%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT136+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:04 PM UTC 2026
% Result : Theorem 132.26s 110.16s
% Output : CNFRefutation 206.43s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_623)
% Comments :
%------------------------------------------------------------------------------
fof(fact_converse__rtranclE2,axiom,
! [X44,X86,X87,X88,X64,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X5,X29),X64),X88) != hAPP(hAPP(c_Product__Type_OPair(X5,X29),X87),X86)
=> ~ ! [X32,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33))),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_mem__splitE,axiom,
! [X78,X4,X47,X29,X34,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X34),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29,X47,tc_fun(X5,tc_HOL_Obool)),X4),X78)))
=> ~ ! [X3,X66] :
( X78 = hAPP(hAPP(c_Product__Type_OPair(X29,X47),X3),X66)
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X34),hAPP(hAPP(X4,X3),X66))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitE) ).
fof(fact_Cons__listrel1E2,axiom,
! [X44,X52,X13,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_List_Olistrel1(X5,X44)))
=> ( ! [X3] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X52)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X13)),X44)) )
=> ~ ! [X75] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X13),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X75),X52)),c_List_Olistrel1(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1E2) ).
fof(fact_lexord__append__leftD,axiom,
! [X44,X63,X53,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X12),X53)),hAPP(hAPP(c_List_Oappend(X5),X12),X63))),c_List_Olexord(X5,X44)))
=> ( ! [X32] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X32),X32)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X53),X63)),c_List_Olexord(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_Cons__listrel1E1,axiom,
! [X44,X52,X51,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),X52)),c_List_Olistrel1(X5,X44)))
=> ( ! [X66] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X5),X66),X51)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X66)),X44)) )
=> ~ ! [X75] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X75)),c_List_Olistrel1(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1E1) ).
fof(fact_listrel__Cons2,axiom,
! [X44,X52,X13,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_List_Olistrel(X5,X44)))
=> ~ ! [X3,X65] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X65)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X13)),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X65),X52)),c_List_Olistrel(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_listrel__Cons1,axiom,
! [X44,X51,X52,X13,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52)),X51)),c_List_Olistrel(X5,X44)))
=> ~ ! [X66,X67] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X66),X67)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X66)),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X52),X67)),c_List_Olistrel(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_compose__assoc,axiom,
! [X48,X49,X50,X46,X1,X47,X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29,X47)),X1),c_FuncSet_OPi(X29,X47,X6,c_COMBK(tc_fun(X47,tc_HOL_Obool),X29,X46))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X47,X50)),X49),c_FuncSet_OPi(X47,X50,X46,c_COMBK(tc_fun(X50,tc_HOL_Obool),X47,X48))))
=> c_FuncSet_Ocompose(X5,X47,X50,X7,X49,c_FuncSet_Ocompose(X5,X29,X47,X7,X1,X2)) = c_FuncSet_Ocompose(X5,X29,X50,X7,c_FuncSet_Ocompose(X29,X47,X50,X6,X49,X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__assoc) ).
fof(fact_compose__def,axiom,
! [X2,X1,X7,X29,X47,X5] : c_FuncSet_Ocompose(X5,X47,X29,X7,X1,X2) = c_FuncSet_Orestrict(X5,X29,hAPP(hAPP(c_COMBB(X47,X29,X5),X1),X2),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__def) ).
fof(fact_funcset__compose,axiom,
! [X46,X1,X47,X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29,X47)),X1),c_FuncSet_OPi(X29,X47,X6,c_COMBK(tc_fun(X47,tc_HOL_Obool),X29,X46))))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X47)),c_FuncSet_Ocompose(X5,X29,X47,X7,X1,X2)),c_FuncSet_OPi(X5,X47,X7,c_COMBK(tc_fun(X47,tc_HOL_Obool),X5,X46)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__compose) ).
fof(fact_RangeE,axiom,
! [X44,X29,X15,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X15),c_Relation_ORange(X29,X5,X44)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X5)),hAPP(hAPP(c_Product__Type_OPair(X29,X5),X3),X15)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).
fof(fact_Id__compose,axiom,
! [X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional(X5,X29,X7)))
=> c_FuncSet_Ocompose(X5,X29,X29,X7,c_FuncSet_Orestrict(X29,X29,c_COMBI(X29),X6),X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__compose) ).
fof(fact_compose__extensional,axiom,
! [X1,X2,X7,X47,X29,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),c_FuncSet_Ocompose(X5,X47,X29,X7,X2,X1)),c_FuncSet_Oextensional(X5,X29,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__extensional) ).
fof(fact_lexord__irreflexive,axiom,
! [X13,X44,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X13),X13)),c_List_Olexord(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_override__on__def,axiom,
! [X1,X2,X29,X7,X16,X5] :
( ( hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> c_Fun_Ooverride__on(X5,X29,X2,X1,X7,X16) = hAPP(X1,X16) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> c_Fun_Ooverride__on(X5,X29,X2,X1,X7,X16) = hAPP(X2,X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__def) ).
fof(fact_override__on__apply__notin,axiom,
! [X1,X2,X29,X7,X16,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> c_Fun_Ooverride__on(X5,X29,X2,X1,X7,X16) = hAPP(X2,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).
fof(fact_compose__Id,axiom,
! [X6,X7,X1,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X1),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X1),c_FuncSet_Oextensional(X5,X29,X7)))
=> c_FuncSet_Ocompose(X5,X5,X29,X7,X1,c_FuncSet_Orestrict(X5,X5,c_COMBI(X5),X7)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__Id) ).
fof(fact_DomainE,axiom,
! [X44,X29,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),c_Relation_ODomain(X5,X29,X44)))
=> ~ ! [X66] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X66)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).
fof(fact_compose__id__inv__into,axiom,
! [X6,X7,X2,X5,X29] :
( c_Set_Oimage(X29,X5,X2,X7) = X6
=> c_FuncSet_Ocompose(X5,X29,X5,X6,X2,c_FuncSet_Orestrict(X5,X29,c_Hilbert__Choice_Oinv__into(X29,X5,X7,X2),X6)) = c_FuncSet_Orestrict(X5,X5,c_COMBI(X5),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__id__inv__into) ).
fof(fact_notin__Lin__iff,axiom,
! [X13,X12,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> ( X12 != X13
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),X22))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X13),X12)),X22)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X15,X16,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X15)),X22))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X15),X16)),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_not__acc__down,axiom,
! [X11,X12,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X11)))
=> ~ ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X69),X12)),X11))
=> hBOOL(hAPP(hAPP(c_member(X5),X69),c_Wellfounded_Oacc(X5,X11))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(fact_not__Nil__listrel1,axiom,
! [X44,X51,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X51)),c_List_Olistrel1(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_Nil__notin__lex,axiom,
! [X44,X52,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X52)),c_List_Olex(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_not__listrel1__Nil,axiom,
! [X44,X51,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_Nil2__notin__lex,axiom,
! [X44,X51,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),c_List_Olist_ONil(X5))),c_List_Olex(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_lexord__Nil__right,axiom,
! [X44,X12,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_surj__compose,axiom,
! [X46,X1,X47,X6,X7,X2,X5,X29] :
( c_Set_Oimage(X29,X5,X2,X7) = X6
=> ( c_Set_Oimage(X5,X47,X1,X6) = X46
=> c_Set_Oimage(X29,X47,c_FuncSet_Ocompose(X29,X5,X47,X7,X1,X2),X7) = X46 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__compose) ).
fof(fact_PiE,axiom,
! [X12,X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,X6)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X12)),hAPP(X6,X12)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_extensional__funcset__arb,axiom,
! [X12,X97,X10,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional__funcset(X5,X29,X10,X97)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X10))
=> hAPP(X2,X12) = c_HOL_Oundefined(X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
fof(fact_cut__def,axiom,
! [X2,X29,X44,X12,X13,X5] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X12)),X44))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X2),X44),X12),X13) = hAPP(X2,X13) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X12)),X44))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X2),X44),X12),X13) = c_HOL_Oundefined(X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__def) ).
fof(fact_in__measures_I1_J,axiom,
! [X13,X12,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [X13,X11,X12,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),c_Relation_ODomain(X5,X5,X11)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Transitive__Closure_Ortrancl(X5,X11)))
<=> X12 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_inf2E,axiom,
! [X13,X12,X6,X7,X29,X5] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),X7,X6),X12),X13))
=> ~ ( hBOOL(hAPP(hAPP(X7,X12),X13))
=> ~ hBOOL(hAPP(hAPP(X6,X12),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).
fof(fact_compose__eq,axiom,
! [X2,X1,X29,X47,X7,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Ocompose(X5,X47,X29,X7,X1,X2),X12) = hAPP(X1,hAPP(X2,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__eq) ).
fof(fact_irrefl__def,axiom,
! [X44,X5] :
( c_Relation_Oirrefl(X5,X44)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_extensional__arb,axiom,
! [X12,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional(X5,X29,X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(X2,X12) = c_HOL_Oundefined(X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__arb) ).
fof(fact_IntE,axiom,
! [X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).
fof(fact_dropWhile__eq__Cons__conv,axiom,
! [X52,X13,X51,X24,X5] :
( c_List_OdropWhile(X5,X24,X51) = hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52)
<=> ( X51 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X24,X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))
& ~ hBOOL(hAPP(X24,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
fof(fact_restrict__def,axiom,
! [X2,X29,X7,X12,X5] :
( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = c_HOL_Oundefined(X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__def) ).
fof(fact_restrict__apply,axiom,
! [X2,X29,X7,X12,X5] :
( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = c_HOL_Oundefined(X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__apply) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X17] : ~ c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X17),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_inf1E,axiom,
! [X12,X6,X7,X5] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X12))
=> ~ ( hBOOL(hAPP(X7,X12))
=> ~ hBOOL(hAPP(X6,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
fof(fact_internal__split__conv,axiom,
! [X15,X16,X4,X5,X47,X29] : hAPP(hAPP(c_Product__Type_Ointernal__split(X29,X47,X5),X4),hAPP(hAPP(c_Product__Type_OPair(X29,X47),X16),X15)) = hAPP(hAPP(X4,X16),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).
fof(fact_internal__split__def,axiom,
! [X47,X29,X5] : c_Product__Type_Ointernal__split(X5,X29,X47) = c_Product__Type_Oprod_Oprod__case(X5,X29,X47),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(fact_takeWhile__tail,axiom,
! [X89,X51,X5,X12,X24] :
( ~ hBOOL(hAPP(X24,X12))
=> c_List_OtakeWhile(X5,X24,hAPP(hAPP(c_List_Oappend(X5),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X89))) = c_List_OtakeWhile(X5,X24,X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__tail) ).
fof(fact_takeWhile_Osimps_I2_J,axiom,
! [X51,X5,X12,X24] :
( ( hBOOL(hAPP(X24,X12))
=> c_List_OtakeWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_OtakeWhile(X5,X24,X51)) )
& ( ~ hBOOL(hAPP(X24,X12))
=> c_List_OtakeWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = c_List_Olist_ONil(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
fof(fact_le__infE,axiom,
! [X20,X21,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X5,X27,X21)
=> ~ c_Orderings_Oord__class_Oless__eq(X5,X27,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X5,X29] :
( class_Orderings_Oord(X29)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,X29),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X29),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X29),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_dropWhile_Osimps_I2_J,axiom,
! [X51,X5,X12,X24] :
( ( hBOOL(hAPP(X24,X12))
=> c_List_OdropWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = c_List_OdropWhile(X5,X24,X51) )
& ( ~ hBOOL(hAPP(X24,X12))
=> c_List_OdropWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
fof(fact_less__le__not__le,axiom,
! [X13,X12,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X21,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X20,X21)
=> ~ c_Orderings_Oord__class_Oless(X5,X21,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
| X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_leD,axiom,
! [X27,X42,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> ~ c_Orderings_Oord__class_Oless(X5,X27,X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
<=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_order__less__asym,axiom,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ~ c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X20,X21,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X20)
=> ~ c_Orderings_Oord__class_Oless(X5,X20,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ~ c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ~ c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
<=> X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(help_c__fconj__2,axiom,
! [X104,X24] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X24),X104))
| hBOOL(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X104,X24] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X24),X104))
| hBOOL(X104) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(help_c__fequal__1,axiom,
! [X13,X12] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X13))
| X12 = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_linorder__cases,axiom,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ( X27 != X42
=> c_Orderings_Oord__class_Oless(X5,X42,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( X27 != X42
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X42)
=> c_Orderings_Oord__class_Oless(X5,X42,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X12,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X27,X42,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> c_Orderings_Oord__class_Oless(X5,X27,X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X42)
=> c_Orderings_Oord__class_Oless__eq(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> c_Orderings_Oord__class_Oless__eq(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_linorder__neqE__nat,axiom,
! [X42,X27] :
( X27 != X42
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X42)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X27,X5] :
( class_Orderings_Opreorder(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,X27,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(help_c__fconj__1,axiom,
! [X104,X24] :
( ~ hBOOL(X24)
| ~ hBOOL(X104)
| hBOOL(hAPP(hAPP(c_fconj,X24),X104)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_less__irrefl__nat,axiom,
! [X109] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X109,X109),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X109] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X109,X109),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_equalityE,axiom,
! [X5,X6,X7] :
( X7 = X6
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
fof(help_c__fNot__1,axiom,
! [X24] :
( ~ hBOOL(hAPP(c_fNot,X24))
| ~ hBOOL(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [X24] :
( ~ ~ hBOOL(X24)
| hBOOL(hAPP(c_fNot,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_rtrancl__induct2,axiom,
! [X24,X44,X80,X81,X82,X83,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X83),X82)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X81),X80))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44)))
=> ( hBOOL(hAPP(hAPP(X24,X83),X82))
=> ( ! [X32,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X83),X82)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44)))
=> ! [X84,X85] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X84),X85))),X44))
=> ( hBOOL(hAPP(hAPP(X24,X32),X33))
=> hBOOL(hAPP(hAPP(X24,X84),X85)) ) ) )
=> hBOOL(hAPP(hAPP(X24,X81),X80)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [X24,X44,X80,X81,X82,X83,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X83),X82)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X81),X80))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44)))
=> ( hBOOL(hAPP(hAPP(X24,X81),X80))
=> ( ! [X32,X33,X84,X85] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X84),X85))),X44))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X84),X85)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X81),X80))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44)))
=> ( hBOOL(hAPP(hAPP(X24,X84),X85))
=> hBOOL(hAPP(hAPP(X24,X32),X33)) ) ) )
=> hBOOL(hAPP(hAPP(X24,X83),X82)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_inf__Int__eq2,axiom,
! [X13,X12,X10,X11,X29,X5] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X11),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X10)),X12),X13))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X12),X13)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),X11,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_adm__wf__def,axiom,
! [X9,X11,X29,X5] :
( c_Recdef_Oadm__wf(X5,X29,X11,X9)
<=> ! [X98,X100,X3] :
( ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X69),X3)),X11))
=> hAPP(X98,X69) = hAPP(X100,X69) )
=> hAPP(hAPP(X9,X98),X3) = hAPP(hAPP(X9,X100),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__wf__def) ).
fof(fact_accp__acc__eq,axiom,
! [X12,X44,X5] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X44)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [X51,X12,X24,X5] : c_List_Opartition(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_fun(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),c_If(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(X24,X12)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_List_Olist_OCons(X5),X12))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBB(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_List_Olist(X5))),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(c_List_Olist_OCons(X5),X12)))),c_List_Opartition(X5,X24,X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(conj_0,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_pred__subset__eq2,axiom,
! [X10,X11,X29,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X11),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X10))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),X11,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_mem__splitI2,axiom,
! [X4,X34,X47,X29,X5,X78] :
( ! [X32,X33] :
( X78 = hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33)
=> hBOOL(hAPP(hAPP(c_member(X47),X34),hAPP(hAPP(X4,X32),X33))) )
=> hBOOL(hAPP(hAPP(c_member(X47),X34),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,tc_fun(X47,tc_HOL_Obool)),X4),X78))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI2) ).
