TPTP Axioms File: SWC001-0.ax
%--------------------------------------------------------------------------
% File : SWC001-0 : TPTP v8.2.0. Released v2.4.0.
% Domain : Software Creation
% Axioms : List specification
% Version : [Wei00] axioms.
% English : Components in a software library specified in first-order logic
% Refs : [Wei00] Weidenbach (2000), Software Reuse of List Functions Ve
% : [FSS98] Fischer et al. (1998), Deduction-Based Software Compon
% Source : [TPTP]
% Names :
% Status : Satisfiable
% Syntax : Number of clauses : 185 ( 54 unt; 33 nHn; 142 RR)
% Number of literals : 604 ( 98 equ; 398 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 0 prp; 1-2 aty)
% Number of functors : 49 ( 49 usr; 3 con; 0-2 aty)
% Number of variables : 326 ( 49 sgn)
% SPC :
% Comments : Created from SWC001+1.ax using FLOTTER
%--------------------------------------------------------------------------
cnf(clause1,axiom,
equalelemsP(nil) ).
cnf(clause2,axiom,
duplicatefreeP(nil) ).
cnf(clause3,axiom,
strictorderedP(nil) ).
cnf(clause4,axiom,
totalorderedP(nil) ).
cnf(clause5,axiom,
strictorderP(nil) ).
cnf(clause6,axiom,
totalorderP(nil) ).
cnf(clause7,axiom,
cyclefreeP(nil) ).
cnf(clause8,axiom,
ssList(nil) ).
cnf(clause9,axiom,
ssItem(skac3) ).
cnf(clause10,axiom,
ssItem(skac2) ).
cnf(clause11,axiom,
~ singletonP(nil) ).
cnf(clause12,axiom,
ssItem(skaf83(U)) ).
cnf(clause13,axiom,
ssList(skaf82(U)) ).
cnf(clause14,axiom,
ssList(skaf81(U)) ).
cnf(clause15,axiom,
ssList(skaf80(U)) ).
cnf(clause16,axiom,
ssItem(skaf79(U)) ).
cnf(clause17,axiom,
ssItem(skaf78(U)) ).
cnf(clause18,axiom,
ssList(skaf77(U)) ).
cnf(clause19,axiom,
ssList(skaf76(U)) ).
cnf(clause20,axiom,
ssList(skaf75(U)) ).
cnf(clause21,axiom,
ssItem(skaf74(U)) ).
cnf(clause22,axiom,
ssList(skaf73(U)) ).
cnf(clause23,axiom,
ssList(skaf72(U)) ).
cnf(clause24,axiom,
ssList(skaf71(U)) ).
cnf(clause25,axiom,
ssItem(skaf70(U)) ).
cnf(clause26,axiom,
ssItem(skaf69(U)) ).
cnf(clause27,axiom,
ssList(skaf68(U)) ).
cnf(clause28,axiom,
ssList(skaf67(U)) ).
cnf(clause29,axiom,
ssList(skaf66(U)) ).
cnf(clause30,axiom,
ssItem(skaf65(U)) ).
cnf(clause31,axiom,
ssItem(skaf64(U)) ).
cnf(clause32,axiom,
ssList(skaf63(U)) ).
cnf(clause33,axiom,
ssList(skaf62(U)) ).
cnf(clause34,axiom,
ssList(skaf61(U)) ).
cnf(clause35,axiom,
ssItem(skaf60(U)) ).
cnf(clause36,axiom,
ssItem(skaf59(U)) ).
cnf(clause37,axiom,
ssList(skaf58(U)) ).
cnf(clause38,axiom,
ssList(skaf57(U)) ).
cnf(clause39,axiom,
ssList(skaf56(U)) ).
cnf(clause40,axiom,
ssItem(skaf55(U)) ).
cnf(clause41,axiom,
ssItem(skaf54(U)) ).
cnf(clause42,axiom,
ssList(skaf53(U)) ).
cnf(clause43,axiom,
ssList(skaf52(U)) ).
