TSTP Solution File: SWC226-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC226-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 : Thu Aug 31 20:20:53 EDT 2023
% Result : Unsatisfiable 1.22s 1.32s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 123
% Syntax : Number of formulae : 248 ( 64 unt; 74 typ; 0 def)
% Number of atoms : 447 ( 124 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 547 ( 274 ~; 273 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 66 >; 19 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 55 ( 55 usr; 8 con; 0-3 aty)
% Number of variables : 231 ( 28 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
nil: $i ).
tff(decl_23,type,
equalelemsP: $i > $o ).
tff(decl_24,type,
duplicatefreeP: $i > $o ).
tff(decl_25,type,
strictorderedP: $i > $o ).
tff(decl_26,type,
totalorderedP: $i > $o ).
tff(decl_27,type,
strictorderP: $i > $o ).
tff(decl_28,type,
totalorderP: $i > $o ).
tff(decl_29,type,
cyclefreeP: $i > $o ).
tff(decl_30,type,
ssList: $i > $o ).
tff(decl_31,type,
skac3: $i ).
tff(decl_32,type,
ssItem: $i > $o ).
tff(decl_33,type,
skac2: $i ).
tff(decl_34,type,
singletonP: $i > $o ).
tff(decl_35,type,
skaf83: $i > $i ).
tff(decl_36,type,
skaf82: $i > $i ).
tff(decl_37,type,
skaf81: $i > $i ).
tff(decl_38,type,
skaf80: $i > $i ).
tff(decl_39,type,
skaf79: $i > $i ).
tff(decl_40,type,
skaf78: $i > $i ).
tff(decl_41,type,
skaf77: $i > $i ).
tff(decl_42,type,
skaf76: $i > $i ).
tff(decl_43,type,
skaf75: $i > $i ).
tff(decl_44,type,
skaf74: $i > $i ).
tff(decl_45,type,
skaf73: $i > $i ).
tff(decl_46,type,
skaf72: $i > $i ).
tff(decl_47,type,
skaf71: $i > $i ).
tff(decl_48,type,
skaf70: $i > $i ).
tff(decl_49,type,
skaf69: $i > $i ).
tff(decl_50,type,
skaf68: $i > $i ).
tff(decl_51,type,
skaf67: $i > $i ).
tff(decl_52,type,
skaf66: $i > $i ).
tff(decl_53,type,
skaf65: $i > $i ).
tff(decl_54,type,
skaf64: $i > $i ).
tff(decl_55,type,
skaf63: $i > $i ).
tff(decl_56,type,
skaf62: $i > $i ).
tff(decl_57,type,
skaf61: $i > $i ).
tff(decl_58,type,
skaf60: $i > $i ).
tff(decl_59,type,
skaf59: $i > $i ).
tff(decl_60,type,
skaf58: $i > $i ).
tff(decl_61,type,
skaf57: $i > $i ).
tff(decl_62,type,
skaf56: $i > $i ).
tff(decl_63,type,
skaf55: $i > $i ).
tff(decl_64,type,
skaf54: $i > $i ).
tff(decl_65,type,
skaf53: $i > $i ).
tff(decl_66,type,
skaf52: $i > $i ).
tff(decl_67,type,
skaf51: $i > $i ).
tff(decl_68,type,
skaf50: $i > $i ).
tff(decl_69,type,
skaf49: $i > $i ).
tff(decl_70,type,
skaf44: $i > $i ).
tff(decl_71,type,
skaf48: ( $i * $i ) > $i ).
tff(decl_72,type,
skaf47: ( $i * $i ) > $i ).
tff(decl_73,type,
skaf46: ( $i * $i ) > $i ).
tff(decl_74,type,
skaf45: ( $i * $i ) > $i ).
tff(decl_75,type,
skaf43: ( $i * $i ) > $i ).
tff(decl_76,type,
skaf42: ( $i * $i ) > $i ).
tff(decl_77,type,
geq: ( $i * $i ) > $o ).
tff(decl_78,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_79,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_80,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_81,type,
leq: ( $i * $i ) > $o ).
tff(decl_82,type,
lt: ( $i * $i ) > $o ).
tff(decl_83,type,
cons: ( $i * $i ) > $i ).
