%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC111-1 : 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 : n009.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 05:18:19 PM UTC 2026
% Result : Unsatisfiable 217.17s 88.81s
% Output : CNFRefutation 217.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 52
% Syntax : Number of clauses : 184 ( 38 unt; 31 nHn; 153 RR)
% Number of literals : 553 ( 151 equ; 363 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 292 ( 49 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/sandbox/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/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause52,axiom,
ssList(skaf43(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
cnf(clause53,axiom,
ssList(skaf42(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001-0.ax',clause138) ).
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(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
cnf(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause12,axiom,
ssItem(skaf83(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause12) ).
cnf(clause13,axiom,
ssList(skaf82(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause132,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).
cnf(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
cnf(clause171,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause171) ).
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(clause145,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).
cnf(clause150,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause150) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(co1_7,negated_conjecture,
segmentP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
cnf(co1_5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
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(co1_11,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
cnf(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
cnf(clause100,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
cnf(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_9,negated_conjecture,
( ~ ssList(X1)
| ~ neq(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(X1,sk3)
| ~ totalorderedP(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
cnf(clause80,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
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_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
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/sandbox/benchmark/Axioms/SWC001-0.ax',clause178) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause67,axiom,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause67) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause144,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).
cnf(co1_13,negated_conjecture,
( nil != sk1
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_12,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(c_0_52,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_53,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_52]) ).
cnf(c_0_54,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_55,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_56,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_57,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_53,c_0_54]),c_0_55]),c_0_56])]) ).
cnf(c_0_58,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_59,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_60,axiom,
ssList(nil),
clause8 ).
cnf(c_0_61,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_62,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_63,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_57,c_0_58]),c_0_59]),c_0_60])]),c_0_61]) ).
cnf(c_0_64,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_65,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_66,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_67,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_68,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_69,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause99 ).
cnf(c_0_70,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_71,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_72,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_73,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_74,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_63,c_0_64]),c_0_59])]) ).
cnf(c_0_75,plain,
( cons(skaf44(X1),X2) = app(X1,X2)
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_58]),c_0_59])]) ).
cnf(c_0_76,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_66,c_0_67]),c_0_60])]),c_0_61]) ).
cnf(c_0_77,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_67,c_0_68]),c_0_60])]) ).
cnf(c_0_78,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_79,plain,
( nil = X1
| skaf82(X1) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72])]) ).
cnf(c_0_80,plain,
( skaf82(X1) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_70]),c_0_71]),c_0_72])]) ).
cnf(c_0_81,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ duplicatefreeP(app(app(X1,X2),X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_61]) ).
cnf(c_0_82,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_60])]) ).
cnf(c_0_83,plain,
( ssItem(X1)
| duplicatefreeP(app(X2,X3))
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_78,c_0_61]) ).
cnf(c_0_84,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,axiom,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause133 ).
cnf(c_0_86,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_87,plain,
( ~ singletonP(X1)
| ~ ssList(X1)
| ~ duplicatefreeP(app(app(nil,X1),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_60])]) ).
cnf(c_0_88,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_89,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_90,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_91,plain,
( ssItem(X1)
| duplicatefreeP(app(skaf82(X2),X3))
| ~ ssList(X3) ),
inference(spm,[status(thm)],[c_0_83,c_0_72]) ).
cnf(c_0_92,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_84,c_0_85]),c_0_61]),c_0_86]) ).
cnf(c_0_93,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_94,plain,
( ~ singletonP(skaf45(X1,nil))
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,skaf45(X1,nil))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_60])]),c_0_90]) ).
cnf(c_0_95,plain,
( ssItem(X1)
| duplicatefreeP(app(skaf82(X2),skaf45(X3,X4))) ),
inference(spm,[status(thm)],[c_0_91,c_0_89]) ).
cnf(c_0_96,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_92,c_0_66]),c_0_60])]),c_0_93]) ).
cnf(c_0_97,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause98 ).
cnf(c_0_99,plain,
( ssItem(X1)
| ~ singletonP(skaf45(skaf82(X2),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_72])]) ).
cnf(c_0_100,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_68,c_0_88]),c_0_89]),c_0_60])]),c_0_90]) ).
cnf(c_0_101,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_102,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_103,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_104,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_105,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_96,c_0_73]),c_0_97]),c_0_98]) ).
cnf(c_0_106,plain,
( ssItem(X1)
| ~ singletonP(skaf82(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_72])]) ).
cnf(c_0_107,plain,
( skaf82(cons(X1,X2)) = X2
| ~ 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_101,c_0_70]),c_0_71]),c_0_72])])]),c_0_97]),c_0_98]) ).
cnf(c_0_108,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_109,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_102]),c_0_97]) ).
cnf(c_0_110,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_103])]),c_0_60])]) ).
cnf(c_0_111,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_112,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_113,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_114,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_66]),c_0_60])]) ).
cnf(c_0_115,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_116,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_65]),c_0_60])]) ).
cnf(c_0_117,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssItem(X3)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_118,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_108]) ).
cnf(c_0_119,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_60])]) ).
cnf(c_0_120,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
co1_11 ).
cnf(c_0_121,negated_conjecture,
segmentP(sk2,sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_122,plain,
( X1 = nil
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_65]) ).
cnf(c_0_123,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause97 ).
cnf(c_0_124,plain,
( hd(cons(X1,X2)) = hd(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_65]),c_0_116]) ).
cnf(c_0_125,plain,
( ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]) ).
cnf(c_0_126,negated_conjecture,
( sk2 = nil
| ~ neq(sk1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
cnf(c_0_127,axiom,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
clause100 ).
cnf(c_0_128,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_129,plain,
( X1 = nil
| cons(X2,X1) != cons(X2,nil)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_97]),c_0_60])]) ).