cnf(clause44,axiom,
ssList(skaf51(U)) ).
cnf(clause45,axiom,
ssItem(skaf50(U)) ).
cnf(clause46,axiom,
ssItem(skaf49(U)) ).
cnf(clause47,axiom,
ssItem(skaf44(U)) ).
cnf(clause48,axiom,
ssList(skaf48(U,V)) ).
cnf(clause49,axiom,
ssList(skaf47(U,V)) ).
cnf(clause50,axiom,
ssList(skaf46(U,V)) ).
cnf(clause51,axiom,
ssList(skaf45(U,V)) ).
cnf(clause52,axiom,
ssList(skaf43(U,V)) ).
cnf(clause53,axiom,
ssList(skaf42(U,V)) ).
cnf(clause54,axiom,
skac3 != skac2 ).
cnf(clause55,axiom,
( ~ ssItem(U)
| geq(U,U) ) ).
cnf(clause56,axiom,
( ~ ssList(U)
| segmentP(U,nil) ) ).
cnf(clause57,axiom,
( ~ ssList(U)
| segmentP(U,U) ) ).
cnf(clause58,axiom,
( ~ ssList(U)
| rearsegP(U,nil) ) ).
cnf(clause59,axiom,
( ~ ssList(U)
| rearsegP(U,U) ) ).
cnf(clause60,axiom,
( ~ ssList(U)
| frontsegP(U,nil) ) ).
cnf(clause61,axiom,
( ~ ssList(U)
| frontsegP(U,U) ) ).
cnf(clause62,axiom,
( ~ ssItem(U)
| leq(U,U) ) ).
cnf(clause63,axiom,
( ~ lt(U,U)
| ~ ssItem(U) ) ).
cnf(clause64,axiom,
( ~ ssItem(U)
| equalelemsP(cons(U,nil)) ) ).
cnf(clause65,axiom,
( ~ ssItem(U)
| duplicatefreeP(cons(U,nil)) ) ).
cnf(clause66,axiom,
( ~ ssItem(U)
| strictorderedP(cons(U,nil)) ) ).
cnf(clause67,axiom,
( ~ ssItem(U)
| totalorderedP(cons(U,nil)) ) ).
cnf(clause68,axiom,
( ~ ssItem(U)
| strictorderP(cons(U,nil)) ) ).
cnf(clause69,axiom,
( ~ ssItem(U)
| totalorderP(cons(U,nil)) ) ).
cnf(clause70,axiom,
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ) ).
cnf(clause71,axiom,
( ~ memberP(nil,U)
| ~ ssItem(U) ) ).
cnf(clause72,axiom,
( ~ ssList(U)
| duplicatefreeP(U)
| ssItem(V) ) ).
cnf(clause73,axiom,
( ~ ssList(U)
| app(U,nil) = U ) ).
cnf(clause74,axiom,
( ~ ssList(U)
| app(nil,U) = U ) ).
cnf(clause75,axiom,
( ~ ssList(U)
| ssList(tl(U))
| nil = U ) ).
cnf(clause76,axiom,
( ~ ssList(U)
| ssItem(hd(U))
| nil = U ) ).
cnf(clause77,axiom,
( ~ ssList(U)
| ssList(tl(U))
| nil = U ) ).
cnf(clause78,axiom,
( ~ ssList(U)
| ssItem(hd(U))
| nil = U ) ).
cnf(clause79,axiom,
( nil != U
| ~ ssList(U)
| segmentP(nil,U) ) ).
cnf(clause80,axiom,
( ~ segmentP(nil,U)
| ~ ssList(U)
| nil = U ) ).
cnf(clause81,axiom,
( nil != U
| ~ ssList(U)
| rearsegP(nil,U) ) ).
cnf(clause82,axiom,
( ~ rearsegP(nil,U)
| ~ ssList(U)
| nil = U ) ).
cnf(clause83,axiom,
( nil != U
| ~ ssList(U)
| frontsegP(nil,U) ) ).