fof(fact_cuts__eq,axiom,
! [X1,X12,X44,X2,X29,X5] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X2),X44),X12) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X1),X44),X12)
<=> ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X66),X12)),X44))
=> hAPP(X2,X66) = hAPP(X1,X66) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cuts__eq) ).
fof(fact__C2_C,axiom,
! [X23,X24,X25,X26,X15,X16] :
( X16 != X15
=> ( X26 != X25
=> ( X16 != X25
=> ( X15 != X26
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X23),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X14] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X15)),hAPP(X24,X14)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X25)),hAPP(X23,X14))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X15)),hAPP(v_F,X24)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X25)),hAPP(v_F,X23))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__C1_C,axiom,
! [X23,X24,X25,X26,X15,X16] :
( X16 != X15
=> ( X26 != X25
=> ( X16 != X25
=> ( X15 != X26
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X23),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X14] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X15)),hAPP(X24,X14)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X25)),hAPP(X23,X14))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X15)),hAPP(v_F,X24)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X25)),hAPP(v_F,X23))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_listrelp__listrel__eq,axiom,
! [X64,X12,X44,X5] :
( c_List_Olistrelp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X44),X12,X64)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X64)),c_List_Olistrel(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_DomainP__Domain__eq,axiom,
! [X12,X44,X29,X5] :
( c_Predicate_ODomainP(X5,X29,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X44),X12)
<=> hBOOL(hAPP(hAPP(c_member(X5),X12),c_Relation_ODomain(X5,X29,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_RangeP__Range__eq,axiom,
! [X12,X44,X29,X5] :
( c_Predicate_ORangeP(X5,X29,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X44),X12)
<=> hBOOL(hAPP(hAPP(c_member(X29),X12),c_Relation_ORange(X5,X29,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X10,X11,X29,X5] :
( hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X11) = hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBC(X29,tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_fun(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),tc_HOL_Obool),X29),c_member(tc_prod(X5,X29)))),c_Product__Type_OPair(X5,X29)))),X10)
<=> X11 = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_adm__lemma,axiom,
! [X9,X11,X29,X5] : c_Recdef_Oadm__wf(X5,X29,X11,hAPP(hAPP(c_COMBC(tc_fun(X5,X29),tc_fun(X5,X5),tc_fun(X5,X29)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X29)),tc_fun(tc_fun(X5,X5),tc_fun(X5,X29)),tc_fun(X5,X29)),c_COMBS(X5,X5,X29)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X29)),tc_fun(X5,tc_fun(X5,X29)),tc_fun(X5,X29)),hAPP(c_COMBB(tc_fun(X5,X29),tc_fun(X5,X29),X5),X9)),hAPP(hAPP(c_COMBC(tc_fun(X5,X29),tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_fun(X5,X29))),c_Recdef_Ocut(X5,X29)),X11)))),c_COMBI(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__lemma) ).
fof(fact_Pi__cong,axiom,
! [X6,X29,X1,X2,X7,X5] :
( ! [X45] :
( hBOOL(hAPP(hAPP(c_member(X5),X45),X7))
=> hAPP(X2,X45) = hAPP(X1,X45) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,X6)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X1),c_FuncSet_OPi(X5,X29,X7,X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__cong) ).
fof(fact_restrictI,axiom,
! [X6,X2,X29,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X3)),hAPP(X6,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),c_FuncSet_Orestrict(X5,X29,X2,X7)),c_FuncSet_OPi(X5,X29,X7,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrictI) ).
fof(fact_Pi__I_H,axiom,
! [X6,X2,X29,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X3)),hAPP(X6,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I_H) ).
fof(fact_Pi__I,axiom,
! [X6,X2,X29,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X3)),hAPP(X6,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X9] :
( c_Arrow__Order__Mirabelle_OIIA(X9)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X35] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X35),c_Arrow__Order__Mirabelle_OProf))
=> ! [X32,X33] :
( ! [X14] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X3,X14)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X35,X14))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X9,X3)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X9,X35))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact_restrict__in__funcset,axiom,
! [X6,X2,X29,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X3)),X6)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),c_FuncSet_Orestrict(X5,X29,X2,X7)),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
fof(fact_funcsetI,axiom,
! [X6,X2,X29,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X3)),X6)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(fact_Eps__split__eq,axiom,
! [X13,X12,X29,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X29),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29,tc_HOL_Obool),tc_fun(X29,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X12)))),hAPP(c_fequal,X13)))) = hAPP(hAPP(c_Product__Type_OPair(X5,X29),X12),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_Id__on__def_H,axiom,
! [X7,X5] : c_Relation_OId__on(X5,X7) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),c_fequal))),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_lexord__linear,axiom,
! [X13,X12,X44,X5] :
( ! [X32,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X32),X33)),X44))
| X32 = X33
| hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X32)),X44)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X13)),c_List_Olexord(X5,X44)))
| X12 = X13
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X13),X12)),c_List_Olexord(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__linear) ).
fof(fact_listsp__conj__eq,axiom,
! [X12,X6,X7,X5] :
( hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X7)),X6)),X12))
<=> ( hBOOL(hAPP(c_List_Olistsp(X5,X7),X12))
& hBOOL(hAPP(c_List_Olistsp(X5,X6),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [X44,X13,X52,X12,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X52),hAPP(hAPP(c_List_Olist_OCons(X5),X13),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X44)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44)))
& X12 = X13 )
| ( X51 = X52
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),X44)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_Pi__mono,axiom,
! [X46,X6,X29,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X29,tc_HOL_Obool),hAPP(X6,X3),hAPP(X46,X3)) )
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X29),tc_HOL_Obool),c_FuncSet_OPi(X5,X29,X7,X6),c_FuncSet_OPi(X5,X29,X7,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_in__lex__prod,axiom,
! [X43,X44,X25,X26,X15,X16,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X26),X25))),c_Wellfounded_Olex__prod(X5,X29,X44,X43)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X26)),X44))
| ( X16 = X26
& hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X29)),hAPP(hAPP(c_Product__Type_OPair(X29,X29),X15),X25)),X43)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact_dictatorI,axiom,
! [X8,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X9),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X32,X33] :
( X32 != X33
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X3,X8)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X9,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X9,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_inv__into__def,axiom,
! [X12,X2,X7,X29,X5] : hAPP(c_Hilbert__Choice_Oinv__into(X5,X29,X7,X2),X12) = c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X7))),hAPP(hAPP(c_COMBC(X5,X29,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X29,tc_fun(X29,tc_HOL_Obool),X5),c_fequal),X2)),X12))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__def) ).
fof(fact_listrel1E,axiom,
! [X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44)))
=> ~ ! [X3,X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X66)),X44))
=> ! [X57,X68] :
( X51 = hAPP(hAPP(c_List_Oappend(X5),X57),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X68))
=> X52 != hAPP(hAPP(c_List_Oappend(X5),X57),hAPP(hAPP(c_List_Olist_OCons(X5),X66),X68)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1E) ).
fof(fact_lists__IntI,axiom,
! [X6,X7,X89,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X89),c_List_Olists(X5,X7)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X89),c_List_Olists(X5,X6)))
=> hBOOL(hAPP(c_List_Olistsp(X5,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X7),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X6))),X89)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__IntI) ).
fof(fact_extensionalityI,axiom,
! [X1,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional(X5,X29,X7)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X1),c_FuncSet_Oextensional(X5,X29,X7)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hAPP(X2,X3) = hAPP(X1,X3) )
=> X2 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensionalityI) ).
fof(fact_lexord__append__left__rightI,axiom,
! [X13,X12,X53,X44,X15,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X53),hAPP(hAPP(c_List_Olist_OCons(X5),X16),X12))),hAPP(hAPP(c_List_Oappend(X5),X53),hAPP(hAPP(c_List_Olist_OCons(X5),X15),X13)))),c_List_Olexord(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
fof(fact_same__fstI,axiom,
! [X5,X11,X13,X38,X29,X12,X24] :
( hBOOL(hAPP(X24,X12))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X29)),hAPP(hAPP(c_Product__Type_OPair(X29,X29),X38),X13)),hAPP(X11,X12)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X12),X38)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X12),X13))),c_Recdef_Osame__fst(X5,X29,X24,X11))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_split__twice,axiom,
! [X78,X1,X90,X50,X2,X5,X47,X29] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29,X47,X5),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X50,X90,tc_prod(X29,X47)),X1),X78)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X50,X90,X5),hAPP(hAPP(c_COMBB(tc_fun(X90,tc_prod(X29,X47)),tc_fun(X90,X5),X50),hAPP(c_COMBB(tc_prod(X29,X47),X5,X90),hAPP(c_Product__Type_Oprod_Oprod__case(X29,X47,X5),X2))),X1)),X78),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__twice) ).
fof(fact_append__eq__append__conv2,axiom,
! [X55,X56,X52,X51,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X51),X52) = hAPP(hAPP(c_List_Oappend(X5),X56),X55)
<=> ? [X57] :
( ( X51 = hAPP(hAPP(c_List_Oappend(X5),X56),X57)
& hAPP(hAPP(c_List_Oappend(X5),X57),X52) = X55 )
| ( hAPP(hAPP(c_List_Oappend(X5),X51),X57) = X56
& X52 = hAPP(hAPP(c_List_Oappend(X5),X57),X55) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_inf__Int__eq,axiom,
! [X12,X10,X11,X5] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X10)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X5),X12),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X11,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_Range__iff,axiom,
! [X44,X29,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),c_Relation_ORange(X29,X5,X44)))
<=> ? [X66] : hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X5)),hAPP(hAPP(c_Product__Type_OPair(X29,X5),X66),X16)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [X44,X52,X13,X51,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_List_Olistrel1(X5,X44)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),X44))
& X51 = X52 )
| ( X12 = X13
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_Cons__in__lex,axiom,
! [X44,X52,X13,X51,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_List_Olex(X5,X44)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),X44))
& c_Nat_Osize__class_Osize(tc_List_Olist(X5),X51) = c_Nat_Osize__class_Osize(tc_List_Olist(X5),X52) )
| ( X12 = X13
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olex(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_lexord__cons__cons,axiom,
! [X44,X13,X15,X12,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X16),X12)),hAPP(hAPP(c_List_Olist_OCons(X5),X15),X13))),c_List_Olexord(X5,X44)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),X44))
| ( X16 = X15
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X13)),c_List_Olexord(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [X52,X51,X44,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_listrel_OCons,axiom,
! [X52,X51,X44,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),X44))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_List_Olistrel(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_OCons) ).
fof(fact_inv__into__funcset,axiom,
! [X6,X7,X2,X5,X29] :
( c_Set_Oimage(X29,X5,X2,X7) = X6
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),c_FuncSet_Orestrict(X5,X29,c_Hilbert__Choice_Oinv__into(X29,X5,X7,X2),X6)),c_FuncSet_OPi(X5,X29,X6,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X7)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__funcset) ).
fof(fact_unanimity__def,axiom,
! [X9] :
( c_Arrow__Order__Mirabelle_Ounanimity(X9)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X32,X33] :
( ! [X14] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X3,X14)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X32),X33)),hAPP(X9,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [X56,X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X44))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X52),X56)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X44))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X56)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X44)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [X12,X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X52))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
fof(fact_lexord__trans,axiom,
! [X34,X44,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X13)),c_List_Olexord(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X13),X34)),c_List_Olexord(X5,X44)))
=> ( c_Relation_Otrans(X5,X44)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X34)),c_List_Olexord(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__trans) ).
fof(fact_append__listrel1I,axiom,
! [X60,X61,X44,X52,X51,X5] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44)))
& X61 = X60 )
| ( X51 = X52
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X61),X60)),c_List_Olistrel1(X5,X44))) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X51),X61)),hAPP(hAPP(c_List_Oappend(X5),X52),X60))),c_List_Olistrel1(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__listrel1I) ).
fof(fact_lexord__append__leftI,axiom,
! [X12,X44,X63,X53,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X53),X63)),c_List_Olexord(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X12),X53)),hAPP(hAPP(c_List_Oappend(X5),X12),X63))),c_List_Olexord(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_listrel1I2,axiom,
! [X12,X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X52))),c_List_Olistrel1(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I2) ).
fof(fact_in__below,axiom,
! [X13,X12,X22,X15,X16] :
( X16 != X15
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X22),X16),X15)))
<=> ( X12 != X13
& ( X13 = X16
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X15)),X22)) )
& ( X13 != X16
=> ( ( X12 = X16
=> ( X13 = X15
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X15),X13)),X22)) ) )
& ( X12 != X16
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),X22)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_in__above,axiom,
! [X13,X12,X22,X15,X16] :
( X16 != X15
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),c_Arrow__Order__Mirabelle_Oabove(X22,X16,X15)))
<=> ( X12 != X13
& ( X12 = X15
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X13)),X22)) )
& ( X12 != X15
=> ( ( X13 = X15
=> ( X12 = X16
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X16)),X22)) ) )
& ( X13 != X15
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),X22)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_override__on__apply__in,axiom,
! [X1,X2,X29,X7,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> c_Fun_Ooverride__on(X5,X29,X2,X1,X7,X16) = hAPP(X1,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
fof(fact_inv__into__into,axiom,
! [X7,X2,X29,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),c_Set_Oimage(X29,X5,X2,X7)))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(c_Hilbert__Choice_Oinv__into(X29,X5,X7,X2),X12)),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).
fof(fact_listrel1I1,axiom,
! [X51,X44,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X51))),c_List_Olistrel1(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I1) ).
fof(fact_split__paired__Eps,axiom,
! [X24,X29,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X29),X24) = c_Hilbert__Choice_OEps(tc_prod(X5,X29),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X29),tc_HOL_Obool,X29),X24)),c_Product__Type_OPair(X5,X29)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_single__valued__confluent,axiom,
! [X34,X13,X12,X44,X5] :
( c_Relation_Osingle__valued(X5,X5,X44)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X34)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X34)),c_Transitive__Closure_Ortrancl(X5,X44)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X34),X13)),c_Transitive__Closure_Ortrancl(X5,X44))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Domain__iff,axiom,
! [X44,X29,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),c_Relation_ODomain(X5,X29,X44)))
<=> ? [X66] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X66)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(fact_Cons__eq__append__conv,axiom,
! [X56,X52,X51,X12,X5] :
( hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51) = hAPP(hAPP(c_List_Oappend(X5),X52),X56)
<=> ( ( X52 = c_List_Olist_ONil(X5)
& hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51) = X56 )
| ? [X62] :
( hAPP(hAPP(c_List_Olist_OCons(X5),X12),X62) = X52
& X51 = hAPP(hAPP(c_List_Oappend(X5),X62),X56) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append__eq__Cons__conv,axiom,
! [X51,X12,X56,X52,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X52),X56) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)
<=> ( ( X52 = c_List_Olist_ONil(X5)
& X56 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51) )
| ? [X62] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X62)
& hAPP(hAPP(c_List_Oappend(X5),X62),X56) = X51 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_inv__into__injective,axiom,
! [X13,X12,X2,X7,X29,X5] :
( hAPP(c_Hilbert__Choice_Oinv__into(X5,X29,X7,X2),X12) = hAPP(c_Hilbert__Choice_Oinv__into(X5,X29,X7,X2),X13)
=> ( hBOOL(hAPP(hAPP(c_member(X29),X12),c_Set_Oimage(X5,X29,X2,X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X29),X13),c_Set_Oimage(X5,X29,X2,X7)))
=> X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_lists__Int__eq,axiom,
! [X6,X7,X5] : c_List_Olistsp(X5,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X7),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X6))) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X7)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__Int__eq) ).