tff(decl_84,type,
memberP: ( $i * $i ) > $o ).
tff(decl_85,type,
app: ( $i * $i ) > $i ).
tff(decl_86,type,
tl: $i > $i ).
tff(decl_87,type,
hd: $i > $i ).
tff(decl_88,type,
neq: ( $i * $i ) > $o ).
tff(decl_89,type,
gt: ( $i * $i ) > $o ).
tff(decl_90,type,
sk1: $i ).
tff(decl_91,type,
sk2: $i ).
tff(decl_92,type,
sk3: $i ).
tff(decl_93,type,
sk4: $i ).
tff(decl_94,type,
sk5: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
sk6: $i ).
cnf(co1_14,negated_conjecture,
app(sk3,sk6) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
cnf(co1_6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
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(co1_1,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
cnf(co1_13,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
cnf(co1_7,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
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(clause118,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
cnf(clause104,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
cnf(clause76,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause76) ).
cnf(clause171,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause171) ).
cnf(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(clause75,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause75) ).
cnf(clause176,axiom,
( X1 = X3
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause176) ).
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(clause96,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
cnf(clause174,axiom,
( frontsegP(X2,X4)
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause174) ).
cnf(clause61,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause61) ).
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(clause73,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
cnf(clause8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
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(clause143,axiom,
( rearsegP(X3,X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause143) ).
cnf(clause136,axiom,
( rearsegP(app(X3,X1),X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause136) ).
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(clause86,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
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(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(clause58,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause58) ).
cnf(clause50,axiom,
ssList(skaf46(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
cnf(clause60,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
cnf(clause74,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
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(clause179,axiom,
( app(app(X1,cons(X2,X3)),cons(X2,X4)) != X5
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ duplicatefreeP(X5)
| ~ ssList(X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
cnf(clause169,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause169) ).
cnf(clause157,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
cnf(clause145,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause145) ).
cnf(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(clause72,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
cnf(co1_9,negated_conjecture,
( memberP(X2,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
cnf(clause71,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
cnf(clause116,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
cnf(clause101,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
cnf(c_0_49,negated_conjecture,
app(sk3,sk6) = sk4,
co1_14 ).
cnf(c_0_50,negated_conjecture,
sk1 = sk3,
co1_6 ).
cnf(c_0_51,axiom,
( nil = X2
| hd(app(X2,X1)) = hd(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
clause123 ).
cnf(c_0_52,negated_conjecture,
app(sk1,sk6) = sk4,
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
ssList(sk1),
co1_1 ).
cnf(c_0_54,negated_conjecture,
ssList(sk6),
co1_13 ).
cnf(c_0_55,negated_conjecture,
nil != sk1,
co1_7 ).
cnf(c_0_56,negated_conjecture,
ssList(sk2),
co1_2 ).
cnf(c_0_57,negated_conjecture,
sk2 = sk4,
co1_5 ).
cnf(c_0_58,axiom,
( nil = X1
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
clause118 ).
cnf(c_0_59,axiom,
( cons(hd(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause104 ).
cnf(c_0_60,negated_conjecture,
hd(sk4) = hd(sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54])]),c_0_55]) ).
cnf(c_0_61,negated_conjecture,
ssList(sk4),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
sk4 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_52]),c_0_54]),c_0_53])]),c_0_55]) ).
cnf(c_0_63,axiom,
( ssItem(hd(X1))
| nil = X1
| ~ ssList(X1) ),
clause76 ).
cnf(c_0_64,axiom,
( X4 = X2
| cons(X1,X2) != cons(X3,X4)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X2) ),
clause171 ).
cnf(c_0_65,negated_conjecture,
cons(hd(sk1),tl(sk4)) = sk4,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]),c_0_62]) ).
cnf(c_0_66,negated_conjecture,
ssItem(hd(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_60]),c_0_61])]),c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( tl(sk4) = X1
| cons(X2,X1) != sk4
| ~ ssItem(X2)
| ~ ssList(tl(sk4))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_68,axiom,
( cons(skaf83(X1),skaf82(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
clause109 ).
cnf(c_0_69,axiom,
ssItem(skaf83(X1)),
clause12 ).