cnf(clause84,axiom,
( ~ frontsegP(nil,U)
| ~ ssList(U)
| nil = U ) ).
cnf(clause85,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ) ).
cnf(clause86,axiom,
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ).
cnf(clause87,axiom,
( ~ ssList(U)
| cyclefreeP(U)
| leq(skaf50(U),skaf49(U)) ) ).
cnf(clause88,axiom,
( ~ ssList(U)
| cyclefreeP(U)
| leq(skaf49(U),skaf50(U)) ) ).
cnf(clause89,axiom,
( skaf79(U) != skaf78(U)
| ~ ssList(U)
| equalelemsP(U) ) ).
cnf(clause90,axiom,
( ~ lt(skaf69(U),skaf70(U))
| ~ ssList(U)
| strictorderedP(U) ) ).
cnf(clause91,axiom,
( ~ leq(skaf64(U),skaf65(U))
| ~ ssList(U)
| totalorderedP(U) ) ).
cnf(clause92,axiom,
( ~ lt(skaf60(U),skaf59(U))
| ~ ssList(U)
| strictorderP(U) ) ).
cnf(clause93,axiom,
( ~ lt(skaf59(U),skaf60(U))
| ~ ssList(U)
| strictorderP(U) ) ).
cnf(clause94,axiom,
( ~ leq(skaf55(U),skaf54(U))
| ~ ssList(U)
| totalorderP(U) ) ).
cnf(clause95,axiom,
( ~ leq(skaf54(U),skaf55(U))
| ~ ssList(U)
| totalorderP(U) ) ).
cnf(clause96,axiom,
( ~ ssItem(U)
| ~ ssList(V)
| tl(cons(U,V)) = V ) ).
cnf(clause97,axiom,
( ~ ssItem(U)
| ~ ssList(V)
| hd(cons(U,V)) = U ) ).
cnf(clause98,axiom,
( cons(U,V) != nil
| ~ ssItem(U)
| ~ ssList(V) ) ).
cnf(clause99,axiom,
( cons(U,V) != V
| ~ ssItem(U)
| ~ ssList(V) ) ).
cnf(clause100,axiom,
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| V = U ) ).
cnf(clause101,axiom,
( ~ singletonP(U)
| ~ ssList(U)
| cons(skaf44(U),nil) = U ) ).
cnf(clause102,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| V = U ) ).
cnf(clause103,axiom,
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) ) ).
cnf(clause104,axiom,
( ~ ssList(U)
| cons(hd(U),tl(U)) = U
| nil = U ) ).
cnf(clause105,axiom,
( ~ gt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(V,U) ) ).
cnf(clause106,axiom,
( ~ lt(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| gt(V,U) ) ).
cnf(clause107,axiom,
( ~ geq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(V,U) ) ).
cnf(clause108,axiom,
( ~ leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| geq(V,U) ) ).
cnf(clause109,axiom,
( ~ ssList(U)
| cons(skaf83(U),skaf82(U)) = U
| nil = U ) ).
cnf(clause110,axiom,
( ~ gt(U,V)
| ~ gt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) ) ).
cnf(clause111,axiom,
( U != V
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ) ).
cnf(clause112,axiom,
( nil != U
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ).
cnf(clause113,axiom,
( nil != U
| ~ ssList(U)
| ~ ssItem(V)
| totalorderedP(cons(V,U)) ) ).
cnf(clause114,axiom,
( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) ) ).
cnf(clause115,axiom,
( U != V
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ) ).
cnf(clause116,axiom,
( cons(U,nil) != V
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ) ).
cnf(clause117,axiom,
( U != V
| ~ neq(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ) ).
cnf(clause118,axiom,
( app(U,V) != nil
| ~ ssList(V)
| ~ ssList(U)
| nil = U ) ).
cnf(clause119,axiom,
( app(U,V) != nil
| ~ ssList(V)
| ~ ssList(U)
| nil = V ) ).