fof(fact_rotate1__def,axiom,
! [X51,X5] : c_List_Orotate1(X5,X51) = c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Oappend(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))),X51),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__def) ).
fof(fact_listsp__lists__eq,axiom,
! [X12,X7,X5] :
( hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X7)),X12))
<=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X12),c_List_Olists(X5,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).
fof(fact_in__measures_I2_J,axiom,
! [X107,X2,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X107))))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X13))
| ( hAPP(X2,X12) = hAPP(X2,X13)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_List_Omeasures(X5,X107))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_rtrancl__trans,axiom,
! [X4,X44,X15,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X15),X4)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X4)),c_Transitive__Closure_Ortrancl(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [X4,X44,X15,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),X44))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X15),X4)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X4)),c_Transitive__Closure_Ortrancl(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [X4,X44,X15,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X15),X4)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X4)),c_Transitive__Closure_Ortrancl(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_listrel__reflcl__if__listrel1,axiom,
! [X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X44)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
fof(fact_lexord__lex,axiom,
! [X44,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X13)),c_List_Olex(X5,X44)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X13)),c_List_Olexord(X5,X44)))
& c_Nat_Osize__class_Osize(tc_List_Olist(X5),X12) = c_Nat_Osize__class_Osize(tc_List_Olist(X5),X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__lex) ).
fof(fact_transD,axiom,
! [X4,X15,X16,X44,X5] :
( c_Relation_Otrans(X5,X44)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),X44))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X15),X4)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X4)),X44)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transD) ).
fof(fact_trans__def,axiom,
! [X44,X5] :
( c_Relation_Otrans(X5,X44)
<=> ! [X3,X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X66)),X44))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X66),X69)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X69)),X44)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).
fof(fact_measures__lesseq,axiom,
! [X107,X5,X13,X12,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X13))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_List_Omeasures(X5,X107)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X107)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).
fof(fact_pair__imageI,axiom,
! [X2,X47,X7,X15,X16,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15)),X7))
=> hBOOL(hAPP(hAPP(c_member(X47),hAPP(hAPP(X2,X16),X15)),c_Set_Oimage(tc_prod(X5,X29),X47,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,X47),X2),X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__imageI) ).
fof(fact_listrel1I,axiom,
! [X52,X60,X61,X51,X44,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),X44))
=> ( X51 = hAPP(hAPP(c_List_Oappend(X5),X61),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X60))
=> ( X52 = hAPP(hAPP(c_List_Oappend(X5),X61),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X60))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I) ).
fof(fact_image__iff,axiom,
! [X7,X2,X29,X34,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X34),c_Set_Oimage(X29,X5,X2,X7)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X29),X3),X7))
& X34 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_single__valuedI,axiom,
! [X44,X29,X5] :
( ! [X3,X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X3),X66)),X44))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X3),X69)),X44))
=> X66 = X69 ) )
=> c_Relation_Osingle__valued(X5,X29,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedI) ).
fof(fact_single__valued__def,axiom,
! [X44,X29,X5] :
( c_Relation_Osingle__valued(X5,X29,X44)
<=> ! [X3,X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X3),X66)),X44))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X3),X69)),X44))
=> X66 = X69 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(fact_curryD,axiom,
! [X15,X16,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X5,X29,tc_HOL_Obool,X2),X16),X15))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryD) ).
fof(fact_curryE,axiom,
! [X15,X16,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X5,X29,tc_HOL_Obool,X2),X16),X15))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryE) ).
fof(fact_funcset__image,axiom,
! [X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6))))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X29,tc_HOL_Obool),c_Set_Oimage(X5,X29,X2,X7),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_subset__image__iff,axiom,
! [X7,X2,X29,X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,c_Set_Oimage(X29,X5,X2,X7))
<=> ? [X105] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X29,tc_HOL_Obool),X105,X7)
& X6 = c_Set_Oimage(X29,X5,X2,X105) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_splitD_H,axiom,
! [X4,X15,X16,X11,X47,X29,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,tc_fun(X47,tc_HOL_Obool)),X11),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15)),X4))
=> hBOOL(hAPP(hAPP(hAPP(X11,X16),X15),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD_H) ).
fof(fact_funcset__mem,axiom,
! [X12,X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X6))))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X12)),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_single__valuedD,axiom,
! [X34,X13,X12,X44,X29,X5] :
( c_Relation_Osingle__valued(X5,X29,X44)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X12),X13)),X44))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X12),X34)),X44))
=> X13 = X34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X5,X29] :
( class_Orderings_Oord(X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X29),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X29,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_lexord__Nil__left,axiom,
! [X44,X13,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X13)),c_List_Olexord(X5,X44)))
<=> ? [X32,X3] : X13 = hAPP(hAPP(c_List_Olist_OCons(X5),X32),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_const__Lin__Prof,axiom,
! [X22] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,X22)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_mlex__leq,axiom,
! [X11,X5,X13,X12,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X13))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),X11))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Wellfounded_Omlex__prod(X5,X2,X11))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_image__Int__subset,axiom,
! [X6,X7,X2,X29,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X29,X5,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29,tc_HOL_Obool),X7,X6)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X29,X5,X2,X7),c_Set_Oimage(X29,X5,X2,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int__subset) ).
fof(fact_in__rel__def,axiom,
! [X13,X12,X11,X29,X5] :
( c_FunDef_Oin__rel(X5,X29,X11,X12,X13)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X12),X13)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_lexn__length,axiom,
! [X74,X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olexn(X5,X44,X74)))
=> ( c_Nat_Osize__class_Osize(tc_List_Olist(X5),X51) = X74
& c_Nat_Osize__class_Osize(tc_List_Olist(X5),X52) = X74 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn__length) ).
fof(fact_acc_OaccI,axiom,
! [X44,X12,X5] :
( ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X66),X12)),X44))
=> hBOOL(hAPP(hAPP(c_member(X5),X66),c_Wellfounded_Oacc(X5,X44))) )
=> hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(fact_acc_Osimps,axiom,
! [X44,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),c_Wellfounded_Oacc(X5,X44)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X16)),X44))
=> hBOOL(hAPP(hAPP(c_member(X5),X3),c_Wellfounded_Oacc(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(fact_split__eta,axiom,
! [X2,X47,X29,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,X47),hAPP(hAPP(c_COMBB(tc_fun(X29,tc_prod(X5,X29)),tc_fun(X29,X47),X5),hAPP(c_COMBB(tc_prod(X5,X29),X47,X29),X2)),c_Product__Type_OPair(X5,X29))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__eta) ).
fof(fact_rtrancl__listrel1__eq__len,axiom,
! [X44,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),X13)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44))))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X5),X12) = c_Nat_Osize__class_Osize(tc_List_Olist(X5),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_listrel__Nil1,axiom,
! [X44,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X51)),c_List_Olistrel(X5,X44)))
=> X51 = c_List_Olist_ONil(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_f__inv__into__f,axiom,
! [X7,X2,X29,X13,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X13),c_Set_Oimage(X29,X5,X2,X7)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X29,X5,X7,X2),X13)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_listrel__Nil2,axiom,
! [X44,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X44)))
=> X51 = c_List_Olist_ONil(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_listrel1__eq__len,axiom,
! [X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel1(X5,X44)))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X5),X51) = c_Nat_Osize__class_Osize(tc_List_Olist(X5),X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_listrel__eq__len,axiom,
! [X44,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X52)),c_List_Olistrel(X5,X44)))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X5),X51) = c_Nat_Osize__class_Osize(tc_List_Olist(X5),X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_split__paired__All,axiom,
! [X29,X5,X24] :
( ! [X91] : hBOOL(hAPP(X24,X91))
<=> ! [X32,X33] : hBOOL(hAPP(X24,hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(fact_curryI,axiom,
! [X15,X16,X29,X5,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X5,X29,tc_HOL_Obool,X2),X16),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryI) ).
fof(fact_transI,axiom,
! [X44,X5] :
( ! [X3,X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X66)),X44))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X66),X69)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X69)),X44)) ) )
=> c_Relation_Otrans(X5,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transI) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X44,X5] :
( c_Nitpick_Orefl_H(X5,X44)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_mem__splitI,axiom,
! [X47,X29,X15,X16,X4,X34,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X34),hAPP(hAPP(X4,X16),X15)))
=> hBOOL(hAPP(hAPP(c_member(X5),X34),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29,X47,tc_fun(X5,tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OPair(X29,X47),X16),X15)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI) ).
fof(fact_lexord__append__rightI,axiom,
! [X44,X12,X5,X13] :
( ? [X33,X69] : X13 = hAPP(hAPP(c_List_Olist_OCons(X5),X33),X69)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),hAPP(hAPP(c_List_Oappend(X5),X12),X13))),c_List_Olexord(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_restrict__extensional,axiom,
! [X7,X2,X29,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),c_FuncSet_Orestrict(X5,X29,X2,X7)),c_FuncSet_Oextensional(X5,X29,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__extensional) ).
fof(fact_Pi__mem,axiom,
! [X12,X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,X6)))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X12)),hAPP(X6,X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_extensional__funcset__mem,axiom,
! [X12,X97,X10,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional__funcset(X5,X29,X10,X97)))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X10))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X12)),X97)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
fof(fact_pred__subset__eq,axiom,
! [X10,X11,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X10))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X11,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_measures__less,axiom,
! [X107,X5,X13,X12,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X13))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X107)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__less) ).
fof(fact_in__mkbot,axiom,
! [X34,X22,X13,X12] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),c_Arrow__Order__Mirabelle_Omkbot(X22,X34)))
<=> ( X13 != X34
& ( X12 = X34
=> X12 != X13 )
& ( X12 != X34
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),X22)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X34,X22,X13,X12] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),c_Arrow__Order__Mirabelle_Omktop(X22,X34)))
<=> ( X12 != X34
& ( X13 = X34
=> X12 != X13 )
& ( X13 != X34
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),X22)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(fact_iff,axiom,
! [X14] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X14)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iff) ).
fof(fact_image__inv__into__cancel,axiom,
! [X106,X103,X7,X2,X5,X29] :
( c_Set_Oimage(X29,X5,X2,X7) = X103
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X106,X103)
=> c_Set_Oimage(X29,X5,X2,c_Set_Oimage(X5,X29,c_Hilbert__Choice_Oinv__into(X29,X5,X7,X2),X106)) = X106 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_below__Lin,axiom,
! [X22,X13,X12] :
( X12 != X13
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X22),X12),X13)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_acc__downwards__aux,axiom,
! [X44,X16,X15,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X15),X16)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X16),c_Wellfounded_Oacc(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(X5),X15),c_Wellfounded_Oacc(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [X15,X44,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),c_Wellfounded_Oacc(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X15),X16)),c_Transitive__Closure_Ortrancl(X5,X44)))
=> hBOOL(hAPP(hAPP(c_member(X5),X15),c_Wellfounded_Oacc(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(fact_dictator__def,axiom,
! [X8,X9] :
( c_Arrow__Order__Mirabelle_Odictator(X9,X8)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> hAPP(X9,X3) = hAPP(X3,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_tfl__cut__apply,axiom,
! [X29,X16,X12,X5,X98,X99] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X16)),X99))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X98),X99),X16),X12) = hAPP(X98,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
fof(fact_cut__apply,axiom,
! [X2,X29,X44,X16,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X16)),X44))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X2),X44),X16),X12) = hAPP(X2,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__apply) ).
fof(fact_acc__downward,axiom,
! [X16,X44,X15,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X15),c_Wellfounded_Oacc(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),X44))
=> hBOOL(hAPP(hAPP(c_member(X5),X16),c_Wellfounded_Oacc(X5,X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
fof(fact_above__Lin,axiom,
! [X22,X13,X12] :
( X12 != X13
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(X22,X12,X13)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_DomainI,axiom,
! [X44,X15,X16,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15)),X44))
=> hBOOL(hAPP(hAPP(c_member(X5),X16),c_Relation_ODomain(X5,X29,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).
fof(fact_RangeI,axiom,
! [X44,X15,X16,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15)),X44))
=> hBOOL(hAPP(hAPP(c_member(X29),X15),c_Relation_ORange(X5,X29,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).
fof(fact_funcset__id,axiom,
! [X7,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X5)),c_COMBI(X5)),c_FuncSet_OPi(X5,X5,X7,c_COMBK(tc_fun(X5,tc_HOL_Obool),X5,X7)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_listrel_ONil,axiom,
! [X44,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_ONil) ).
fof(fact_Id__on__iff,axiom,
! [X7,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Relation_OId__on(X5,X7)))
<=> ( X12 = X13
& hBOOL(hAPP(hAPP(c_member(X5),X12),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(fact_in__measure,axiom,
! [X2,X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Wellfounded_Omeasure(X5,X2)))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_inf2D1,axiom,
! [X13,X12,X6,X7,X29,X5] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),X7,X6),X12),X13))
=> hBOOL(hAPP(hAPP(X7,X12),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [X13,X12,X6,X7,X29,X5] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),X7,X6),X12),X13))
=> hBOOL(hAPP(hAPP(X6,X12),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [X44,X51,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X51)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X44)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_mktop__Lin,axiom,
! [X12,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(X22,X12)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mkbot__Lin,axiom,
! [X12,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(X22,X12)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_takeWhile__not__last,axiom,
! [X5,X51] :
( X51 != c_List_Olist_ONil(X5)
=> ( c_List_Odistinct(X5,X51)
=> c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),c_List_Olast(X5,X51))),X51) = c_List_Obutlast(X5,X51) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [X51,X44,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X44)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X51),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X44))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X44)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_image__image,axiom,
! [X7,X1,X47,X2,X5,X29] : c_Set_Oimage(X29,X5,X2,c_Set_Oimage(X47,X29,X1,X7)) = c_Set_Oimage(X47,X5,hAPP(hAPP(c_COMBB(X29,X5,X47),X2),X1),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_extensional__subset,axiom,
! [X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional(X5,X29,X7)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional(X5,X29,X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__subset) ).
fof(fact_splitD,axiom,
! [X15,X16,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15)))
=> hBOOL(hAPP(hAPP(X2,X16),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD) ).
fof(fact_prod_Orecs,axiom,
! [X15,X16,X40,X5,X47,X29] : c_Product__Type_Oprod_Oprod__rec(X29,X47,X5,X40,hAPP(hAPP(c_Product__Type_OPair(X29,X47),X16),X15)) = hAPP(hAPP(X40,X16),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
fof(fact_mlex__less,axiom,
! [X11,X5,X13,X12,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X13))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Wellfounded_Omlex__prod(X5,X2,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_imageI,axiom,
! [X2,X29,X7,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X12)),c_Set_Oimage(X5,X29,X2,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_list_Osimps_I5_J,axiom,
! [X31,X16,X39,X40,X29,X5] : c_List_Olist_Olist__case(X5,X29,X40,X39,hAPP(hAPP(c_List_Olist_OCons(X29),X16),X31)) = hAPP(hAPP(X39,X16),X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_inf2I,axiom,
! [X29,X5,X6,X13,X12,X7] :
( hBOOL(hAPP(hAPP(X7,X12),X13))
=> ( hBOOL(hAPP(hAPP(X6,X12),X13))
=> hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),X7,X6),X12),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).