cnf(c_0_70,axiom,
ssList(skaf82(X1)),
clause13 ).
cnf(c_0_71,negated_conjecture,
( skaf82(sk4) = tl(sk4)
| ~ ssList(tl(sk4)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70])])]),c_0_61])]),c_0_62]) ).
cnf(c_0_72,axiom,
( ssList(tl(X1))
| nil = X1
| ~ ssList(X1) ),
clause75 ).
cnf(c_0_73,negated_conjecture,
skaf82(sk4) = tl(sk4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_61])]),c_0_62]) ).
cnf(c_0_74,axiom,
( X1 = X3
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
clause176 ).
cnf(c_0_75,negated_conjecture,
ssList(tl(sk4)),
inference(spm,[status(thm)],[c_0_70,c_0_73]) ).
cnf(c_0_76,axiom,
( frontsegP(X3,X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause144 ).
cnf(c_0_77,axiom,
( ssList(app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2) ),
clause85 ).
cnf(c_0_78,negated_conjecture,
( hd(sk1) = X1
| ~ frontsegP(sk4,cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_65]),c_0_66]),c_0_75])]) ).
cnf(c_0_79,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_76]),c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( skaf83(X1) = hd(sk1)
| nil = X1
| ~ frontsegP(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_68]),c_0_69]),c_0_70])]) ).
cnf(c_0_81,negated_conjecture,
frontsegP(sk4,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_52]),c_0_54]),c_0_53])]) ).
cnf(c_0_82,negated_conjecture,
skaf83(sk1) = hd(sk1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_53])]),c_0_55]) ).
cnf(c_0_83,axiom,
( tl(cons(X1,X2)) = X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause96 ).
cnf(c_0_84,negated_conjecture,
cons(hd(sk1),skaf82(sk1)) = sk1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_82]),c_0_53])]),c_0_55]) ).
cnf(c_0_85,negated_conjecture,
skaf82(sk1) = tl(sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_66]),c_0_70])]) ).
cnf(c_0_86,axiom,
( frontsegP(X2,X4)
| ~ frontsegP(cons(X1,X2),cons(X3,X4))
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssItem(X3)
| ~ ssItem(X1) ),
clause174 ).
cnf(c_0_87,negated_conjecture,
cons(hd(sk1),tl(sk1)) = sk1,
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
ssList(tl(sk1)),
inference(spm,[status(thm)],[c_0_70,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( frontsegP(X1,tl(sk1))
| ~ frontsegP(cons(X2,X1),sk1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_66]),c_0_88])]) ).
cnf(c_0_90,negated_conjecture,
( frontsegP(tl(sk1),tl(sk1))
| ~ frontsegP(sk1,sk1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_87]),c_0_66]),c_0_88])]) ).
cnf(c_0_91,axiom,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
clause61 ).
cnf(c_0_92,axiom,
( X2 = X3
| app(X1,X2) != app(X1,X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3) ),
clause150 ).
cnf(c_0_93,axiom,
( app(X1,nil) = X1
| ~ ssList(X1) ),
clause73 ).
cnf(c_0_94,axiom,
ssList(nil),
clause8 ).
cnf(c_0_95,axiom,
( app(X2,skaf45(X1,X2)) = X1
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause132 ).
cnf(c_0_96,negated_conjecture,
frontsegP(tl(sk1),tl(sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_53])]) ).
cnf(c_0_97,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_92,c_0_93]),c_0_94])]) ).
cnf(c_0_98,negated_conjecture,
app(tl(sk1),skaf45(tl(sk1),tl(sk1))) = tl(sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_88])]) ).
cnf(c_0_99,axiom,
ssList(skaf45(X1,X2)),
clause51 ).
cnf(c_0_100,axiom,
( rearsegP(X3,X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause143 ).
cnf(c_0_101,negated_conjecture,
skaf45(tl(sk1),tl(sk1)) = 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_99]),c_0_88])]) ).
cnf(c_0_102,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_100]),c_0_77]) ).
cnf(c_0_103,negated_conjecture,
app(tl(sk1),nil) = tl(sk1),
inference(rw,[status(thm)],[c_0_98,c_0_101]) ).