cnf(clause120,axiom,
( ~ ssItem(U)
| ~ ssList(V)
| app(cons(U,nil),V) = cons(U,V) ) ).
cnf(clause121,axiom,
( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| U = V ) ).
cnf(clause122,axiom,
( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| U = V ) ).
cnf(clause123,axiom,
( ~ ssList(U)
| ~ ssList(V)
| nil = V
| hd(app(V,U)) = hd(V) ) ).
cnf(clause124,axiom,
( ~ strictorderedP(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U)
| strictorderedP(V)
| nil = V ) ).
cnf(clause125,axiom,
( ~ totalorderedP(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U)
| totalorderedP(V)
| nil = V ) ).
cnf(clause126,axiom,
( ~ geq(U,V)
| ~ geq(V,U)
| ~ ssItem(U)
| ~ ssItem(V)
| V = U ) ).
cnf(clause127,axiom,
( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| V = U ) ).
cnf(clause128,axiom,
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| V = U ) ).
cnf(clause129,axiom,
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| V = U ) ).
cnf(clause130,axiom,
( ~ leq(U,V)
| ~ leq(V,U)
| ~ ssItem(U)
| ~ ssItem(V)
| V = U ) ).
cnf(clause131,axiom,
( ~ rearsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| app(skaf46(U,V),V) = U ) ).
cnf(clause132,axiom,
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| app(V,skaf45(U,V)) = U ) ).
cnf(clause133,axiom,
( ~ ssList(U)
| ~ ssList(V)
| nil = V
| tl(app(V,U)) = app(tl(V),U) ) ).
cnf(clause134,axiom,
( ~ strictorderedP(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U)
| lt(U,hd(V))
| nil = V ) ).
cnf(clause135,axiom,
( ~ totalorderedP(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U)
| leq(U,hd(V))
| nil = V ) ).
cnf(clause136,axiom,
( ~ rearsegP(U,V)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| rearsegP(app(W,U),V) ) ).
cnf(clause137,axiom,
( ~ frontsegP(U,V)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| frontsegP(app(U,W),V) ) ).
cnf(clause138,axiom,
( U != V
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ) ).
cnf(clause139,axiom,
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| memberP(cons(W,U),V) ) ).
cnf(clause140,axiom,
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ) ).
cnf(clause141,axiom,
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) ) ).
cnf(clause142,axiom,
( ~ ssList(U)
| equalelemsP(U)
| app(skaf80(U),cons(skaf78(U),cons(skaf79(U),skaf81(U)))) = U ) ).
cnf(clause143,axiom,
( app(U,V) != W
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) ) ).
cnf(clause144,axiom,
( app(U,V) != W
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) ) ).
cnf(clause145,axiom,
( nil != U
| nil != V
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) = nil ) ).
cnf(clause146,axiom,
( ~ gt(U,V)
| ~ gt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| gt(U,W) ) ).
cnf(clause147,axiom,
( ~ leq(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,W) ) ).
cnf(clause148,axiom,
( ~ geq(U,V)
| ~ geq(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| geq(U,W) ) ).
cnf(clause149,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| app(app(W,V),U) = app(W,app(V,U)) ) ).
cnf(clause150,axiom,
( app(U,V) != app(U,W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| V = W ) ).
cnf(clause151,axiom,
( app(U,V) != app(W,V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| U = W ) ).
cnf(clause152,axiom,
( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(U,W) ) ).
cnf(clause153,axiom,
( ~ rearsegP(U,V)
| ~ rearsegP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| rearsegP(U,W) ) ).
cnf(clause154,axiom,
( ~ frontsegP(U,V)
| ~ frontsegP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| frontsegP(U,W) ) ).
cnf(clause155,axiom,
( ~ lt(U,V)
| ~ lt(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,W) ) ).
cnf(clause156,axiom,
( ~ leq(U,V)
| ~ leq(V,W)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,W) ) ).
cnf(clause157,axiom,
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| cons(U,app(V,W)) = app(cons(U,V),W) ) ).