fof(fact_image__eqI,axiom,
! [X5,X7,X29,X12,X2,X15] :
( X15 = hAPP(X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X29),X12),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X15),c_Set_Oimage(X29,X5,X2,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X29,X2,X15,X7,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> ( X15 = hAPP(X2,X12)
=> hBOOL(hAPP(hAPP(c_member(X29),X15),c_Set_Oimage(X5,X29,X2,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_extensional__funcset__def,axiom,
! [X97,X10,X29,X5] : c_FuncSet_Oextensional__funcset(X5,X29,X10,X97) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,X29),tc_HOL_Obool),c_FuncSet_OPi(X5,X29,X10,c_COMBK(tc_fun(X29,tc_HOL_Obool),X5,X97)),c_FuncSet_Oextensional(X5,X29,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
fof(fact_Range__Int__subset,axiom,
! [X6,X7,X29,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Relation_ORange(X29,X5,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X29,X5),tc_HOL_Obool),X7,X6)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),c_Relation_ORange(X29,X5,X7),c_Relation_ORange(X29,X5,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_Domain__Int__subset,axiom,
! [X6,X7,X29,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Relation_ODomain(X5,X29,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),X7,X6)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),c_Relation_ODomain(X5,X29,X7),c_Relation_ODomain(X5,X29,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_append__in__lists__conv,axiom,
! [X7,X52,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X51),X52)),c_List_Olists(X5,X7)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X51),c_List_Olists(X5,X7)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X52),c_List_Olists(X5,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_Id__on__eqI,axiom,
! [X7,X5,X15,X16] :
( X16 = X15
=> ( hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X15)),c_Relation_OId__on(X5,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Pi__anti__mono,axiom,
! [X6,X29,X7,X103,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X103,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X29),tc_HOL_Obool),c_FuncSet_OPi(X5,X29,X7,X6),c_FuncSet_OPi(X5,X29,X103,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_curry__conv,axiom,
! [X15,X16,X2,X5,X47,X29] : hAPP(hAPP(c_Product__Type_Ocurry(X29,X47,X5,X2),X16),X15) = hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X29,X47),X16),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__conv) ).
fof(fact_curry__def,axiom,
! [X13,X12,X4,X5,X47,X29] : hAPP(hAPP(c_Product__Type_Ocurry(X29,X47,X5,X4),X12),X13) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X29,X47),X12),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__def) ).
fof(fact_list_Osimps_I4_J,axiom,
! [X39,X40,X29,X5] : c_List_Olist_Olist__case(X5,X29,X40,X39,c_List_Olist_ONil(X29)) = X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_image__mono,axiom,
! [X2,X29,X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X29,tc_HOL_Obool),c_Set_Oimage(X5,X29,X2,X7),c_Set_Oimage(X5,X29,X2,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_Cons__in__lists__iff,axiom,
! [X7,X51,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),c_List_Olists(X5,X7)))
<=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X51),c_List_Olists(X5,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_Id__onE,axiom,
! [X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X4),c_Relation_OId__on(X5,X7)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> X4 != hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(fact_pred__equals__eq,axiom,
! [X10,X11,X5] :
( hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11) = hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X10)
<=> X11 = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X44,X16,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X16),X16)),c_Transitive__Closure_Ortrancl(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_third__alt,axiom,
! [X20,X21] :
( X21 != X20
=> ? [X17] : c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X21),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X20),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X17),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_third__alt) ).
fof(fact_extensional__restrict,axiom,
! [X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional(X5,X29,X7)))
=> c_FuncSet_Orestrict(X5,X29,X2,X7) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__restrict) ).
fof(fact_prod__caseI,axiom,
! [X29,X5,X15,X16,X40] :
( hBOOL(hAPP(hAPP(X40,X16),X15))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,tc_HOL_Obool),X40),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__caseI) ).
fof(fact_splitI,axiom,
! [X29,X5,X15,X16,X2] :
( hBOOL(hAPP(hAPP(X2,X16),X15))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitI) ).
fof(fact_image__restrict__eq,axiom,
! [X7,X2,X5,X29] : c_Set_Oimage(X29,X5,c_FuncSet_Orestrict(X29,X5,X2,X7),X7) = c_Set_Oimage(X29,X5,X2,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__restrict__eq) ).
fof(fact_listrelp_OCons,axiom,
! [X52,X51,X5,X13,X12,X44] :
( hBOOL(hAPP(hAPP(X44,X12),X13))
=> ( c_List_Olistrelp(X5,X44,X51,X52)
=> c_List_Olistrelp(X5,X44,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [X70,X71,X72,X73,X44,X5] :
( c_List_Olistrelp(X5,X44,hAPP(hAPP(c_List_Olist_OCons(X5),X73),X72),hAPP(hAPP(c_List_Olist_OCons(X5),X71),X70))
<=> ( hBOOL(hAPP(hAPP(X44,X73),X71))
& c_List_Olistrelp(X5,X44,X72,X70) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_lists_Osimps,axiom,
! [X7,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X16),c_List_Olists(X5,X7)))
<=> ( X16 = c_List_Olist_ONil(X5)
| ? [X32,X79] :
( X16 = hAPP(hAPP(c_List_Olist_OCons(X5),X32),X79)
& hBOOL(hAPP(hAPP(c_member(X5),X32),X7))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X79),c_List_Olists(X5,X7))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_Osimps) ).
fof(fact_listsp__infI,axiom,
! [X6,X89,X7,X5] :
( hBOOL(hAPP(c_List_Olistsp(X5,X7),X89))
=> ( hBOOL(hAPP(c_List_Olistsp(X5,X6),X89))
=> hBOOL(hAPP(c_List_Olistsp(X5,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)),X89)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__infI) ).
fof(fact_complete__Lin,axiom,
! [X15,X16] :
( X16 != X15
=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X15)),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(fact_maps__simps_I1_J,axiom,
! [X51,X12,X2,X5,X29] : c_List_Omaps(X29,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X29),X12),X51)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(X2,X12)),c_List_Omaps(X29,X5,X2,X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).
fof(fact_r__into__rtrancl,axiom,
! [X44,X78,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X78),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X78),c_Transitive__Closure_Ortrancl(X5,X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_lists__accI,axiom,
! [X44,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X51),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X44))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X51),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X44)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accI) ).
fof(fact_lists__accD,axiom,
! [X44,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X51),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X44))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X51),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X44)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accD) ).
fof(fact_Int__iff,axiom,
! [X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)))
<=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
& hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).
fof(fact_IntD2,axiom,
! [X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).
fof(fact_IntI,axiom,
! [X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X6))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
fof(fact_Int__mono,axiom,
! [X48,X6,X46,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X46)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X46,X48)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [X41,X42,X28,X27,X5] : c_List_Osplice(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28),hAPP(hAPP(c_List_Olist_OCons(X5),X42),X41)) = hAPP(hAPP(c_List_Olist_OCons(X5),X27),hAPP(hAPP(c_List_Olist_OCons(X5),X42),c_List_Osplice(X5,X28,X41))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_split__curry,axiom,
! [X2,X47,X29,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,X47),c_Product__Type_Ocurry(X5,X29,X47,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__curry) ).
fof(fact_accp_Osimps,axiom,
! [X16,X44,X5] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X44),X16))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X44,X3),X16))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X44),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(fact_accp_Oequations,axiom,
! [X16,X44,X5] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X44),X16))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X44,X3),X16))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X44),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(help_c__COMBS__1,axiom,
! [X11,X104,X24,X5,X47,X29] : hAPP(hAPP(hAPP(c_COMBS(X29,X47,X5),X24),X104),X11) = hAPP(hAPP(X24,X11),hAPP(X104,X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_trans__lex__prod,axiom,
! [X76,X29,X77,X5] :
( c_Relation_Otrans(X5,X77)
=> ( c_Relation_Otrans(X29,X76)
=> c_Relation_Otrans(tc_prod(X5,X29),c_Wellfounded_Olex__prod(X5,X29,X77,X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
fof(fact_RangeP_Oequations,axiom,
! [X71,X44,X29,X5] :
( c_Predicate_ORangeP(X5,X29,X44,X71)
<=> ? [X32] : hBOOL(hAPP(hAPP(X44,X32),X71)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(help_c__COMBC__1,axiom,
! [X11,X104,X24,X5,X47,X29] : hAPP(hAPP(hAPP(c_COMBC(X29,X47,X5),X24),X104),X11) = hAPP(hAPP(X24,X11),X104),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBB__1,axiom,
! [X11,X104,X24,X47,X5,X29] : hAPP(hAPP(hAPP(c_COMBB(X29,X5,X47),X24),X104),X11) = hAPP(X24,hAPP(X104,X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_inf1D1,axiom,
! [X12,X6,X7,X5] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X12))
=> hBOOL(hAPP(X7,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(fact_inf1D2,axiom,
! [X12,X6,X7,X5] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X12))
=> hBOOL(hAPP(X6,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).
fof(fact_append__in__listsp__conv,axiom,
! [X52,X51,X7,X5] :
( hBOOL(hAPP(c_List_Olistsp(X5,X7),hAPP(hAPP(c_List_Oappend(X5),X51),X52)))
<=> ( hBOOL(hAPP(c_List_Olistsp(X5,X7),X51))
& hBOOL(hAPP(c_List_Olistsp(X5,X7),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).
fof(fact_listsp_Oequations_I2_J,axiom,
! [X71,X73,X7,X5] :
( hBOOL(hAPP(c_List_Olistsp(X5,X7),hAPP(hAPP(c_List_Olist_OCons(X5),X73),X71)))
<=> ( hBOOL(hAPP(X7,X73))
& hBOOL(hAPP(c_List_Olistsp(X5,X7),X71)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).
fof(fact_append1__eq__conv,axiom,
! [X13,X52,X12,X51,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5))) = hAPP(hAPP(c_List_Oappend(X5),X52),hAPP(hAPP(c_List_Olist_OCons(X5),X13),c_List_Olist_ONil(X5)))
<=> ( X51 = X52
& X12 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_listsp_Osimps,axiom,
! [X16,X7,X5] :
( hBOOL(hAPP(c_List_Olistsp(X5,X7),X16))
<=> ( X16 = c_List_Olist_ONil(X5)
| ? [X32,X79] :
( X16 = hAPP(hAPP(c_List_Olist_OCons(X5),X32),X79)
& hBOOL(hAPP(X7,X32))
& hBOOL(hAPP(c_List_Olistsp(X5,X7),X79)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Osimps) ).
fof(fact_some__eq__trivial,axiom,
! [X12,X5] : c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X12)) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_Domain__mono,axiom,
! [X43,X44,X29,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),X44,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Relation_ODomain(X5,X29,X44),c_Relation_ODomain(X5,X29,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(fact_curry__split,axiom,
! [X2,X47,X29,X5] : c_Product__Type_Ocurry(X5,X29,X47,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X29,X47),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__split) ).
fof(fact_rtrancl__subset,axiom,
! [X10,X11,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X11,X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X10,c_Transitive__Closure_Ortrancl(X5,X11))
=> c_Transitive__Closure_Ortrancl(X5,X10) = c_Transitive__Closure_Ortrancl(X5,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [X15,X16,X40,X5,X47,X29] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29,X47,X5),X40),hAPP(hAPP(c_Product__Type_OPair(X29,X47),X16),X15)) = hAPP(hAPP(X40,X16),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_split__conv,axiom,
! [X15,X16,X2,X5,X47,X29] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29,X47,X5),X2),hAPP(hAPP(c_Product__Type_OPair(X29,X47),X16),X15)) = hAPP(hAPP(X2,X16),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).
fof(fact_Int__greatest,axiom,
! [X6,X7,X46,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X46,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X46,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X46,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).
fof(fact_Int__assoc,axiom,
! [X46,X6,X7,X5] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X46) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X6,X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).
fof(fact_Int__left__commute,axiom,
! [X46,X6,X7,X5] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X6,X46)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).
fof(fact_inf__mono,axiom,
! [X101,X20,X93,X21,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X93)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X20,X101)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20),c_Lattices_Osemilattice__inf__class_Oinf(X5,X93,X101)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).
fof(fact_listrel1__mono,axiom,
! [X43,X44,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X44,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),c_List_Olistrel1(X5,X44),c_List_Olistrel1(X5,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel__mono,axiom,
! [X43,X44,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X44,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),c_List_Olistrel(X5,X44),c_List_Olistrel(X5,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__mono) ).
fof(fact_inf1I,axiom,
! [X5,X6,X12,X7] :
( hBOOL(hAPP(X7,X12))
=> ( hBOOL(hAPP(X6,X12))
=> hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [X43,X44,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X44,c_Transitive__Closure_Ortrancl(X5,X43))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X5,X44),c_Transitive__Closure_Ortrancl(X5,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_append__assoc,axiom,
! [X54,X41,X28,X5] : hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Oappend(X5),X28),X41)),X54) = hAPP(hAPP(c_List_Oappend(X5),X28),hAPP(hAPP(c_List_Oappend(X5),X41),X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).
fof(fact_append__Cons,axiom,
! [X41,X28,X27,X5] : hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28)),X41) = hAPP(hAPP(c_List_Olist_OCons(X5),X27),hAPP(hAPP(c_List_Oappend(X5),X28),X41)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).
fof(fact_predicate2D,axiom,
! [X13,X12,X104,X24,X29,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),X24,X104)
=> ( hBOOL(hAPP(hAPP(X24,X12),X13))
=> hBOOL(hAPP(hAPP(X104,X12),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X104,X29,X5,X13,X12,X24] :
( hBOOL(hAPP(hAPP(X24,X12),X13))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),X24,X104)
=> hBOOL(hAPP(hAPP(X104,X12),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_set__rev__mp,axiom,
! [X6,X7,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> hBOOL(hAPP(hAPP(c_member(X5),X12),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_psubsetD,axiom,
! [X4,X6,X7,X5] :
( c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_set__mp,axiom,
! [X12,X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X12),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_in__mono,axiom,
! [X12,X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X12),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_subsetD,axiom,
! [X4,X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_rtrancl__mono,axiom,
! [X43,X44,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X44,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X5,X44),c_Transitive__Closure_Ortrancl(X5,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_DomainP_Ointros,axiom,
! [X29,X5,X15,X16,X44] :
( hBOOL(hAPP(hAPP(X44,X16),X15))
=> c_Predicate_ODomainP(X5,X29,X44,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_RangeP_Ointros,axiom,
! [X29,X5,X15,X16,X44] :
( hBOOL(hAPP(hAPP(X44,X16),X15))
=> c_Predicate_ORangeP(X5,X29,X44,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_takeWhile__dropWhile__id,axiom,
! [X51,X24,X5] : hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X24,X51)),c_List_OdropWhile(X5,X24,X51)) = X51,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [X44,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),c_List_Olistrel1(X5,c_Transitive__Closure_Ortrancl(X5,X44)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_butlast__snoc,axiom,
! [X27,X28,X5] : c_List_Obutlast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),hAPP(hAPP(c_List_Olist_OCons(X5),X27),c_List_Olist_ONil(X5)))) = X28,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__snoc) ).
fof(fact_last__snoc,axiom,
! [X27,X28,X5] : c_List_Olast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),hAPP(hAPP(c_List_Olist_OCons(X5),X27),c_List_Olist_ONil(X5)))) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__snoc) ).
fof(fact_single__valued__subset,axiom,
! [X43,X44,X29,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X29),tc_HOL_Obool),X44,X43)
=> ( c_Relation_Osingle__valued(X5,X29,X43)
=> c_Relation_Osingle__valued(X5,X29,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(fact_length__dropWhile__le,axiom,
! [X51,X24,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X5),c_List_OdropWhile(X5,X24,X51)),c_Nat_Osize__class_Osize(tc_List_Olist(X5),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).
fof(fact_length__takeWhile__le,axiom,
! [X51,X24,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X5),c_List_OtakeWhile(X5,X24,X51)),c_Nat_Osize__class_Osize(tc_List_Olist(X5),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_inf__greatest,axiom,
! [X94,X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X94)
=> c_Orderings_Oord__class_Oless__eq(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,X94)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).
fof(fact_le__infI,axiom,
! [X20,X21,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X20)
=> c_Orderings_Oord__class_Oless__eq(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).
fof(fact_le__inf__iff,axiom,
! [X34,X13,X12,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,c_Lattices_Osemilattice__inf__class_Oinf(X5,X13,X34))
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
& c_Orderings_Oord__class_Oless__eq(X5,X12,X34) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).