cnf(c_0_130,plain,
( hd(cons(X1,nil)) = X1
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_131,plain,
( ssItem(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_59]) ).
cnf(c_0_132,negated_conjecture,
( sk1 = nil
| sk2 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),c_0_60])]) ).
cnf(c_0_133,plain,
( skaf82(X1) = nil
| nil = X1
| cons(skaf83(X1),nil) != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_70]),c_0_71]),c_0_72])]) ).
cnf(c_0_134,plain,
( skaf83(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_70]),c_0_71]),c_0_72])]) ).
cnf(c_0_135,plain,
( hd(cons(X1,nil)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_97]),c_0_60])]) ).
cnf(c_0_136,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_131,c_0_59]) ).
cnf(c_0_137,negated_conjecture,
( ~ ssList(X1)
| ~ neq(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(X1,sk3)
| ~ totalorderedP(X1) ),
co1_9 ).
cnf(c_0_138,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
clause80 ).
cnf(c_0_139,negated_conjecture,
( sk1 = nil
| segmentP(nil,sk1) ),
inference(spm,[status(thm)],[c_0_121,c_0_132]) ).
cnf(c_0_140,axiom,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
clause173 ).
cnf(c_0_141,plain,
( skaf82(X1) = nil
| nil = X1
| cons(hd(X1),nil) != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_142,plain,
( hd(cons(X1,nil)) = X1
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136])]) ).
cnf(c_0_143,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_144,negated_conjecture,
( ~ neq(sk1,X1)
| ~ segmentP(X1,sk1)
| ~ segmentP(sk2,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_113]),c_0_112]),c_0_113]) ).
cnf(c_0_145,negated_conjecture,
sk1 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_128])]) ).
cnf(c_0_146,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
clause56 ).
cnf(c_0_147,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_140]) ).
cnf(c_0_148,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_149,plain,
( tl(cons(X1,app(X2,X3))) = app(tl(cons(X1,X2)),X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_102]),c_0_97]),c_0_98]) ).
cnf(c_0_150,plain,
( tl(X1) = nil
| nil = X1
| cons(hd(X1),nil) != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_141]) ).
cnf(c_0_151,negated_conjecture,
hd(cons(X1,nil)) = X1,
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_152,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_136])]) ).
cnf(c_0_153,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_136])]) ).
cnf(c_0_154,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_155,negated_conjecture,
( ~ neq(nil,X1)
| ~ segmentP(sk2,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145]),c_0_145]),c_0_146]) ).
cnf(c_0_156,axiom,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
clause67 ).
cnf(c_0_157,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_147,c_0_68]),c_0_60])]),c_0_61]) ).
cnf(c_0_158,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_148]) ).
cnf(c_0_159,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_160,plain,
( tl(cons(X1,app(X2,X3))) = app(tl(cons(X1,X2)),X3)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_136])]) ).
cnf(c_0_161,negated_conjecture,
tl(cons(X1,nil)) = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152])]),c_0_153]) ).
cnf(c_0_162,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_154,c_0_73]),c_0_97]),c_0_98]) ).
cnf(c_0_163,negated_conjecture,
( X1 = nil
| ~ segmentP(sk2,X1)
| ~ ssList(X1)
| ~ totalorderedP(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_127]),c_0_60])]) ).
cnf(c_0_164,plain,
totalorderedP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_136])]) ).
cnf(c_0_165,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_157,c_0_88]),c_0_89])]) ).
cnf(c_0_166,plain,
( nil = X1
| frontsegP(X1,cons(hd(X1),X2))
| ~ frontsegP(tl(X1),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_154]),c_0_93]),c_0_159]) ).
cnf(c_0_167,plain,
( ssList(cons(X1,X2))
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_136])]) ).
cnf(c_0_168,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_169,plain,
( tl(cons(X1,X2)) = app(nil,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_68]),c_0_161]),c_0_60])]) ).
cnf(c_0_170,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_162,c_0_70]),c_0_71]),c_0_72])]) ).
cnf(c_0_171,negated_conjecture,
~ segmentP(sk2,cons(X1,nil)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_152])]),c_0_153]) ).
cnf(c_0_172,plain,
( nil = X1
| segmentP(X1,cons(hd(X1),X2))
| ~ frontsegP(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167]) ).
cnf(c_0_173,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_168]),c_0_61]) ).
cnf(c_0_174,plain,
( app(nil,skaf82(X1)) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_72])]) ).
cnf(c_0_175,negated_conjecture,
( nil != sk1
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
co1_13 ).
cnf(c_0_176,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
co1_12 ).
cnf(c_0_177,negated_conjecture,
( sk2 = nil
| ~ frontsegP(tl(sk2),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_143]),c_0_60])]) ).
cnf(c_0_178,plain,
( nil = X1
| frontsegP(tl(X1),nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_72]),c_0_60])]) ).
cnf(c_0_179,negated_conjecture,
( sk1 != nil
| ~ neq(sk1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_121])]) ).
cnf(c_0_180,negated_conjecture,
neq(sk2,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_145])]) ).
cnf(c_0_181,negated_conjecture,
sk2 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_143])]) ).
cnf(c_0_182,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_145]),c_0_145])]) ).
cnf(c_0_183,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_181]),c_0_182]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC111-1 : 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
% 0.15/0.33 % Computer : n009.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 04:26:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 217.17/88.81 % Version : CSE_E---1.7
% 217.17/88.81 % Problem : theBenchmark.p
% 217.17/88.81 % SZS status Unsatisfiable for theBenchmark.p
% 217.17/88.81 % SZS output start CNFRefutation
% See solution above
% 217.67/89.32 % Total time : 70.742s
%------------------------------------------------------------------------------