cnf(clause158,axiom,
( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W)
| memberP(U,W) ) ).
cnf(clause159,axiom,
( ~ leq(U,hd(V))
| ~ totalorderedP(V)
| ~ ssList(V)
| ~ ssItem(U)
| totalorderedP(cons(U,V))
| nil = V ) ).
cnf(clause160,axiom,
( ~ lt(U,hd(V))
| ~ strictorderedP(V)
| ~ ssList(V)
| ~ ssItem(U)
| strictorderedP(cons(U,V))
| nil = V ) ).
cnf(clause161,axiom,
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| W = U ) ).
cnf(clause162,axiom,
( ~ ssList(U)
| duplicatefreeP(U)
| app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U ) ).
cnf(clause163,axiom,
( ~ ssList(U)
| strictorderedP(U)
| app(app(skaf71(U),cons(skaf69(U),skaf72(U))),cons(skaf70(U),skaf73(U))) = U ) ).
cnf(clause164,axiom,
( ~ ssList(U)
| totalorderedP(U)
| app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U ) ).
cnf(clause165,axiom,
( ~ ssList(U)
| strictorderP(U)
| app(app(skaf61(U),cons(skaf59(U),skaf62(U))),cons(skaf60(U),skaf63(U))) = U ) ).
cnf(clause166,axiom,
( ~ ssList(U)
| totalorderP(U)
| app(app(skaf56(U),cons(skaf54(U),skaf57(U))),cons(skaf55(U),skaf58(U))) = U ) ).
cnf(clause167,axiom,
( ~ ssList(U)
| cyclefreeP(U)
| app(app(skaf51(U),cons(skaf49(U),skaf52(U))),cons(skaf50(U),skaf53(U))) = U ) ).
cnf(clause168,axiom,
( ~ segmentP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| app(app(skaf47(U,V),V),skaf48(V,U)) = U ) ).
cnf(clause169,axiom,
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ).
cnf(clause170,axiom,
( cons(U,V) != cons(W,X)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| U = W ) ).
cnf(clause171,axiom,
( cons(U,V) != cons(W,X)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(X)
| ~ ssList(V)
| X = V ) ).
cnf(clause172,axiom,
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) ) ).
cnf(clause173,axiom,
( app(app(U,V),W) != X
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ) ).
cnf(clause174,axiom,
( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U)
| frontsegP(V,X) ) ).
cnf(clause175,axiom,
( app(U,cons(V,W)) != X
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ) ).
cnf(clause176,axiom,
( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U)
| U = W ) ).
cnf(clause177,axiom,
( tl(U) != tl(V)
| hd(U) != hd(V)
| ~ ssList(U)
| ~ ssList(V)
| nil = V
| U = V
| nil = U ) ).
cnf(clause178,axiom,
( ~ frontsegP(U,V)
| W != X
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(W)
| frontsegP(cons(W,U),cons(X,V)) ) ).
cnf(clause179,axiom,
( app(app(U,cons(V,W)),cons(V,X)) != Y
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(Y) ) ).
cnf(clause180,axiom,
( app(U,cons(V,cons(W,X))) != Y
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| V = W ) ).
cnf(clause181,axiom,
( app(app(U,cons(V,W)),cons(X,Y)) != Z
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) ) ).
cnf(clause182,axiom,
( app(app(U,cons(V,W)),cons(X,Y)) != Z
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) ) ).
cnf(clause183,axiom,
( app(app(U,cons(V,W)),cons(X,Y)) != Z
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderP(Z)
| ~ ssList(Z)
| lt(V,X)
| lt(X,V) ) ).
cnf(clause184,axiom,
( app(app(U,cons(V,W)),cons(X,Y)) != Z
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderP(Z)
| ~ ssList(Z)
| leq(V,X)
| leq(X,V) ) ).
cnf(clause185,axiom,
( ~ leq(U,V)
| ~ leq(V,U)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ cyclefreeP(Z)
| ~ ssList(Z) ) ).
%--------------------------------------------------------------------------