fof(fact_accp__downward,axiom,
! [X16,X15,X44,X5] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X44),X15))
=> ( hBOOL(hAPP(hAPP(X44,X16),X15))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X44),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
fof(fact_acc__subset,axiom,
! [X76,X77,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X77,X76)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Oacc(X5,X76),c_Wellfounded_Oacc(X5,X77)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(fact_inf__assoc,axiom,
! [X94,X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42),X94) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf_Oassoc,axiom,
! [X93,X20,X21,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20),X93) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,c_Lattices_Osemilattice__inf__class_Oinf(X5,X20,X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [X94,X42,X27,X5] :
( class_Lattices_Olattice(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42),X94) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_inf__left__commute,axiom,
! [X94,X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,X94)) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf_Oleft__commute,axiom,
! [X93,X21,X20,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X20,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X93)) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,c_Lattices_Osemilattice__inf__class_Oinf(X5,X20,X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [X94,X42,X27,X5] :
( class_Lattices_Olattice(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,X94)) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_append__butlast__last__id,axiom,
! [X5,X28] :
( X28 != c_List_Olist_ONil(X5)
=> hAPP(hAPP(c_List_Oappend(X5),c_List_Obutlast(X5,X28)),hAPP(hAPP(c_List_Olist_OCons(X5),c_List_Olast(X5,X28)),c_List_Olist_ONil(X5))) = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
fof(fact_accp__subset,axiom,
! [X76,X77,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),X77,X76)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Oaccp(X5,X76),c_Wellfounded_Oaccp(X5,X77)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__subset) ).
fof(fact_subset__psubset__trans,axiom,
! [X46,X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X6,X46)
=> c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X7,X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X46,X6,X7,X5] :
( c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X46)
=> c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X7,X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_subset__trans,axiom,
! [X46,X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X46)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_trans__Int,axiom,
! [X43,X44,X5] :
( c_Relation_Otrans(X5,X44)
=> ( c_Relation_Otrans(X5,X43)
=> c_Relation_Otrans(X5,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X44,X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Int) ).
fof(fact_listsp__inf__eq,axiom,
! [X6,X7,X5] : c_List_Olistsp(X5,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),c_List_Olistsp(X5,X7),c_List_Olistsp(X5,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).
fof(fact_Int__left__absorb,axiom,
! [X6,X7,X5] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [X44,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),c_List_Olistrel(X5,X44),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_Pair__inject,axiom,
! [X92,X19,X20,X21,X29,X5] :
( hAPP(hAPP(c_Product__Type_OPair(X5,X29),X21),X20) = hAPP(hAPP(c_Product__Type_OPair(X5,X29),X19),X92)
=> ~ ( X21 = X19
=> X20 != X92 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(fact_Pair__eq,axiom,
! [X25,X26,X15,X16,X29,X5] :
( hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X15) = hAPP(hAPP(c_Product__Type_OPair(X5,X29),X26),X25)
<=> ( X16 = X26
& X15 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
fof(fact_impossible__Cons,axiom,
! [X27,X41,X28,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X5),X28),c_Nat_Osize__class_Osize(tc_List_Olist(X5),X41))
=> X28 != hAPP(hAPP(c_List_Olist_OCons(X5),X27),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_impossible__Cons) ).
fof(fact_inf__apply,axiom,
! [X12,X1,X2,X29,X5] :
( class_Lattices_Olattice(X5)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29,X5),X2,X1),X12) = c_Lattices_Osemilattice__inf__class_Oinf(X5,hAPP(X2,X12),hAPP(X1,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).
fof(fact_inf__fun__def,axiom,
! [X12,X1,X2,X29,X5] :
( class_Lattices_Olattice(X5)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29,X5),X2,X1),X12) = c_Lattices_Osemilattice__inf__class_Oinf(X5,hAPP(X2,X12),hAPP(X1,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).
fof(fact_rotate__simps,axiom,
! [X28,X27,X29,X5] :
( c_List_Orotate1(X5,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5)
& c_List_Orotate1(X29,hAPP(hAPP(c_List_Olist_OCons(X29),X27),X28)) = hAPP(hAPP(c_List_Oappend(X29),X28),hAPP(hAPP(c_List_Olist_OCons(X29),X27),c_List_Olist_ONil(X29))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__simps) ).
fof(fact_snoc__eq__iff__butlast,axiom,
! [X52,X12,X51,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Olist_ONil(X5))) = X52
<=> ( X52 != c_List_Olist_ONil(X5)
& c_List_Obutlast(X5,X52) = X51
& c_List_Olast(X5,X52) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_append__eq__appendI,axiom,
! [X58,X41,X54,X59,X28,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X28),X59) = X54
=> ( X41 = hAPP(hAPP(c_List_Oappend(X5),X59),X58)
=> hAPP(hAPP(c_List_Oappend(X5),X28),X41) = hAPP(hAPP(c_List_Oappend(X5),X54),X58) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
fof(fact_Cons__eq__appendI,axiom,
! [X54,X28,X41,X59,X27,X5] :
( hAPP(hAPP(c_List_Olist_OCons(X5),X27),X59) = X41
=> ( X28 = hAPP(hAPP(c_List_Oappend(X5),X59),X54)
=> hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28) = hAPP(hAPP(c_List_Oappend(X5),X41),X54) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
fof(fact_listsp__mono,axiom,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),c_List_Olistsp(X5,X7),c_List_Olistsp(X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__mono) ).
fof(fact_lists__mono,axiom,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),c_List_Olists(X5,X7),c_List_Olists(X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__mono) ).
fof(fact_listrelp_ONil,axiom,
! [X44,X5] : c_List_Olistrelp(X5,X44,c_List_Olist_ONil(X5),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
fof(fact_listrelp_Oequations_I1_J,axiom,
! [X44,X5] : c_List_Olistrelp(X5,X44,c_List_Olist_ONil(X5),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(fact_maps__simps_I2_J,axiom,
! [X2,X5,X29] : c_List_Omaps(X29,X5,X2,c_List_Olist_ONil(X29)) = c_List_Olist_ONil(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).
fof(fact_less__infI1,axiom,
! [X20,X27,X21,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X27)
=> c_Orderings_Oord__class_Oless(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20),X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).
fof(fact_less__infI2,axiom,
! [X21,X27,X20,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X20,X27)
=> c_Orderings_Oord__class_Oless(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20),X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).
fof(fact_le__infI1,axiom,
! [X20,X27,X21,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X27)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20),X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [X21,X27,X20,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X20,X27)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20),X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).
fof(fact_image__ident,axiom,
! [X96,X5] : c_Set_Oimage(X5,X5,c_COMBI(X5),X96) = X96,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_set__eq__subset,axiom,
! [X5,X6,X7] :
( X7 = X6
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X7)
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_eq__mem,axiom,
! [X13,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),hAPP(c_fequal,X13)))
<=> X12 = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__funE,axiom,
! [X12,X1,X2,X5,X29] :
( class_Orderings_Oord(X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X29),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X29,hAPP(X2,X12),hAPP(X1,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X12,X1,X2,X5,X29] :
( class_Orderings_Oord(X29)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X29),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X29,hAPP(X2,X12),hAPP(X1,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_order__less__trans,axiom,
! [X94,X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ( c_Orderings_Oord__class_Oless(X5,X42,X94)
=> c_Orderings_Oord__class_Oless(X5,X27,X94) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X94,X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> ( c_Orderings_Oord__class_Oless(X5,X42,X94)
=> c_Orderings_Oord__class_Oless(X5,X27,X94) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X94,X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X94)
=> c_Orderings_Oord__class_Oless(X5,X27,X94) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X94,X27,X42,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X42,X27)
=> ( c_Orderings_Oord__class_Oless(X5,X94,X42)
=> c_Orderings_Oord__class_Oless(X5,X94,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X94,X27,X42,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> ( c_Orderings_Oord__class_Oless(X5,X94,X42)
=> c_Orderings_Oord__class_Oless(X5,X94,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X94,X27,X42,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X42,X27)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X94,X42)
=> c_Orderings_Oord__class_Oless(X5,X94,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X94,X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X94)
=> c_Orderings_Oord__class_Oless__eq(X5,X27,X94) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X94,X27,X42,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X94,X42)
=> c_Orderings_Oord__class_Oless__eq(X5,X94,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_lists_ONil,axiom,
! [X7,X5] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olists(X5,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_ONil) ).
fof(fact_Int__lower1,axiom,
! [X6,X7,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [X6,X7,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).
fof(fact_inf__left__idem,axiom,
! [X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42)) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf_Oleft__idem,axiom,
! [X20,X21,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20)) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [X42,X27,X5] :
( class_Lattices_Olattice(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42)) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_partition_Osimps_I1_J,axiom,
! [X24,X5] : c_List_Opartition(X5,X24,c_List_Olist_ONil(X5)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_splice_Osimps_I2_J,axiom,
! [X36,X37,X5] : c_List_Osplice(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X37),X36),c_List_Olist_ONil(X5)) = hAPP(hAPP(c_List_Olist_OCons(X5),X37),X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
fof(fact_some__eq__ex,axiom,
! [X5,X24] :
( hBOOL(hAPP(X24,c_Hilbert__Choice_OEps(X5,X24)))
<=> ? [X91] : hBOOL(hAPP(X24,X91)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
fof(fact_psubset__eq,axiom,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X7,X6)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
& X7 != X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
<=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X7,X6)
| X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_Int__absorb2,axiom,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [X7,X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).
fof(fact_predicate1D,axiom,
! [X12,X104,X24,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X24,X104)
=> ( hBOOL(hAPP(X24,X12))
=> hBOOL(hAPP(X104,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X104,X5,X12,X24] :
( hBOOL(hAPP(X24,X12))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X24,X104)
=> hBOOL(hAPP(X104,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_psubset__imp__subset,axiom,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_butlast__append,axiom,
! [X28,X5,X41] :
( ( X41 = c_List_Olist_ONil(X5)
=> c_List_Obutlast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),X41)) = c_List_Obutlast(X5,X28) )
& ( X41 != c_List_Olist_ONil(X5)
=> c_List_Obutlast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),X41)) = hAPP(hAPP(c_List_Oappend(X5),X28),c_List_Obutlast(X5,X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__append) ).
fof(fact_butlast_Osimps_I2_J,axiom,
! [X27,X5,X28] :
( ( X28 = c_List_Olist_ONil(X5)
=> c_List_Obutlast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28)) = c_List_Olist_ONil(X5) )
& ( X28 != c_List_Olist_ONil(X5)
=> c_List_Obutlast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28)) = hAPP(hAPP(c_List_Olist_OCons(X5),X27),c_List_Obutlast(X5,X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
fof(fact_mem__def,axiom,
! [X7,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
<=> hBOOL(hAPP(X7,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_nat__less__cases,axiom,
! [X24,X74,X108] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X108,X74)
=> hBOOL(hAPP(hAPP(X24,X74),X108)) )
=> ( ( X108 = X74
=> hBOOL(hAPP(hAPP(X24,X74),X108)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X74,X108)
=> hBOOL(hAPP(hAPP(X24,X74),X108)) )
=> hBOOL(hAPP(hAPP(X24,X74),X108)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_order__eq__iff,axiom,
! [X13,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( X12 = X13
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
& c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X12,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X13,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
<=> X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X42,X27,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> X27 = X42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X27,X42,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> X27 = X42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_inf__le1,axiom,
! [X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [X42,X27,X5] :
( class_Lattices_Olattice(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le2,axiom,
! [X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42),X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [X42,X27,X5] :
( class_Lattices_Olattice(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42),X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_list_Oinject,axiom,
! [X30,X26,X31,X16,X5] :
( hAPP(hAPP(c_List_Olist_OCons(X5),X16),X31) = hAPP(hAPP(c_List_Olist_OCons(X5),X26),X30)
<=> ( X16 = X26
& X31 = X30 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
fof(fact_append__same__eq,axiom,
! [X56,X51,X52,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X52),X51) = hAPP(hAPP(c_List_Oappend(X5),X56),X51)
<=> X52 = X56 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).
fof(fact_same__append__eq,axiom,
! [X56,X52,X51,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X51),X52) = hAPP(hAPP(c_List_Oappend(X5),X51),X56)
<=> X52 = X56 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).
fof(fact_Int__commute,axiom,
! [X6,X7,X5] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X6,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).
fof(fact_xt1_I11_J,axiom,
! [X21,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X20,X21)
=> ( X21 != X20
=> c_Orderings_Oord__class_Oless(X5,X20,X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X20,X21,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X20)
=> ( X21 != X20
=> c_Orderings_Oord__class_Oless(X5,X21,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X42,X27,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
| X27 = X42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X20,X21,X5] :
( class_Orderings_Oorder(X5)
=> ( X21 != X20
=> ( c_Orderings_Oord__class_Oless__eq(X5,X21,X20)
=> c_Orderings_Oord__class_Oless(X5,X21,X20) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X13,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
<=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
| X12 = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X13,X12,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
& X12 != X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X20,X21,X5] :
( class_Orderings_Oorder(X5)
=> ( X21 != X20
=> ( c_Orderings_Oord__class_Oless__eq(X5,X20,X21)
=> c_Orderings_Oord__class_Oless(X5,X20,X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_le__iff__inf,axiom,
! [X13,X12,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
<=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X12,X13) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__absorb1,axiom,
! [X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42) = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).
fof(fact_inf__absorb2,axiom,
! [X27,X42,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42) = X42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).
fof(fact_order__less__imp__le,axiom,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> c_Orderings_Oord__class_Oless__eq(X5,X27,X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_distinct__dropWhile,axiom,
! [X24,X51,X5] :
( c_List_Odistinct(X5,X51)
=> c_List_Odistinct(X5,c_List_OdropWhile(X5,X24,X51)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).
fof(fact_distinct__takeWhile,axiom,
! [X24,X51,X5] :
( c_List_Odistinct(X5,X51)
=> c_List_Odistinct(X5,c_List_OtakeWhile(X5,X24,X51)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
fof(fact_distinct__insert,axiom,
! [X27,X28,X5] :
( c_List_Odistinct(X5,X28)
=> c_List_Odistinct(X5,c_List_Oinsert(X5,X27,X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).
fof(fact_nat__less__le,axiom,
! [X74,X108] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X108,X74)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X108,X74)
& X108 != X74 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_last__appendL,axiom,
! [X28,X5,X41] :
( X41 = c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),X41)) = c_List_Olast(X5,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendL) ).
fof(fact_last__append,axiom,
! [X28,X5,X41] :
( ( X41 = c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),X41)) = c_List_Olast(X5,X28) )
& ( X41 != c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),X41)) = c_List_Olast(X5,X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__append) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X42,X27] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X42)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_last__appendR,axiom,
! [X28,X5,X41] :
( X41 != c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Oappend(X5),X28),X41)) = c_List_Olast(X5,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendR) ).
fof(fact_last_Osimps,axiom,
! [X27,X5,X28] :
( ( X28 = c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28)) = X27 )
& ( X28 != c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28)) = c_List_Olast(X5,X28) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last_Osimps) ).
fof(fact_last__ConsR,axiom,
! [X27,X5,X28] :
( X28 != c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28)) = c_List_Olast(X5,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsR) ).
fof(fact_someI__ex,axiom,
! [X5,X24] :
( ? [X91] : hBOOL(hAPP(X24,X91))
=> hBOOL(hAPP(X24,c_Hilbert__Choice_OEps(X5,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
fof(fact_tfl__some,axiom,
! [X5,X102] :
( ? [X3] : hBOOL(hAPP(X102,X3))
=> hBOOL(hAPP(X102,c_Hilbert__Choice_OEps(X5,X102))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
fof(fact_someI,axiom,
! [X5,X12,X24] :
( hBOOL(hAPP(X24,X12))
=> hBOOL(hAPP(X24,c_Hilbert__Choice_OEps(X5,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_last__ConsL,axiom,
! [X27,X5,X28] :
( X28 = c_List_Olist_ONil(X5)
=> c_List_Olast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28)) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsL) ).
