TSTP Solution File: SWC111-1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : SWC111-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 21 04:27:41 EDT 2024
% Result : Unsatisfiable 13.21s 2.18s
% Output : CNFRefutation 13.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 59
% Syntax : Number of clauses : 241 ( 55 unt; 37 nHn; 207 RR)
% Number of literals : 711 ( 199 equ; 458 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 : 18 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 371 ( 43 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(co1_11,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
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(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(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
cnf(clause80,axiom,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
cnf(clause168,axiom,
( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause168) ).
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(clause136,axiom,
( rearsegP(app(X3,X1),X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause136) ).
cnf(clause58,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause58) ).
cnf(co1_2,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
cnf(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
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(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(clause49,axiom,
ssList(skaf47(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause49) ).
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(clause47,axiom,
ssItem(skaf44(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
cnf(clause131,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause131) ).
cnf(clause48,axiom,
ssList(skaf48(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause48) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
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(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(clause85,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
cnf(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(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
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(clause99,axiom,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
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(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(clause170,axiom,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause170) ).
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(clause109,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
cnf(clause98,axiom,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
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(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(clause97,axiom,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
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(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(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
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(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(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(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(clause51,axiom,
ssList(skaf45(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
cnf(clause56,axiom,
( segmentP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
cnf(clause67,axiom,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause67) ).
cnf(clause117,axiom,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause117) ).
cnf(co1_12,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
cnf(c_0_59,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
inference(fof_simplification,[status(thm)],[co1_11]) ).
cnf(c_0_60,negated_conjecture,
segmentP(sk4,sk3),
co1_7 ).
cnf(c_0_61,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_62,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_63,negated_conjecture,
( nil = sk2
| ~ neq(sk1,nil)
| ~ segmentP(sk2,sk1) ),
c_0_59 ).
cnf(c_0_64,negated_conjecture,
segmentP(sk2,sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_65,plain,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause100]) ).
cnf(c_0_66,negated_conjecture,
( sk2 = nil
| ~ neq(sk1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_67,plain,
( neq(X2,X1)
| X2 = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
c_0_65 ).
cnf(c_0_68,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_69,axiom,
ssList(nil),
clause8 ).
cnf(c_0_70,plain,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause80]) ).
cnf(c_0_71,negated_conjecture,
( sk1 = nil
| sk2 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69])]) ).
cnf(c_0_72,plain,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
c_0_70 ).
cnf(c_0_73,negated_conjecture,
( sk1 = nil
| segmentP(nil,sk1) ),
inference(spm,[status(thm)],[c_0_64,c_0_71]) ).
cnf(c_0_74,plain,
( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause168]) ).
cnf(c_0_75,negated_conjecture,
sk1 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_68])]) ).
cnf(c_0_76,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(fof_simplification,[status(thm)],[clause138]) ).
cnf(c_0_77,plain,
( rearsegP(app(X3,X1),X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause136]) ).
cnf(c_0_78,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause58]) ).
cnf(c_0_79,plain,
( app(app(skaf47(X1,X2),X2),skaf48(X2,X1)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
c_0_74 ).
cnf(c_0_80,negated_conjecture,
segmentP(sk2,nil),
inference(rw,[status(thm)],[c_0_64,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_82,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause73]) ).
cnf(c_0_83,plain,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
inference(fof_simplification,[status(thm)],[clause179]) ).
cnf(c_0_84,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
c_0_76 ).
cnf(c_0_85,plain,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause101]) ).
cnf(c_0_86,plain,
( rearsegP(app(X3,X1),X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
c_0_77 ).
cnf(c_0_87,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
c_0_78 ).
cnf(c_0_88,negated_conjecture,
app(app(skaf47(sk2,nil),nil),skaf48(nil,sk2)) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_69]),c_0_81])]) ).
cnf(c_0_89,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
c_0_82 ).
cnf(c_0_90,axiom,
ssList(skaf47(X1,X2)),
clause49 ).
cnf(c_0_91,plain,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
c_0_83 ).
cnf(c_0_92,plain,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause169]) ).
cnf(c_0_93,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_94,plain,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
c_0_85 ).
cnf(c_0_95,axiom,
ssItem(skaf44(X1)),
clause47 ).
cnf(c_0_96,plain,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause131]) ).
cnf(c_0_97,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_69])]) ).
cnf(c_0_98,negated_conjecture,
app(skaf47(sk2,nil),skaf48(nil,sk2)) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_99,axiom,
ssList(skaf48(X1,X2)),
clause48 ).
cnf(c_0_100,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_91]) ).