cnf(c_0_104,axiom,
( rearsegP(app(X3,X1),X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause136 ).
cnf(c_0_105,negated_conjecture,
rearsegP(tl(sk1),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_94]),c_0_88])]) ).
cnf(c_0_106,negated_conjecture,
( rearsegP(app(X1,tl(sk1)),nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_94]),c_0_88])]) ).
cnf(c_0_107,axiom,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause120 ).
cnf(c_0_108,negated_conjecture,
( rearsegP(cons(X1,tl(sk1)),nil)
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_88])]) ).
cnf(c_0_109,axiom,
( ssList(cons(X1,X2))
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause86 ).
cnf(c_0_110,axiom,
( app(app(X3,X2),X1) = app(X3,app(X2,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause149 ).
cnf(c_0_111,negated_conjecture,
( rearsegP(cons(X1,tl(sk1)),nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_94])]) ).
cnf(c_0_112,axiom,
( app(skaf46(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
clause131 ).
cnf(c_0_113,axiom,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
clause58 ).
cnf(c_0_114,negated_conjecture,
( X1 = sk6
| app(sk1,X1) != sk4
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_52]),c_0_54]),c_0_53])]) ).
cnf(c_0_115,negated_conjecture,
( app(sk1,app(sk6,X1)) = app(sk4,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_52]),c_0_53]),c_0_54])]) ).
cnf(c_0_116,negated_conjecture,
rearsegP(sk1,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_87]),c_0_66])]) ).
cnf(c_0_117,plain,
( app(skaf46(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_94])]) ).
cnf(c_0_118,axiom,
ssList(skaf46(X1,X2)),
clause50 ).
cnf(c_0_119,negated_conjecture,
( app(sk6,X1) = sk6
| app(sk4,X1) != sk4
| ~ ssList(app(sk6,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,axiom,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
clause60 ).
cnf(c_0_121,negated_conjecture,
app(skaf46(sk1,nil),nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_116]),c_0_94]),c_0_53])]) ).
cnf(c_0_122,plain,
( skaf46(X1,nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_117]),c_0_118])]) ).
cnf(c_0_123,negated_conjecture,
( app(sk6,nil) = sk6
| ~ ssList(app(sk6,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_93]),c_0_94]),c_0_61])]) ).
cnf(c_0_124,plain,
( app(nil,skaf45(X1,nil)) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_120]),c_0_94])]) ).
cnf(c_0_125,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_110]),c_0_77]) ).
cnf(c_0_126,negated_conjecture,
app(sk1,nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_53])]) ).
cnf(c_0_127,negated_conjecture,
app(sk6,nil) = sk6,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_77]),c_0_54]),c_0_94])]) ).
cnf(c_0_128,axiom,
( app(nil,X1) = X1
| ~ ssList(X1) ),
clause74 ).
cnf(c_0_129,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_92,c_0_124]),c_0_99]),c_0_94])])]) ).
cnf(c_0_130,negated_conjecture,
( ssList(app(X1,sk1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_94]),c_0_53])]) ).
cnf(c_0_131,axiom,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
clause138 ).
cnf(c_0_132,negated_conjecture,
( app(sk6,app(nil,X1)) = app(sk6,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_127]),c_0_54]),c_0_94])]) ).
cnf(c_0_133,plain,
( skaf45(X1,nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_124]),c_0_99])]) ).
cnf(c_0_134,negated_conjecture,
skaf45(app(nil,sk1),nil) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_53]),c_0_94])]) ).
cnf(c_0_135,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[c_0_131]) ).
cnf(c_0_136,negated_conjecture,
( app(sk4,app(nil,X1)) = app(sk1,app(sk6,X1))
| ~ ssList(app(nil,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_132]) ).
cnf(c_0_137,negated_conjecture,
( app(nil,sk1) = sk1
| ~ ssList(app(nil,sk1)) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_138,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_139,negated_conjecture,
( memberP(sk4,hd(sk1))
| ~ ssList(tl(sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_65]),c_0_66])]) ).
cnf(c_0_140,negated_conjecture,
( app(sk4,app(nil,X1)) = app(sk1,app(sk6,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_77]),c_0_94])]) ).