fof(help_c__COMBK__1,axiom,
! [X116,X115,X29,X5] : hAPP(c_COMBK(X5,X29,X115),X116) = X115,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_linorder__neq__iff,axiom,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( X12 != X13
<=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
| c_Orderings_Oord__class_Oless(X5,X13,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
| X27 = X42
| c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_insert__Nil,axiom,
! [X27,X5] : c_List_Oinsert(X5,X27,c_List_Olist_ONil(X5)) = hAPP(hAPP(c_List_Olist_OCons(X5),X27),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).
fof(fact_linorder__le__less__linear,axiom,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
| c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
| c_Orderings_Oord__class_Oless__eq(X5,X42,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_inf__commute,axiom,
! [X42,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).
fof(fact_inf_Ocommute,axiom,
! [X20,X21,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X20,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [X42,X27,X5] :
( class_Lattices_Olattice(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X42) = c_Lattices_Osemilattice__inf__class_Oinf(X5,X42,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_nat__neq__iff,axiom,
! [X74,X108] :
( X108 != X74
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X108,X74)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X74,X108) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_nat__le__linear,axiom,
! [X109,X110] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X110,X109)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X109,X110) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X42,X27,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> X42 != X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X42,X27,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> X27 != X42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X42,X27,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> X27 != X42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_listsp_Oequations_I1_J,axiom,
! [X7,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X7),c_List_Olist_ONil(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).
fof(fact_listsp_ONil,axiom,
! [X7,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X7),c_List_Olist_ONil(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).
fof(fact_append__is__Nil__conv,axiom,
! [X52,X51,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X51),X52) = c_List_Olist_ONil(X5)
<=> ( X51 = c_List_Olist_ONil(X5)
& X52 = c_List_Olist_ONil(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_Nil__is__append__conv,axiom,
! [X52,X51,X5] :
( c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Oappend(X5),X51),X52)
<=> ( X51 = c_List_Olist_ONil(X5)
& X52 = c_List_Olist_ONil(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_append__self__conv2,axiom,
! [X52,X51,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X51),X52) = X52
<=> X51 = c_List_Olist_ONil(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).
fof(fact_append__self__conv,axiom,
! [X52,X51,X5] :
( hAPP(hAPP(c_List_Oappend(X5),X51),X52) = X51
<=> X52 = c_List_Olist_ONil(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).
fof(fact_self__append__conv,axiom,
! [X52,X5,X51] :
( X51 = hAPP(hAPP(c_List_Oappend(X5),X51),X52)
<=> X52 = c_List_Olist_ONil(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv) ).
fof(fact_self__append__conv2,axiom,
! [X51,X5,X52] :
( X52 = hAPP(hAPP(c_List_Oappend(X5),X51),X52)
<=> X51 = c_List_Olist_ONil(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).
fof(fact_list_Osimps_I3_J,axiom,
! [X18,X19,X5] : hAPP(hAPP(c_List_Olist_OCons(X5),X19),X18) != c_List_Olist_ONil(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X18,X19,X5] : c_List_Olist_ONil(X5) != hAPP(hAPP(c_List_Olist_OCons(X5),X19),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_less__not__refl3,axiom,
! [X111,X112] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X112,X111)
=> X112 != X111 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X110,X109] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X109,X110)
=> X110 != X109 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [X44,X5] : c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X44)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_not__Cons__self2,axiom,
! [X28,X27,X5] : hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28) != X28,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [X27,X5,X28] : X28 != hAPP(hAPP(c_List_Olist_OCons(X5),X27),X28),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(fact_Range__Id__on,axiom,
! [X7,X5] : c_Relation_ORange(X5,X5,c_Relation_OId__on(X5,X7)) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).
fof(fact_Domain__Id__on,axiom,
! [X7,X5] : c_Relation_ODomain(X5,X5,c_Relation_OId__on(X5,X7)) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_equalityD1,axiom,
! [X5,X6,X7] :
( X7 = X6
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X5,X6,X7] :
( X7 = X6
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_single__valued__Id__on,axiom,
! [X7,X5] : c_Relation_Osingle__valued(X5,X5,c_Relation_OId__on(X5,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
fof(help_c__fequal__2,axiom,
! [X13,X12] :
( X12 != X13
| hBOOL(hAPP(hAPP(c_fequal,X12),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_Int__absorb,axiom,
! [X7,X5] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X7) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_distinct1__rotate,axiom,
! [X51,X5] :
( c_List_Odistinct(X5,c_List_Orotate1(X5,X51))
<=> c_List_Odistinct(X5,X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct1__rotate) ).
fof(fact_subset__refl,axiom,
! [X7,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_listrel__trans,axiom,
! [X44,X5] :
( c_Relation_Otrans(X5,X44)
=> c_Relation_Otrans(tc_List_Olist(X5),c_List_Olistrel(X5,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__trans) ).
fof(fact_lexord__transI,axiom,
! [X44,X5] :
( c_Relation_Otrans(X5,X44)
=> c_Relation_Otrans(tc_List_Olist(X5),c_List_Olexord(X5,X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__transI) ).
fof(fact_eq__Nil__appendI,axiom,
! [X5,X41,X28] :
( X28 = X41
=> X28 = hAPP(hAPP(c_List_Oappend(X5),c_List_Olist_ONil(X5)),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
fof(fact_distinct__butlast,axiom,
! [X5,X28] :
( X28 != c_List_Olist_ONil(X5)
=> ( c_List_Odistinct(X5,X28)
=> c_List_Odistinct(X5,c_List_Obutlast(X5,X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__butlast) ).
fof(fact_length__rotate1,axiom,
! [X28,X5] : c_Nat_Osize__class_Osize(tc_List_Olist(X5),c_List_Orotate1(X5,X28)) = c_Nat_Osize__class_Osize(tc_List_Olist(X5),X28),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate1) ).
fof(fact_order__eq__refl,axiom,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( X27 = X42
=> c_Orderings_Oord__class_Oless__eq(X5,X27,X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_append__Nil,axiom,
! [X41,X5] : hAPP(hAPP(c_List_Oappend(X5),c_List_Olist_ONil(X5)),X41) = X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).
fof(fact_dropWhile_Osimps_I1_J,axiom,
! [X24,X5] : c_List_OdropWhile(X5,X24,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
fof(fact_takeWhile_Osimps_I1_J,axiom,
! [X24,X5] : c_List_OtakeWhile(X5,X24,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(fact_inf__idem,axiom,
! [X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X27,X27) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(fact_inf_Oidem,axiom,
! [X21,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X21) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(fact_order__refl,axiom,
! [X27,X5] :
( class_Orderings_Opreorder(X5)
=> c_Orderings_Oord__class_Oless__eq(X5,X27,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_splice_Osimps_I1_J,axiom,
! [X41,X5] : c_List_Osplice(X5,c_List_Olist_ONil(X5),X41) = X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(fact_splice__Nil2,axiom,
! [X28,X5] : c_List_Osplice(X5,X28,c_List_Olist_ONil(X5)) = X28,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).
fof(fact_append__Nil2,axiom,
! [X28,X5] : hAPP(hAPP(c_List_Oappend(X5),X28),c_List_Olist_ONil(X5)) = X28,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).
fof(fact_eq__imp__le,axiom,
! [X109,X110] :
( X110 = X109
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X110,X109) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_rtrancl__idemp,axiom,
! [X44,X5] : c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Ortrancl(X5,X44)) = c_Transitive__Closure_Ortrancl(X5,X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_le__refl,axiom,
! [X109] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X109,X109),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_trans__Id__on,axiom,
! [X7,X5] : c_Relation_Otrans(X5,c_Relation_OId__on(X5,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id__on) ).
fof(fact_trans__rtrancl,axiom,
! [X44,X5] : c_Relation_Otrans(X5,c_Transitive__Closure_Ortrancl(X5,X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
fof(fact_some__sym__eq__trivial,axiom,
! [X12,X5] : c_Hilbert__Choice_OEps(X5,hAPP(c_fequal,X12)) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X113,X114] :
( class_Orderings_Oorder(X114)
=> class_Orderings_Oorder(tc_fun(X113,X114)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X113,X114] :
( class_Orderings_Oord(X114)
=> class_Orderings_Oord(tc_fun(X113,X114)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X113,X114] :
( class_Orderings_Opreorder(X114)
=> class_Orderings_Opreorder(tc_fun(X113,X114)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [X113,X114] :
( class_Lattices_Olattice(X114)
=> class_Lattices_Osemilattice__inf(tc_fun(X113,X114)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [X113,X114] :
( class_Lattices_Olattice(X114)
=> class_Lattices_Olattice(tc_fun(X113,X114)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(fact_rotate1__is__Nil__conv,axiom,
! [X51,X5] :
( c_List_Orotate1(X5,X51) = c_List_Olist_ONil(X5)
<=> X51 = c_List_Olist_ONil(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_butlast_Osimps_I1_J,axiom,
! [X5] : c_List_Obutlast(X5,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
fof(help_c__COMBI__1,axiom,
! [X115,X5] : hAPP(c_COMBI(X5),X115) = X115,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [X5] : c_List_Odistinct(X5,c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(fact__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_H_A_058_AProf_096) ).
fof(fact__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(fact_dist,axiom,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_c____),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dist) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(arity_Nat__Onat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(arity_HOL__Obool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(i_0_509,plain,
! [X44,X86,X87,X88,X64,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X5,X29),X64),X88) != hAPP(hAPP(c_Product__Type_OPair(X5,X29),X87),X86)
=> ~ ! [X32,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33))),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X29),tc_prod(X5,X29))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X29),tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X32),X33)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X5,X29),X44))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2]) ).
fof(i_0_510,plain,
! [X78,X4,X47,X29,X34,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X34),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29,X47,tc_fun(X5,tc_HOL_Obool)),X4),X78)))
=> ~ ! [X3,X66] :
( X78 = hAPP(hAPP(c_Product__Type_OPair(X29,X47),X3),X66)
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X34),hAPP(hAPP(X4,X3),X66))) ) ),
inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).
fof(i_0_511,plain,
! [X44,X52,X13,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_List_Olistrel1(X5,X44)))
=> ( ! [X3] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X52)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X13)),X44)) )
=> ~ ! [X75] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X13),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X75),X52)),c_List_Olistrel1(X5,X44))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Cons__listrel1E2]) ).
fof(i_0_512,plain,
! [X44,X63,X53,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X12),X53)),hAPP(hAPP(c_List_Oappend(X5),X12),X63))),c_List_Olexord(X5,X44)))
=> ( ! [X32] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X32),X32)),X44))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X53),X63)),c_List_Olexord(X5,X44))) ) ),
inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).
fof(i_0_513,plain,
! [X44,X52,X51,X12,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)),X52)),c_List_Olistrel1(X5,X44)))
=> ( ! [X66] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X5),X66),X51)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X66)),X44)) )
=> ~ ! [X75] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),X75)),c_List_Olistrel1(X5,X44))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Cons__listrel1E1]) ).
fof(i_0_514,plain,
! [X44,X52,X13,X51,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))),c_List_Olistrel(X5,X44)))
=> ~ ! [X3,X65] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X65)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X13)),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X65),X52)),c_List_Olistrel(X5,X44))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).
fof(i_0_515,plain,
! [X44,X51,X52,X13,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52)),X51)),c_List_Olistrel(X5,X44)))
=> ~ ! [X66,X67] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X5),X66),X67)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X66)),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X52),X67)),c_List_Olistrel(X5,X44))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).
fof(i_0_516,plain,
! [X2400,X2401,X2402,X2403,X2404,X2405,X2406,X2407,X2408,X2409,X2410] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2410,X2409)),X2408),c_FuncSet_OPi(X2410,X2409,X2407,c_COMBK(tc_fun(X2409,tc_HOL_Obool),X2410,X2406))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2409,X2405)),X2404),c_FuncSet_OPi(X2409,X2405,X2406,c_COMBK(tc_fun(X2405,tc_HOL_Obool),X2409,X2403))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2405,X2402)),X2401),c_FuncSet_OPi(X2405,X2402,X2403,c_COMBK(tc_fun(X2402,tc_HOL_Obool),X2405,X2400))))
| c_FuncSet_Ocompose(X2410,X2405,X2402,X2407,X2401,c_FuncSet_Ocompose(X2410,X2409,X2405,X2407,X2404,X2408)) = c_FuncSet_Ocompose(X2410,X2409,X2402,X2407,c_FuncSet_Ocompose(X2409,X2405,X2402,X2406,X2401,X2404),X2408) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__assoc])]) ).
fof(i_0_517,plain,
! [X3496,X3497,X3498,X3499,X3500,X3501] : c_FuncSet_Ocompose(X3501,X3500,X3499,X3498,X3497,X3496) = c_FuncSet_Orestrict(X3501,X3499,hAPP(hAPP(c_COMBB(X3500,X3499,X3501),X3497),X3496),X3498),
inference(variable_rename,[status(thm)],[fact_compose__def]) ).
fof(i_0_518,plain,
! [X2392,X2393,X2394,X2395,X2396,X2397,X2398,X2399] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2399,X2398)),X2397),c_FuncSet_OPi(X2399,X2398,X2396,c_COMBK(tc_fun(X2398,tc_HOL_Obool),X2399,X2395))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2398,X2394)),X2393),c_FuncSet_OPi(X2398,X2394,X2395,c_COMBK(tc_fun(X2394,tc_HOL_Obool),X2398,X2392))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2399,X2394)),c_FuncSet_Ocompose(X2399,X2398,X2394,X2396,X2393,X2397)),c_FuncSet_OPi(X2399,X2394,X2396,c_COMBK(tc_fun(X2394,tc_HOL_Obool),X2399,X2392)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__compose])]) ).
fof(i_0_519,plain,
! [X44,X29,X15,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X15),c_Relation_ORange(X29,X5,X44)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29,X5)),hAPP(hAPP(c_Product__Type_OPair(X29,X5),X3),X15)),X44)) ),
inference(fof_simplification,[status(thm)],[fact_RangeE]) ).
fof(i_0_520,plain,
! [X3484,X3485,X3486,X3487,X3488] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3488,X3487)),X3486),c_FuncSet_OPi(X3488,X3487,X3485,c_COMBK(tc_fun(X3487,tc_HOL_Obool),X3488,X3484))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3488,X3487)),X3486),c_FuncSet_Oextensional(X3488,X3487,X3485)))
| c_FuncSet_Ocompose(X3488,X3487,X3487,X3485,c_FuncSet_Orestrict(X3487,X3487,c_COMBI(X3487),X3484),X3486) = X3486 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__compose])]) ).
fof(i_0_521,plain,
! [X3455,X3456,X3457,X3458,X3459,X3460] : hBOOL(hAPP(hAPP(c_member(tc_fun(X3460,X3459)),c_FuncSet_Ocompose(X3460,X3458,X3459,X3457,X3456,X3455)),c_FuncSet_Oextensional(X3460,X3459,X3457))),
inference(variable_rename,[status(thm)],[fact_compose__extensional]) ).
fof(i_0_522,plain,
! [X13,X44,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X44))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X13),X13)),c_List_Olexord(X5,X44))) ),
inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).
fof(i_0_523,plain,
! [X1,X2,X29,X7,X16,X5] :
( ( hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> c_Fun_Ooverride__on(X5,X29,X2,X1,X7,X16) = hAPP(X1,X16) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> c_Fun_Ooverride__on(X5,X29,X2,X1,X7,X16) = hAPP(X2,X16) ) ),
inference(fof_simplification,[status(thm)],[fact_override__on__def]) ).
