
cnf(c_0_116,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_103]),c_0_58]),c_0_104]) ).
cnf(c_0_117,plain,
( hd(X1) = hd(X2)
| nil = X2
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_69]),c_0_70])]) ).
cnf(c_0_118,negated_conjecture,
( frontsegP(sk4,sk5)
| nil = sk4 ),
co1_12 ).
cnf(c_0_119,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_106,c_0_107]),c_0_108]),c_0_109])]),c_0_61]) ).
cnf(c_0_120,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_91,c_0_107]),c_0_108]),c_0_109])]) ).
cnf(c_0_121,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk4,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_122,negated_conjecture,
( sk4 = nil
| frontsegP(X1,sk5)
| ~ frontsegP(X2,sk3)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_112]),c_0_99]) ).
cnf(c_0_123,axiom,
( X1 = X3
| app(X1,X2) != app(X3,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause151 ).
cnf(c_0_124,plain,
( frontsegP(cons(X1,X2),X3)
| ~ frontsegP(cons(X1,nil),X3)
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_125,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_115])]) ).
cnf(c_0_126,plain,
( cons(hd(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_107]),c_0_108]),c_0_109])]) ).
cnf(c_0_127,negated_conjecture,
( hd(sk5) = hd(sk4)
| sk4 = nil
| sk5 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_111])]),c_0_99]) ).
cnf(c_0_128,plain,
( nil = X1
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_129,negated_conjecture,
( ssItem(X1)
| duplicatefreeP(app(sk4,sk4)) ),
inference(spm,[status(thm)],[c_0_121,c_0_111]) ).
cnf(c_0_130,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_131,negated_conjecture,
( sk4 = nil
| frontsegP(X1,sk5)
| ~ frontsegP(X1,app(sk3,X2))
| ~ ssList(app(sk3,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_71]),c_0_98])]) ).
cnf(c_0_132,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
clause61 ).
cnf(c_0_133,plain,
( X1 = nil
| app(X1,nil) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_93]),c_0_57])]) ).
cnf(c_0_134,plain,
( frontsegP(cons(X1,X2),X3)
| ~ frontsegP(cons(X1,nil),X3)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_115])]),c_0_125])]) ).
cnf(c_0_135,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_136,negated_conjecture,
( cons(hd(sk4),skaf82(sk5)) = sk5
| sk4 = nil
| sk5 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_99]) ).
cnf(c_0_137,negated_conjecture,
( sk4 = nil
| ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_111])]) ).
cnf(c_0_138,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(sk2,X1)
| ~ segmentP(sk1,X1) ),
co1_8 ).
cnf(c_0_139,negated_conjecture,
neq(sk2,nil),
co1_7 ).
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_130]) ).
cnf(c_0_141,axiom,
( X2 = X1
| ~ frontsegP(X1,X2)
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause129 ).
cnf(c_0_142,negated_conjecture,
( sk4 = nil
| frontsegP(app(sk3,X1),sk5)
| ~ ssList(app(sk3,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_143,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_133,c_0_63]),c_0_57])]),c_0_61]) ).
cnf(c_0_144,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_145,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_146,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
clause58 ).
cnf(c_0_147,plain,
( frontsegP(cons(X1,X2),nil)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_57]),c_0_125])]) ).
cnf(c_0_148,negated_conjecture,
( cons(hd(sk5),skaf82(sk5)) = sk5
| sk5 = nil
| sk4 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_136]),c_0_109])]),c_0_137]) ).
cnf(c_0_149,negated_conjecture,
( ~ neq(X1,nil)
| ~ segmentP(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ ssList(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_89]),c_0_95]) ).
cnf(c_0_150,negated_conjecture,
neq(sk4,nil),
inference(rw,[status(thm)],[c_0_139,c_0_95]) ).
cnf(c_0_151,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_56]),c_0_57])]),c_0_61]) ).
cnf(c_0_152,negated_conjecture,
( neq(sk5,nil)
| nil = sk3 ),
co1_14 ).
cnf(c_0_153,negated_conjecture,
( ssList(sk5)
| nil = sk3 ),
co1_10 ).
cnf(c_0_154,negated_conjecture,
( app(sk3,X1) = sk5
| sk4 = nil
| ~ frontsegP(sk5,app(sk3,X1))
| ~ ssList(app(sk3,X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_99]) ).
cnf(c_0_155,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_143,c_0_144]),c_0_145]),c_0_57])]),c_0_146]) ).
cnf(c_0_156,negated_conjecture,
( sk4 = nil
| sk5 = nil
| frontsegP(sk5,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_109])]) ).
cnf(c_0_157,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause117 ).
cnf(c_0_158,negated_conjecture,
( ~ segmentP(sk3,sk4)
| ~ segmentP(sk4,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_111])]) ).
cnf(c_0_159,plain,
( segmentP(X1,X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_69]),c_0_70])]) ).
cnf(c_0_160,negated_conjecture,
( sk3 = nil
| ~ segmentP(sk3,sk5)
| ~ segmentP(sk4,sk5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_152]),c_0_153]) ).
cnf(c_0_161,negated_conjecture,
( frontsegP(sk3,sk5)
| nil = sk3 ),
co1_16 ).
cnf(c_0_162,negated_conjecture,
( sk4 = nil
| sk5 = nil
| app(sk3,X1) != nil
| ~ ssList(X1) ),
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_154,c_0_155]),c_0_57]),c_0_145]),c_0_98])]),c_0_156]) ).
cnf(c_0_163,plain,
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_157]) ).
cnf(c_0_164,negated_conjecture,
( ~ frontsegP(sk3,sk4)
| ~ segmentP(sk4,sk4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_111]),c_0_98])]) ).
cnf(c_0_165,axiom,
( segmentP(X1,X1)
| ~ ssList(X1) ),
clause57 ).
cnf(c_0_166,negated_conjecture,
( sk3 = nil
| ~ segmentP(sk4,sk5) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_159]),c_0_98])]),c_0_153]),c_0_161]) ).
cnf(c_0_167,negated_conjecture,
( frontsegP(sk4,sk5)
| nil = sk3 ),
co1_15 ).
cnf(c_0_168,negated_conjecture,
( neq(sk5,nil)
| nil = sk4 ),
co1_11 ).
cnf(c_0_169,negated_conjecture,
( sk5 = nil
| sk4 = nil
| sk3 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_62]),c_0_57]),c_0_98])]) ).
cnf(c_0_170,plain,
~ neq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_115])]) ).
cnf(c_0_171,negated_conjecture,
~ frontsegP(sk3,sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_111])]) ).
cnf(c_0_172,negated_conjecture,
sk3 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_159]),c_0_111])]),c_0_153]),c_0_167]) ).
cnf(c_0_173,negated_conjecture,
( sk4 = nil
| sk3 != nil ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170]) ).
cnf(c_0_174,axiom,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
clause83 ).
cnf(c_0_175,negated_conjecture,
~ frontsegP(nil,sk4),
inference(rw,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_176,negated_conjecture,
sk4 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_172])]) ).
cnf(c_0_177,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_174]),c_0_57])]) ).
cnf(c_0_178,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_176]),c_0_177])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC081-1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n021.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 04:25:10 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 107.85/63.37 % Version : CSE_E---1.7
% 107.85/63.37 % Problem : theBenchmark.p
% 107.85/63.37 % SZS status Unsatisfiable for theBenchmark.p
% 107.85/63.37 % SZS output start CNFRefutation
% See solution above
% 108.34/63.82 % Total time : 45.829s
%------------------------------------------------------------------------------