cnf(c_0_141,negated_conjecture,
app(nil,sk1) = sk1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_77]),c_0_94]),c_0_53])]) ).
cnf(c_0_142,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_138]) ).
cnf(c_0_143,axiom,
( app(skaf42(X1,X2),cons(X2,skaf43(X2,X1))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
clause169 ).
cnf(c_0_144,negated_conjecture,
memberP(sk4,hd(sk1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_72]),c_0_61])]),c_0_62]) ).
cnf(c_0_145,negated_conjecture,
app(sk1,app(sk6,sk1)) = app(sk4,sk1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_53])]) ).
cnf(c_0_146,axiom,
( cons(X1,app(X2,X3)) = app(cons(X1,X2),X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
clause157 ).
cnf(c_0_147,axiom,
( app(X1,X2) = nil
| nil != X1
| nil != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
clause145 ).
cnf(c_0_148,negated_conjecture,
( ~ ssList(app(app(X1,cons(hd(sk1),X2)),sk1))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ duplicatefreeP(app(app(X1,cons(hd(sk1),X2)),sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_87]),c_0_66]),c_0_88])]) ).
cnf(c_0_149,negated_conjecture,
app(skaf42(sk4,hd(sk1)),cons(hd(sk1),skaf43(hd(sk1),sk4))) = sk4,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_66]),c_0_61])]) ).
cnf(c_0_150,negated_conjecture,
ssList(app(sk4,sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_145]),c_0_53]),c_0_54])]) ).
cnf(c_0_151,axiom,
ssList(skaf43(X1,X2)),
clause52 ).
cnf(c_0_152,axiom,
ssList(skaf42(X1,X2)),
clause53 ).
cnf(c_0_153,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_146]),c_0_109]) ).
cnf(c_0_154,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_147])]),c_0_94])]) ).
cnf(c_0_155,negated_conjecture,
~ duplicatefreeP(app(sk4,sk1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150]),c_0_151]),c_0_152])]) ).
cnf(c_0_156,axiom,
( duplicatefreeP(X1)
| ssItem(X2)
| ~ ssList(X1) ),
clause72 ).
cnf(c_0_157,negated_conjecture,
( memberP(X2,sk5(X3,X2,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != sk1 ),
co1_9 ).
cnf(c_0_158,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_94])]) ).
cnf(c_0_159,axiom,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
clause71 ).
cnf(c_0_160,negated_conjecture,
ssItem(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_150])]) ).
cnf(c_0_161,axiom,
( singletonP(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| ~ ssList(X2) ),
clause116 ).
cnf(c_0_162,negated_conjecture,
( memberP(nil,sk5(X1,nil,X2))
| app(cons(X2,nil),X1) != sk1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_128]),c_0_94])]),c_0_158]) ).
cnf(c_0_163,plain,
~ memberP(nil,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).
cnf(c_0_164,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_161]) ).
cnf(c_0_165,negated_conjecture,
( app(cons(X1,nil),X2) != sk1
| ~ ssList(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_160])]),c_0_163]) ).
cnf(c_0_166,axiom,
( cons(skaf44(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
clause101 ).
cnf(c_0_167,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_109]),c_0_94])]) ).
cnf(c_0_168,negated_conjecture,
( app(X1,X2) != sk1
| ~ singletonP(X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_169,plain,
( app(cons(X1,nil),X2) = cons(X1,X2)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_160])]) ).
cnf(c_0_170,plain,
singletonP(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_160])]) ).
cnf(c_0_171,plain,
ssList(cons(X1,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_160])]) ).
cnf(c_0_172,negated_conjecture,
( cons(X1,X2) != sk1
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170]),c_0_171])]) ).
cnf(c_0_173,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_87]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC226-1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 18:11:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.22/1.32 % Version : CSE_E---1.5
% 1.22/1.32 % Problem : theBenchmark.p
% 1.22/1.32 % Proof found
% 1.22/1.32 % SZS status Theorem for theBenchmark.p
% 1.22/1.32 % SZS output start Proof
% See solution above
% 1.22/1.33 % Total time : 0.735000 s
% 1.22/1.33 % SZS output end Proof
% 1.22/1.33 % Total time : 0.741000 s
%------------------------------------------------------------------------------