fof(i_0_524,plain,
! [X1,X2,X29,X7,X16,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X16),X7))
=> c_Fun_Ooverride__on(X5,X29,X2,X1,X7,X16) = hAPP(X2,X16) ),
inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin]) ).
fof(i_0_525,plain,
! [X3479,X3480,X3481,X3482,X3483] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3483,X3482)),X3481),c_FuncSet_OPi(X3483,X3482,X3480,c_COMBK(tc_fun(X3482,tc_HOL_Obool),X3483,X3479))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3483,X3482)),X3481),c_FuncSet_Oextensional(X3483,X3482,X3480)))
| c_FuncSet_Ocompose(X3483,X3483,X3482,X3480,X3481,c_FuncSet_Orestrict(X3483,X3483,c_COMBI(X3483),X3480)) = X3481 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__Id])]) ).
fof(i_0_526,plain,
! [X44,X29,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),c_Relation_ODomain(X5,X29,X44)))
=> ~ ! [X66] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X29)),hAPP(hAPP(c_Product__Type_OPair(X5,X29),X16),X66)),X44)) ),
inference(fof_simplification,[status(thm)],[fact_DomainE]) ).
fof(i_0_527,plain,
! [X3590,X3591,X3592,X3593,X3594] :
( c_Set_Oimage(X3594,X3593,X3592,X3591) != X3590
| c_FuncSet_Ocompose(X3593,X3594,X3593,X3590,X3592,c_FuncSet_Orestrict(X3593,X3594,c_Hilbert__Choice_Oinv__into(X3594,X3593,X3591,X3592),X3590)) = c_FuncSet_Orestrict(X3593,X3593,c_COMBI(X3593),X3590) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__id__inv__into])]) ).
fof(i_0_528,plain,
! [X13,X12,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> ( X12 != X13
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),X22))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X13),X12)),X22)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_529,plain,
! [X15,X16,X22] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X22),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X15)),X22))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X15),X16)),X22)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_530,plain,
! [X11,X12,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),c_Wellfounded_Oacc(X5,X11)))
=> ~ ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X69),X12)),X11))
=> hBOOL(hAPP(hAPP(c_member(X5),X69),c_Wellfounded_Oacc(X5,X11))) ) ),
inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).
fof(i_0_531,plain,
! [X44,X51,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X51)),c_List_Olistrel1(X5,X44))),
inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).
fof(i_0_532,plain,
! [X44,X52,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X52)),c_List_Olex(X5,X44))),
inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).
fof(i_0_533,plain,
! [X44,X51,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X44))),
inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).
fof(i_0_534,plain,
! [X44,X51,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X51),c_List_Olist_ONil(X5))),c_List_Olex(X5,X44))),
inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).
fof(i_0_535,plain,
! [X44,X12,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X12),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X44))),
inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).
fof(i_0_536,plain,
! [X3352,X3353,X3354,X3355,X3356,X3357,X3358,X3359] :
( c_Set_Oimage(X3359,X3358,X3357,X3356) != X3355
| c_Set_Oimage(X3358,X3354,X3353,X3355) != X3352
| c_Set_Oimage(X3359,X3354,c_FuncSet_Ocompose(X3359,X3358,X3354,X3356,X3353,X3357),X3356) = X3352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__compose])]) ).
fof(i_0_537,plain,
! [X12,X6,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_OPi(X5,X29,X7,X6)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X29),hAPP(X2,X12)),hAPP(X6,X12)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_538,plain,
! [X12,X97,X10,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional__funcset(X5,X29,X10,X97)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X10))
=> hAPP(X2,X12) = c_HOL_Oundefined(X29) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__funcset__arb]) ).
fof(i_0_539,plain,
! [X2,X29,X44,X12,X13,X5] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X12)),X44))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X2),X44),X12),X13) = hAPP(X2,X13) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X13),X12)),X44))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X5,X29),X2),X44),X12),X13) = c_HOL_Oundefined(X29) ) ),
inference(fof_simplification,[status(thm)],[fact_cut__def]) ).
fof(i_0_540,plain,
! [X13,X12,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J]) ).
fof(i_0_541,plain,
! [X13,X11,X12,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),c_Relation_ODomain(X5,X5,X11)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X12),X13)),c_Transitive__Closure_Ortrancl(X5,X11)))
<=> X12 = X13 ) ),
inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(i_0_542,plain,
! [X13,X12,X6,X7,X29,X5] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X29,tc_HOL_Obool)),X7,X6),X12),X13))
=> ~ ( hBOOL(hAPP(hAPP(X7,X12),X13))
=> ~ hBOOL(hAPP(hAPP(X6,X12),X13)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf2E]) ).
fof(i_0_543,plain,
! [X2411,X2412,X2413,X2414,X2415,X2416,X2417] :
( ~ hBOOL(hAPP(hAPP(c_member(X2417),X2416),X2415))
| hAPP(c_FuncSet_Ocompose(X2417,X2414,X2413,X2415,X2412,X2411),X2416) = hAPP(X2412,hAPP(X2411,X2416)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__eq])]) ).
fof(i_0_544,plain,
! [X44,X5] :
( c_Relation_Oirrefl(X5,X44)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X44)) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(i_0_545,plain,
! [X12,X7,X2,X29,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X29)),X2),c_FuncSet_Oextensional(X5,X29,X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(X2,X12) = c_HOL_Oundefined(X29) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__arb]) ).
fof(i_0_546,plain,
! [X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_IntE]) ).
fof(i_0_547,plain,
! [X52,X13,X51,X24,X5] :
( c_List_OdropWhile(X5,X24,X51) = hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52)
<=> ( X51 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X24,X51)),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X52))
& ~ hBOOL(hAPP(X24,X13)) ) ),
inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).
fof(i_0_548,plain,
! [X2,X29,X7,X12,X5] :
( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = c_HOL_Oundefined(X29) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__def]) ).
fof(i_0_549,plain,
! [X2,X29,X7,X12,X5] :
( ( hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X12),X7))
=> hAPP(c_FuncSet_Orestrict(X5,X29,X2,X7),X12) = c_HOL_Oundefined(X29) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__apply]) ).
fof(i_0_550,plain,
~ ! [X17] : ~ c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X17),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(i_0_551,plain,
! [X12,X6,X7,X5] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool),X7,X6),X12))
=> ~ ( hBOOL(hAPP(X7,X12))
=> ~ hBOOL(hAPP(X6,X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf1E]) ).
fof(i_0_552,plain,
! [X3316,X3317,X3318,X3319,X3320,X3321] : hAPP(hAPP(c_Product__Type_Ointernal__split(X3321,X3320,X3319),X3318),hAPP(hAPP(c_Product__Type_OPair(X3321,X3320),X3317),X3316)) = hAPP(hAPP(X3318,X3317),X3316),
inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).
fof(i_0_553,plain,
! [X3306,X3307,X3308] : c_Product__Type_Ointernal__split(X3308,X3307,X3306) = c_Product__Type_Oprod_Oprod__case(X3308,X3307,X3306),
inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).
fof(i_0_554,plain,
! [X89,X51,X5,X12,X24] :
( ~ hBOOL(hAPP(X24,X12))
=> c_List_OtakeWhile(X5,X24,hAPP(hAPP(c_List_Oappend(X5),X51),hAPP(hAPP(c_List_Olist_OCons(X5),X12),X89))) = c_List_OtakeWhile(X5,X24,X51) ),
inference(fof_simplification,[status(thm)],[fact_takeWhile__tail]) ).
fof(i_0_555,plain,
! [X51,X5,X12,X24] :
( ( hBOOL(hAPP(X24,X12))
=> c_List_OtakeWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_OtakeWhile(X5,X24,X51)) )
& ( ~ hBOOL(hAPP(X24,X12))
=> c_List_OtakeWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = c_List_Olist_ONil(X5) ) ),
inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).
fof(i_0_556,plain,
! [X20,X21,X27,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X27,c_Lattices_Osemilattice__inf__class_Oinf(X5,X21,X20))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X5,X27,X21)
=> ~ c_Orderings_Oord__class_Oless__eq(X5,X27,X20) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__infE]) ).
fof(i_0_557,plain,
! [X1,X2,X5,X29] :
( class_Orderings_Oord(X29)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X5,X29),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X29),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X29),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_558,plain,
! [X51,X5,X12,X24] :
( ( hBOOL(hAPP(X24,X12))
=> c_List_OdropWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = c_List_OdropWhile(X5,X24,X51) )
& ( ~ hBOOL(hAPP(X24,X12))
=> c_List_OdropWhile(X5,X24,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),X51) ) ),
inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).
fof(i_0_559,plain,
! [X13,X12,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
& ~ c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_560,plain,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> X12 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_561,plain,
! [X21,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X20,X21)
=> ~ c_Orderings_Oord__class_Oless(X5,X21,X20) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_562,plain,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> ( c_Orderings_Oord__class_Oless(X5,X13,X12)
| X12 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_563,plain,
! [X27,X42,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> ~ c_Orderings_Oord__class_Oless(X5,X27,X42) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_564,plain,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> c_Orderings_Oord__class_Oless__eq(X5,X13,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_565,plain,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
<=> c_Orderings_Oord__class_Oless(X5,X13,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_566,plain,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ~ c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_567,plain,
! [X20,X21,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X21,X20)
=> ~ c_Orderings_Oord__class_Oless(X5,X20,X21) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_568,plain,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ~ c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_569,plain,
! [X42,X27,X5] :
( class_Orderings_Opreorder(X5)
=> ( c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ~ c_Orderings_Oord__class_Oless(X5,X42,X27) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_570,plain,
! [X13,X12,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X5,X12,X13)
<=> X12 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_571,plain,
! [X104,X24] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X24),X104))
| hBOOL(X24) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_572,plain,
! [X104,X24] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X24),X104))
| hBOOL(X104) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_573,plain,
! [X13,X12] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X13))
| X12 = X13 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_574,plain,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X42)
=> ( X27 != X42
=> c_Orderings_Oord__class_Oless(X5,X42,X27) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_575,plain,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( X27 != X42
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X42)
=> c_Orderings_Oord__class_Oless(X5,X42,X27) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_576,plain,
! [X12,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X13,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X12,X13)
<=> X12 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_577,plain,
! [X27,X42,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X42,X27)
=> c_Orderings_Oord__class_Oless(X5,X27,X42) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_578,plain,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless(X5,X27,X42)
=> c_Orderings_Oord__class_Oless__eq(X5,X42,X27) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_579,plain,
! [X42,X27,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X5,X27,X42)
=> c_Orderings_Oord__class_Oless__eq(X5,X42,X27) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_580,plain,
! [X42,X27] :
( X27 != X42
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X42)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X27) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_581,plain,
! [X27,X5] :
( class_Orderings_Opreorder(X5)
=> ~ c_Orderings_Oord__class_Oless(X5,X27,X27) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_582,plain,
! [X104,X24] :
( ~ hBOOL(X24)
| ~ hBOOL(X104)
| hBOOL(hAPP(hAPP(c_fconj,X24),X104)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_583,plain,
! [X109] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X109,X109),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_584,plain,
! [X109] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X109,X109),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_585,plain,
! [X5,X6,X7] :
( X7 = X6
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7,X6)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6,X7) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_586,plain,
! [X24] :
( ~ hBOOL(hAPP(c_fNot,X24))
| ~ hBOOL(X24) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(i_0_587,plain,
! [X24] :
( hBOOL(X24)
| hBOOL(hAPP(c_fNot,X24)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(i_0_588,plain,
! [X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3021,X3020),tc_prod(X3021,X3020))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3021,X3020),tc_prod(X3021,X3020)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3019),X3018)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),esk65_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)),esk66_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)))),c_Transitive__Closure_Ortrancl(tc_prod(X3021,X3020),X3015)))
| hBOOL(hAPP(hAPP(X3014,X3017),X3016))
| ~ hBOOL(hAPP(hAPP(X3014,X3019),X3018))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3021,X3020),tc_prod(X3021,X3020))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3021,X3020),tc_prod(X3021,X3020)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3019),X3018)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3017),X3016))),c_Transitive__Closure_Ortrancl(tc_prod(X3021,X3020),X3015))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3021,X3020),tc_prod(X3021,X3020))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3021,X3020),tc_prod(X3021,X3020)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),esk65_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)),esk66_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021))),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),esk67_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)),esk68_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)))),X3015))
| hBOOL(hAPP(hAPP(X3014,X3017),X3016))
| ~ hBOOL(hAPP(hAPP(X3014,X3019),X3018))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3021,X3020),tc_prod(X3021,X3020))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3021,X3020),tc_prod(X3021,X3020)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3019),X3018)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3017),X3016))),c_Transitive__Closure_Ortrancl(tc_prod(X3021,X3020),X3015))) )
& ( hBOOL(hAPP(hAPP(X3014,esk65_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)),esk66_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)))
| hBOOL(hAPP(hAPP(X3014,X3017),X3016))
| ~ hBOOL(hAPP(hAPP(X3014,X3019),X3018))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3021,X3020),tc_prod(X3021,X3020))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3021,X3020),tc_prod(X3021,X3020)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3019),X3018)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3017),X3016))),c_Transitive__Closure_Ortrancl(tc_prod(X3021,X3020),X3015))) )
& ( ~ hBOOL(hAPP(hAPP(X3014,esk67_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)),esk68_8(X3014,X3015,X3016,X3017,X3018,X3019,X3020,X3021)))
| hBOOL(hAPP(hAPP(X3014,X3017),X3016))
| ~ hBOOL(hAPP(hAPP(X3014,X3019),X3018))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3021,X3020),tc_prod(X3021,X3020))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3021,X3020),tc_prod(X3021,X3020)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3019),X3018)),hAPP(hAPP(c_Product__Type_OPair(X3021,X3020),X3017),X3016))),c_Transitive__Closure_Ortrancl(tc_prod(X3021,X3020),X3015))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2])])])]) ).
fof(i_0_589,plain,
! [X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3033,X3032),tc_prod(X3033,X3032))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3033,X3032),tc_prod(X3033,X3032)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),esk69_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)),esk70_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033))),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),esk71_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)),esk72_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)))),X3027))
| hBOOL(hAPP(hAPP(X3026,X3031),X3030))
| ~ hBOOL(hAPP(hAPP(X3026,X3029),X3028))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3033,X3032),tc_prod(X3033,X3032))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3033,X3032),tc_prod(X3033,X3032)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3031),X3030)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3029),X3028))),c_Transitive__Closure_Ortrancl(tc_prod(X3033,X3032),X3027))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3033,X3032),tc_prod(X3033,X3032))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3033,X3032),tc_prod(X3033,X3032)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),esk71_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)),esk72_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033))),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3029),X3028))),c_Transitive__Closure_Ortrancl(tc_prod(X3033,X3032),X3027)))
| hBOOL(hAPP(hAPP(X3026,X3031),X3030))
| ~ hBOOL(hAPP(hAPP(X3026,X3029),X3028))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3033,X3032),tc_prod(X3033,X3032))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3033,X3032),tc_prod(X3033,X3032)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3031),X3030)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3029),X3028))),c_Transitive__Closure_Ortrancl(tc_prod(X3033,X3032),X3027))) )
& ( hBOOL(hAPP(hAPP(X3026,esk71_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)),esk72_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)))
| hBOOL(hAPP(hAPP(X3026,X3031),X3030))
| ~ hBOOL(hAPP(hAPP(X3026,X3029),X3028))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3033,X3032),tc_prod(X3033,X3032))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3033,X3032),tc_prod(X3033,X3032)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3031),X3030)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3029),X3028))),c_Transitive__Closure_Ortrancl(tc_prod(X3033,X3032),X3027))) )
& ( ~ hBOOL(hAPP(hAPP(X3026,esk69_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)),esk70_8(X3026,X3027,X3028,X3029,X3030,X3031,X3032,X3033)))
| hBOOL(hAPP(hAPP(X3026,X3031),X3030))
| ~ hBOOL(hAPP(hAPP(X3026,X3029),X3028))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3033,X3032),tc_prod(X3033,X3032))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3033,X3032),tc_prod(X3033,X3032)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3031),X3030)),hAPP(hAPP(c_Product__Type_OPair(X3033,X3032),X3029),X3028))),c_Transitive__Closure_Ortrancl(tc_prod(X3033,X3032),X3027))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct2])])])]) ).