cnf(c_0_101,plain,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
c_0_92 ).
cnf(c_0_102,plain,
( memberP(X1,skaf44(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_69])]) ).
cnf(c_0_103,plain,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
c_0_96 ).
cnf(c_0_104,negated_conjecture,
rearsegP(sk2,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_90]),c_0_99])]) ).
cnf(c_0_105,plain,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause116]) ).
cnf(c_0_106,plain,
( ~ singletonP(X1)
| ~ ssList(app(app(X2,cons(skaf44(X1),X3)),X1))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(app(app(X2,cons(skaf44(X1),X3)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_94]),c_0_95]),c_0_69])]) ).
cnf(c_0_107,plain,
( app(skaf42(X1,skaf44(X1)),cons(skaf44(X1),skaf43(skaf44(X1),X1))) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_95])]) ).
cnf(c_0_108,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_109,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_110,plain,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause72]) ).
cnf(c_0_111,plain,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause85]) ).
cnf(c_0_112,plain,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(fof_simplification,[status(thm)],[clause157]) ).
cnf(c_0_113,plain,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause86]) ).
cnf(c_0_114,plain,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause145]) ).
cnf(c_0_115,plain,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause99]) ).
cnf(c_0_116,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause104]) ).
cnf(c_0_117,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause75]) ).
cnf(c_0_118,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause76]) ).
cnf(c_0_119,negated_conjecture,
app(skaf46(sk2,nil),nil) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_69]),c_0_81])]) ).
cnf(c_0_120,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_121,plain,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause96]) ).
cnf(c_0_122,plain,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_105 ).
cnf(c_0_123,plain,
( ~ singletonP(X1)
| ~ ssList(app(X1,X1))
| ~ ssList(X1)
| ~ duplicatefreeP(app(X1,X1)) ),
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])]) ).
cnf(c_0_124,plain,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
c_0_110 ).
cnf(c_0_125,plain,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
c_0_111 ).
cnf(c_0_126,plain,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
c_0_112 ).
cnf(c_0_127,plain,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_113 ).
cnf(c_0_128,plain,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
c_0_114 ).
cnf(c_0_129,plain,
( cons(X1,X2) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_115 ).
cnf(c_0_130,plain,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
c_0_116 ).
cnf(c_0_131,plain,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
c_0_117 ).
cnf(c_0_132,plain,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
c_0_118 ).
cnf(c_0_133,plain,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause133]) ).
cnf(c_0_134,plain,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause118]) ).
cnf(c_0_135,plain,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause123]) ).
cnf(c_0_136,negated_conjecture,
skaf46(sk2,nil) = sk2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_119]),c_0_120])]) ).
cnf(c_0_137,plain,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_121 ).
cnf(c_0_138,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_122]) ).
cnf(c_0_139,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(app(X2,X2))
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_140,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_141,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_128])]),c_0_69])]) ).
cnf(c_0_142,plain,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause170]) ).
cnf(c_0_143,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_132]) ).
cnf(c_0_144,plain,
( nil = X2
| tl(app(X2,X1)) = app(tl(X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
c_0_133 ).
cnf(c_0_145,plain,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
c_0_134 ).
cnf(c_0_146,plain,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause171]) ).
cnf(c_0_147,plain,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause109]) ).
cnf(c_0_148,plain,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause98]) ).
cnf(c_0_149,plain,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
c_0_135 ).
cnf(c_0_150,negated_conjecture,
app(sk2,nil) = sk2,
inference(rw,[status(thm)],[c_0_119,c_0_136]) ).
cnf(c_0_151,plain,
( tl(X1) = nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_94]),c_0_95]),c_0_69])]) ).
cnf(c_0_152,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_127]),c_0_69])]) ).
cnf(c_0_153,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause120]) ).
cnf(c_0_154,plain,
( ssItem(X1)
| ~ singletonP(X2)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_139,c_0_125]) ).
cnf(c_0_155,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_69])]) ).
cnf(c_0_156,plain,
( X1 = X3
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
c_0_142 ).
cnf(c_0_157,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_143,c_0_144]),c_0_125]),c_0_145]) ).
cnf(c_0_158,plain,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
c_0_146 ).
cnf(c_0_159,plain,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
c_0_147 ).
cnf(c_0_160,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_161,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_162,plain,
( cons(X1,X2) != nil
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_148 ).
cnf(c_0_163,plain,
( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_149]),c_0_125]),c_0_145]) ).
cnf(c_0_164,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_131,c_0_144]),c_0_125]),c_0_145]) ).
cnf(c_0_165,negated_conjecture,
( app(tl(sk2),nil) = tl(sk2)
| sk2 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_150]),c_0_81]),c_0_69])]) ).
cnf(c_0_166,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_167,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_153 ).
cnf(c_0_168,plain,
( ssItem(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_152]),c_0_155]) ).
cnf(c_0_169,plain,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(fof_simplification,[status(thm)],[clause97]) ).
cnf(c_0_170,plain,
( skaf44(cons(X1,X2)) = X1
| ~ singletonP(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
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_156,c_0_94]),c_0_95]),c_0_69])])]),c_0_127]) ).
cnf(c_0_171,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_157,c_0_89]),c_0_69])]),c_0_131]) ).
cnf(c_0_172,plain,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
inference(fof_simplification,[status(thm)],[clause178]) ).
cnf(c_0_173,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_158,c_0_159]),c_0_160]),c_0_161])])]),c_0_127]),c_0_162]) ).
cnf(c_0_174,negated_conjecture,
( cons(hd(sk2),tl(sk2)) = sk2
| sk2 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_150]),c_0_81]),c_0_69])]) ).
cnf(c_0_175,negated_conjecture,
( sk2 = nil
| ssList(tl(sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_81]),c_0_69])]) ).
cnf(c_0_176,plain,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause132]) ).
cnf(c_0_177,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause60]) ).
cnf(c_0_178,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_127]),c_0_69])]) ).
cnf(c_0_179,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_167,c_0_94]),c_0_95])]) ).
cnf(c_0_180,plain,
ssItem(X1),
inference(spm,[status(thm)],[c_0_168,c_0_95]) ).
cnf(c_0_181,plain,
( hd(cons(X1,X2)) = X1
| ~ ssItem(X1)
| ~ ssList(X2) ),
c_0_169 ).
cnf(c_0_182,plain,
( skaf44(cons(X1,nil)) = X1
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_152]),c_0_69])]) ).
cnf(c_0_183,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_171,c_0_137]),c_0_127]),c_0_162]) ).
cnf(c_0_184,plain,
( frontsegP(cons(X3,X1),cons(X4,X2))
| ~ frontsegP(X1,X2)
| X3 != X4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
c_0_172 ).
cnf(c_0_185,negated_conjecture,
( skaf82(sk2) = tl(sk2)
| sk2 = nil
| ~ ssItem(hd(sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]) ).
cnf(c_0_186,plain,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
inference(fof_simplification,[status(thm)],[clause150]) ).
cnf(c_0_187,plain,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
c_0_176 ).
cnf(c_0_188,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
c_0_177 ).
cnf(c_0_189,plain,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(fof_simplification,[status(thm)],[clause149]) ).
cnf(c_0_190,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause74]) ).
cnf(c_0_191,plain,
( tl(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_178,c_0_179]),c_0_95]),c_0_69])]) ).
cnf(c_0_192,plain,
singletonP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_180])]) ).
cnf(c_0_193,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_180])]) ).
cnf(c_0_194,plain,
( skaf44(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_94]),c_0_95]),c_0_69])]) ).
cnf(c_0_195,plain,
skaf44(cons(X1,nil)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_180])]) ).
cnf(c_0_196,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_167]),c_0_69])]) ).
cnf(c_0_197,negated_conjecture,
( ~ ssList(X1)
| ~ neq(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(X1,sk3)
| ~ totalorderedP(X1) ),
inference(fof_simplification,[status(thm)],[co1_9]) ).
cnf(c_0_198,plain,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
inference(fof_simplification,[status(thm)],[clause173]) ).
cnf(c_0_199,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_184]) ).
cnf(c_0_200,negated_conjecture,
( skaf82(sk2) = tl(sk2)
| sk2 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_132]),c_0_81])]) ).
cnf(c_0_201,plain,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
c_0_186 ).
cnf(c_0_202,plain,
( app(nil,skaf45(X1,nil)) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_69])]) ).
cnf(c_0_203,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_204,plain,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
c_0_189 ).
cnf(c_0_205,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
c_0_190 ).
cnf(c_0_206,plain,
tl(app(cons(X1,nil),nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_193])]) ).
cnf(c_0_207,plain,
hd(cons(X1,nil)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_192]),c_0_193])]) ).
cnf(c_0_208,plain,
cons(X1,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_180])]) ).
cnf(c_0_209,negated_conjecture,
( ~ ssList(X1)
| ~ neq(sk3,X1)
| ~ segmentP(sk4,X1)
| ~ segmentP(X1,sk3)
| ~ totalorderedP(X1) ),
c_0_197 ).
cnf(c_0_210,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(fof_simplification,[status(thm)],[clause56]) ).
cnf(c_0_211,plain,
( segmentP(X4,X2)
| app(app(X1,X2),X3) != X4
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4) ),
c_0_198 ).
cnf(c_0_212,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_188]),c_0_69])]) ).
cnf(c_0_213,negated_conjecture,
( cons(skaf83(sk2),tl(sk2)) = sk2
| sk2 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_200]),c_0_81])]) ).
cnf(c_0_214,plain,
( skaf45(app(nil,X1),nil) = X1
| ~ ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_203]),c_0_69])])]) ).
cnf(c_0_215,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_204,c_0_205]),c_0_69])]) ).
cnf(c_0_216,plain,
app(cons(X1,nil),nil) = cons(X1,nil),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_206]),c_0_207]),c_0_193]),c_0_69])]),c_0_208]) ).
cnf(c_0_217,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_209,c_0_62]),c_0_61]),c_0_62]) ).
cnf(c_0_218,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
c_0_210 ).
cnf(c_0_219,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_211]) ).
cnf(c_0_220,negated_conjecture,
( sk2 = nil
| frontsegP(sk2,cons(skaf83(sk2),nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_160])]),c_0_175]) ).
cnf(c_0_221,plain,
( skaf45(app(nil,X1),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_125]),c_0_69])]) ).
cnf(c_0_222,plain,
app(nil,cons(X1,nil)) = cons(X1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_193]),c_0_69])]) ).
cnf(c_0_223,plain,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(fof_simplification,[status(thm)],[clause67]) ).
cnf(c_0_224,plain,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(fof_simplification,[status(thm)],[clause117]) ).
cnf(c_0_225,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
inference(fof_simplification,[status(thm)],[co1_12]) ).
cnf(c_0_226,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_217,c_0_75]),c_0_75]),c_0_218]) ).
cnf(c_0_227,plain,
( segmentP(app(X1,X2),skaf45(X1,nil))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_202]),c_0_203]),c_0_69])]),c_0_125]) ).
cnf(c_0_228,negated_conjecture,
( app(cons(skaf83(sk2),nil),skaf45(sk2,cons(skaf83(sk2),nil))) = sk2
| sk2 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_220]),c_0_81])]),c_0_193])]) ).
cnf(c_0_229,plain,
skaf45(cons(X1,nil),nil) = cons(X1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_193])]) ).
cnf(c_0_230,plain,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
c_0_223 ).
cnf(c_0_231,plain,
( X1 != X2
| ~ neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
c_0_224 ).
cnf(c_0_232,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
c_0_225 ).
cnf(c_0_233,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_226,c_0_67]),c_0_69])]) ).
cnf(c_0_234,negated_conjecture,
( sk2 = nil
| segmentP(sk2,cons(skaf83(sk2),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_229]),c_0_203]),c_0_193])]) ).
cnf(c_0_235,plain,
totalorderedP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_180])]) ).
cnf(c_0_236,plain,
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_231]) ).
cnf(c_0_237,negated_conjecture,
neq(sk2,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_75])]) ).
cnf(c_0_238,negated_conjecture,
sk2 = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_193]),c_0_235])]),c_0_208]) ).
cnf(c_0_239,plain,
~ neq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_180])]) ).
cnf(c_0_240,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_237,c_0_238]),c_0_239]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC111-1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 03:30:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.21/0.48 Running first-order model finding
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.21/2.18 # Version: 3.1.0
% 13.21/2.18 # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.21/2.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.21/2.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.21/2.18 # Starting new_bool_3 with 300s (1) cores
% 13.21/2.18 # Starting new_bool_1 with 300s (1) cores
% 13.21/2.18 # Starting sh5l with 300s (1) cores
% 13.21/2.18 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 10276 completed with status 0
% 13.21/2.18 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 13.21/2.18 # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.21/2.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.21/2.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.21/2.18 # No SInE strategy applied
% 13.21/2.18 # Search class: FGHSM-FSLM21-MFFFFFNN
% 13.21/2.18 # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 13.21/2.18 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2s with 406s (1) cores
% 13.21/2.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 13.21/2.18 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 13.21/2.18 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 13.21/2.18 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S0S with 136s (1) cores
% 13.21/2.18 # G-E--_208_C18_F1_SE_CS_SP_PS_S2s with pid 10282 completed with status 0
% 13.21/2.18 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2s
% 13.21/2.18 # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.21/2.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.21/2.18 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.21/2.18 # No SInE strategy applied
% 13.21/2.18 # Search class: FGHSM-FSLM21-MFFFFFNN
% 13.21/2.18 # Scheduled 9 strats onto 5 cores with 1500 seconds (1500 total)
% 13.21/2.18 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2s with 406s (1) cores
% 13.21/2.18 # Preprocessing time : 0.003 s
% 13.21/2.18 # Presaturation interreduction done
% 13.21/2.18
% 13.21/2.18 # Proof found!
% 13.21/2.18 # SZS status Unsatisfiable
% 13.21/2.18 # SZS output start CNFRefutation
% See solution above
% 13.21/2.18 # Parsed axioms : 198
% 13.21/2.18 # Removed by relevancy pruning/SinE : 0
% 13.21/2.18 # Initial clauses : 198
% 13.21/2.18 # Removed in clause preprocessing : 0
% 13.21/2.18 # Initial clauses in saturation : 198
% 13.21/2.18 # Processed clauses : 15039
% 13.21/2.18 # ...of these trivial : 56
% 13.21/2.18 # ...subsumed : 12023
% 13.21/2.18 # ...remaining for further processing : 2960
% 13.21/2.18 # Other redundant clauses eliminated : 1014
% 13.21/2.18 # Clauses deleted for lack of memory : 0
% 13.21/2.18 # Backward-subsumed : 65
% 13.21/2.18 # Backward-rewritten : 1251
% 13.21/2.18 # Generated clauses : 80145
% 13.21/2.18 # ...of the previous two non-redundant : 75467
% 13.21/2.18 # ...aggressively subsumed : 0
% 13.21/2.18 # Contextual simplify-reflections : 543
% 13.21/2.18 # Paramodulations : 79103
% 13.21/2.18 # Factorizations : 2
% 13.21/2.18 # NegExts : 0
% 13.21/2.18 # Equation resolutions : 1041
% 13.21/2.18 # Disequality decompositions : 0
% 13.21/2.18 # Total rewrite steps : 87717
% 13.21/2.18 # ...of those cached : 86733
% 13.21/2.18 # Propositional unsat checks : 0
% 13.21/2.18 # Propositional check models : 0
% 13.21/2.18 # Propositional check unsatisfiable : 0
% 13.21/2.18 # Propositional clauses : 0
% 13.21/2.18 # Propositional clauses after purity: 0
% 13.21/2.18 # Propositional unsat core size : 0
% 13.21/2.18 # Propositional preprocessing time : 0.000
% 13.21/2.18 # Propositional encoding time : 0.000
% 13.21/2.18 # Propositional solver time : 0.000
% 13.21/2.18 # Success case prop preproc time : 0.000
% 13.21/2.18 # Success case prop encoding time : 0.000
% 13.21/2.18 # Success case prop solver time : 0.000
% 13.21/2.18 # Current number of processed clauses : 1431
% 13.21/2.18 # Positive orientable unit clauses : 101
% 13.21/2.18 # Positive unorientable unit clauses: 0
% 13.21/2.18 # Negative unit clauses : 37
% 13.21/2.18 # Non-unit-clauses : 1293
% 13.21/2.18 # Current number of unprocessed clauses: 58686
% 13.21/2.18 # ...number of literals in the above : 331593
% 13.21/2.18 # Current number of archived formulas : 0
% 13.21/2.18 # Current number of archived clauses : 1506
% 13.21/2.18 # Clause-clause subsumption calls (NU) : 843067
% 13.21/2.18 # Rec. Clause-clause subsumption calls : 179430
% 13.21/2.18 # Non-unit clause-clause subsumptions : 8805
% 13.21/2.18 # Unit Clause-clause subsumption calls : 5366
% 13.21/2.18 # Rewrite failures with RHS unbound : 0
% 13.21/2.18 # BW rewrite match attempts : 76
% 13.21/2.18 # BW rewrite match successes : 57
% 13.21/2.18 # Condensation attempts : 0
% 13.21/2.18 # Condensation successes : 0
% 13.21/2.18 # Termbank termtop insertions : 1698516
% 13.21/2.18 # Search garbage collected termcells : 549
% 13.21/2.18
% 13.21/2.18 # -------------------------------------------------
% 13.21/2.18 # User time : 1.581 s
% 13.21/2.18 # System time : 0.044 s
% 13.21/2.18 # Total time : 1.625 s
% 13.21/2.18 # Maximum resident set size: 2144 pages
% 13.21/2.18
% 13.21/2.18 # -------------------------------------------------
% 13.21/2.18 # User time : 7.822 s
% 13.21/2.18 # System time : 0.318 s
% 13.21/2.18 # Total time : 8.139 s
% 13.21/2.18 # Maximum resident set size: 1876 pages
% 13.21/2.18 % E---3.1 exiting
%------------------------------------------------------------------------------