fof(i_0_590,plain,
! [X3054,X3055,X3056,X3057,X3058,X3059,X3060] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3060,X3059),tc_prod(X3060,X3059))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3060,X3059),tc_prod(X3060,X3059)),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3058),X3057)),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),esk73_7(X3054,X3055,X3056,X3057,X3058,X3059,X3060)),esk74_7(X3054,X3055,X3056,X3057,X3058,X3059,X3060)))),X3054))
| hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3058),X3057) = hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3056),X3055)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3060,X3059),tc_prod(X3060,X3059))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3060,X3059),tc_prod(X3060,X3059)),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3058),X3057)),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3056),X3055))),c_Transitive__Closure_Ortrancl(tc_prod(X3060,X3059),X3054))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3060,X3059),tc_prod(X3060,X3059))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3060,X3059),tc_prod(X3060,X3059)),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),esk73_7(X3054,X3055,X3056,X3057,X3058,X3059,X3060)),esk74_7(X3054,X3055,X3056,X3057,X3058,X3059,X3060))),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3056),X3055))),c_Transitive__Closure_Ortrancl(tc_prod(X3060,X3059),X3054)))
| hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3058),X3057) = hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3056),X3055)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3060,X3059),tc_prod(X3060,X3059))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3060,X3059),tc_prod(X3060,X3059)),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3058),X3057)),hAPP(hAPP(c_Product__Type_OPair(X3060,X3059),X3056),X3055))),c_Transitive__Closure_Ortrancl(tc_prod(X3060,X3059),X3054))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_509])])])]) ).
fof(i_0_591,plain,
! [X3213,X3214,X3215,X3216,X3217,X3218] :
( ( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3218,tc_fun(X3217,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3218,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),X3218),c_COMBC(X3217,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_prod(X3218,X3217)),tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),X3218),hAPP(c_COMBB(tc_prod(X3218,X3217),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool),X3217),c_member(tc_prod(X3218,X3217)))),c_Product__Type_OPair(X3218,X3217)))),X3216),hAPP(hAPP(c_COMBC(X3218,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),X3218),c_COMBC(X3217,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_prod(X3218,X3217)),tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),X3218),hAPP(c_COMBB(tc_prod(X3218,X3217),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool),X3217),c_member(tc_prod(X3218,X3217)))),c_Product__Type_OPair(X3218,X3217)))),X3215)),X3214),X3213))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3218,X3217)),hAPP(hAPP(c_Product__Type_OPair(X3218,X3217),X3214),X3213)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),X3216,X3215))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3218,X3217)),hAPP(hAPP(c_Product__Type_OPair(X3218,X3217),X3214),X3213)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),X3216,X3215)))
| hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3218,tc_fun(X3217,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3218,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),X3218),c_COMBC(X3217,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_prod(X3218,X3217)),tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),X3218),hAPP(c_COMBB(tc_prod(X3218,X3217),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool),X3217),c_member(tc_prod(X3218,X3217)))),c_Product__Type_OPair(X3218,X3217)))),X3216),hAPP(hAPP(c_COMBC(X3218,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_fun(X3217,tc_HOL_Obool)),X3218),c_COMBC(X3217,tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3217,tc_prod(X3218,X3217)),tc_fun(X3217,tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool)),X3218),hAPP(c_COMBB(tc_prod(X3218,X3217),tc_fun(tc_fun(tc_prod(X3218,X3217),tc_HOL_Obool),tc_HOL_Obool),X3217),c_member(tc_prod(X3218,X3217)))),c_Product__Type_OPair(X3218,X3217)))),X3215)),X3214),X3213)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).
fof(i_0_592,plain,
! [X3692,X3693,X3694,X3695,X3696,X3697,X3698,X3700,X3701,X3702,X3703,X3707] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3695,X3695)),hAPP(hAPP(c_Product__Type_OPair(X3695,X3695),esk97_7(X3692,X3693,X3694,X3695,X3696,X3697,X3698)),X3698)),X3693))
| hAPP(hAPP(X3692,X3696),X3698) = hAPP(hAPP(X3692,X3697),X3698)
| ~ c_Recdef_Oadm__wf(X3695,X3694,X3693,X3692) )
& ( hAPP(X3696,esk97_7(X3692,X3693,X3694,X3695,X3696,X3697,X3698)) != hAPP(X3697,esk97_7(X3692,X3693,X3694,X3695,X3696,X3697,X3698))
| hAPP(hAPP(X3692,X3696),X3698) = hAPP(hAPP(X3692,X3697),X3698)
| ~ c_Recdef_Oadm__wf(X3695,X3694,X3693,X3692) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3703,X3703)),hAPP(hAPP(c_Product__Type_OPair(X3703,X3703),X3707),esk100_4(X3700,X3701,X3702,X3703))),X3701))
| hAPP(esk98_4(X3700,X3701,X3702,X3703),X3707) = hAPP(esk99_4(X3700,X3701,X3702,X3703),X3707)
| c_Recdef_Oadm__wf(X3703,X3702,X3701,X3700) )
& ( hAPP(hAPP(X3700,esk98_4(X3700,X3701,X3702,X3703)),esk100_4(X3700,X3701,X3702,X3703)) != hAPP(hAPP(X3700,esk99_4(X3700,X3701,X3702,X3703)),esk100_4(X3700,X3701,X3702,X3703))
| c_Recdef_Oadm__wf(X3703,X3702,X3701,X3700) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_adm__wf__def])])])])])]) ).
fof(i_0_593,plain,
! [X2914,X2915,X2916] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2916,hAPP(hAPP(c_COMBC(X2916,tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_fun(X2916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2916,tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_fun(X2916,tc_HOL_Obool)),X2916),c_COMBC(X2916,tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2916,tc_prod(X2916,X2916)),tc_fun(X2916,tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool)),X2916),hAPP(c_COMBB(tc_prod(X2916,X2916),tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool),X2916),c_member(tc_prod(X2916,X2916)))),c_Product__Type_OPair(X2916,X2916)))),X2915)),X2914))
| hBOOL(hAPP(hAPP(c_member(X2916),X2914),c_Wellfounded_Oacc(X2916,X2915))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2916),X2914),c_Wellfounded_Oacc(X2916,X2915)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2916,hAPP(hAPP(c_COMBC(X2916,tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_fun(X2916,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2916,tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_fun(X2916,tc_HOL_Obool)),X2916),c_COMBC(X2916,tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2916,tc_prod(X2916,X2916)),tc_fun(X2916,tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool)),X2916),hAPP(c_COMBB(tc_prod(X2916,X2916),tc_fun(tc_fun(tc_prod(X2916,X2916),tc_HOL_Obool),tc_HOL_Obool),X2916),c_member(tc_prod(X2916,X2916)))),c_Product__Type_OPair(X2916,X2916)))),X2915)),X2914)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).
fof(i_0_594,plain,
! [X3074,X3075,X3076,X3077] : c_List_Opartition(X3077,X3076,hAPP(hAPP(c_List_Olist_OCons(X3077),X3075),X3074)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3077),tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077))),hAPP(hAPP(c_COMBS(tc_List_Olist(X3077),tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077))),tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3077),tc_fun(tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)))),tc_fun(tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077))),tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)))),tc_List_Olist(X3077)),c_COMBS(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077))),tc_fun(tc_List_Olist(X3077),tc_fun(tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)))),tc_List_Olist(X3077)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_fun(tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077))),tc_List_Olist(X3077)),c_If(tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)),hAPP(X3076,X3075)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X3077),tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077))),tc_List_Olist(X3077)),c_Product__Type_OPair(tc_List_Olist(X3077),tc_List_Olist(X3077))),hAPP(c_List_Olist_OCons(X3077),X3075))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3077),tc_fun(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077))),tc_fun(tc_fun(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_fun(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)))),tc_List_Olist(X3077)),c_COMBB(tc_List_Olist(X3077),tc_prod(tc_List_Olist(X3077),tc_List_Olist(X3077)),tc_List_Olist(X3077))),c_Product__Type_OPair(tc_List_Olist(X3077),tc_List_Olist(X3077)))),hAPP(c_List_Olist_OCons(X3077),X3075)))),c_List_Opartition(X3077,X3076,X3074)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).
fof(i_0_595,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_596,plain,
! [X4016,X4017,X4018,X4019] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4019,tc_fun(X4018,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4019,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),X4019),c_COMBC(X4018,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_prod(X4019,X4018)),tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),X4019),hAPP(c_COMBB(tc_prod(X4019,X4018),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool),X4018),c_member(tc_prod(X4019,X4018)))),c_Product__Type_OPair(X4019,X4018)))),X4017),hAPP(hAPP(c_COMBC(X4019,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),X4019),c_COMBC(X4018,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_prod(X4019,X4018)),tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),X4019),hAPP(c_COMBB(tc_prod(X4019,X4018),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool),X4018),c_member(tc_prod(X4019,X4018)))),c_Product__Type_OPair(X4019,X4018)))),X4016))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),X4017,X4016) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),X4017,X4016)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4019,tc_fun(X4018,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4019,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),X4019),c_COMBC(X4018,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_prod(X4019,X4018)),tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),X4019),hAPP(c_COMBB(tc_prod(X4019,X4018),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool),X4018),c_member(tc_prod(X4019,X4018)))),c_Product__Type_OPair(X4019,X4018)))),X4017),hAPP(hAPP(c_COMBC(X4019,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_fun(X4018,tc_HOL_Obool)),X4019),c_COMBC(X4018,tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4018,tc_prod(X4019,X4018)),tc_fun(X4018,tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool)),X4019),hAPP(c_COMBB(tc_prod(X4019,X4018),tc_fun(tc_fun(tc_prod(X4019,X4018),tc_HOL_Obool),tc_HOL_Obool),X4018),c_member(tc_prod(X4019,X4018)))),c_Product__Type_OPair(X4019,X4018)))),X4016)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_597,plain,
! [X3397,X3398,X3399,X3400,X3401,X3402] :
( ( X3402 = hAPP(hAPP(c_Product__Type_OPair(X3401,X3400),esk86_6(X3397,X3398,X3399,X3400,X3401,X3402)),esk87_6(X3397,X3398,X3399,X3400,X3401,X3402))
| hBOOL(hAPP(hAPP(c_member(X3399),X3398),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3401,X3400,tc_fun(X3399,tc_HOL_Obool)),X3397),X3402))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3399),X3398),hAPP(hAPP(X3397,esk86_6(X3397,X3398,X3399,X3400,X3401,X3402)),esk87_6(X3397,X3398,X3399,X3400,X3401,X3402))))
| hBOOL(hAPP(hAPP(c_member(X3399),X3398),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3401,X3400,tc_fun(X3399,tc_HOL_Obool)),X3397),X3402))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).
fof(i_0_598,plain,
! [X3641,X3642,X3643,X3644,X3645,X3646,X3647,X3648,X3649,X3650,X3651,X3652,X3653] :
( ( hAPP(hAPP(hAPP(c_Recdef_Ocut(X3646,X3645),X3644),X3643),X3642) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X3646,X3645),X3641),X3643),X3642)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3646,X3646)),hAPP(hAPP(c_Product__Type_OPair(X3646,X3646),X3647),X3642)),X3643))
| hAPP(X3644,X3647) = hAPP(X3641,X3647) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3653,X3653)),hAPP(hAPP(c_Product__Type_OPair(X3653,X3653),esk93_6(X3648,X3649,X3650,X3651,X3652,X3653)),X3649)),X3650))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X3653,X3652),X3651),X3650),X3649) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X3653,X3652),X3648),X3650),X3649) )
& ( hAPP(X3651,esk93_6(X3648,X3649,X3650,X3651,X3652,X3653)) != hAPP(X3648,esk93_6(X3648,X3649,X3650,X3651,X3652,X3653))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X3653,X3652),X3651),X3650),X3649) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X3653,X3652),X3648),X3650),X3649) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cuts__eq])])])])])]) ).
fof(i_0_599,plain,
! [X2201,X2202,X2203,X2204,X2205,X2206] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(v_F,X2202)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(v_F,X2201)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(X2202,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(X2201,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2201),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2202),c_Arrow__Order__Mirabelle_OProf))
| X2205 = X2204
| X2206 = X2203
| X2204 = X2203
| X2206 = X2205 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(v_F,X2201)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(v_F,X2202)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(X2202,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(X2201,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2201),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2202),c_Arrow__Order__Mirabelle_OProf))
| X2205 = X2204
| X2206 = X2203
| X2204 = X2203
| X2206 = X2205 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(v_F,X2202)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(v_F,X2201)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(X2202,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(X2201,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2201),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2202),c_Arrow__Order__Mirabelle_OProf))
| X2205 = X2204
| X2206 = X2203
| X2204 = X2203
| X2206 = X2205 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(v_F,X2201)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(v_F,X2202)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2205)),hAPP(X2202,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2204),X2203)),hAPP(X2201,esk6_6(X2201,X2202,X2203,X2204,X2205,X2206))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2201),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2202),c_Arrow__Order__Mirabelle_OProf))
| X2205 = X2204
| X2206 = X2203
| X2204 = X2203
| X2206 = X2205 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_600,plain,
! [X2194,X2195,X2196,X2197,X2198,X2199] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2199),X2198)),hAPP(X2195,esk5_6(X2194,X2195,X2196,X2197,X2198,X2199))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2197),X2196)),hAPP(X2194,esk5_6(X2194,X2195,X2196,X2197,X2198,X2199))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2199),X2198)),hAPP(v_F,X2195)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2197),X2196)),hAPP(v_F,X2194)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2194),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2195),c_Arrow__Order__Mirabelle_OProf))
| X2198 = X2197
| X2199 = X2196
| X2197 = X2196
| X2199 = X2198 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2199),X2198)),hAPP(X2195,esk5_6(X2194,X2195,X2196,X2197,X2198,X2199))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2197),X2196)),hAPP(X2194,esk5_6(X2194,X2195,X2196,X2197,X2198,X2199))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2199),X2198)),hAPP(v_F,X2195)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2197),X2196)),hAPP(v_F,X2194)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2194),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2195),c_Arrow__Order__Mirabelle_OProf))
| X2198 = X2197
| X2199 = X2196
| X2197 = X2196
| X2199 = X2198 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).
fof(i_0_601,plain,
! [X2614,X2615,X2616,X2617] :
( ( ~ c_List_Olistrelp(X2617,hAPP(hAPP(c_COMBC(X2617,tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_fun(X2617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2617,tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_fun(X2617,tc_HOL_Obool)),X2617),c_COMBC(X2617,tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2617,tc_prod(X2617,X2617)),tc_fun(X2617,tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool)),X2617),hAPP(c_COMBB(tc_prod(X2617,X2617),tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool),X2617),c_member(tc_prod(X2617,X2617)))),c_Product__Type_OPair(X2617,X2617)))),X2616),X2615,X2614)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2617),tc_List_Olist(X2617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2617),tc_List_Olist(X2617)),X2615),X2614)),c_List_Olistrel(X2617,X2616))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2617),tc_List_Olist(X2617))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2617),tc_List_Olist(X2617)),X2615),X2614)),c_List_Olistrel(X2617,X2616)))
| c_List_Olistrelp(X2617,hAPP(hAPP(c_COMBC(X2617,tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_fun(X2617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2617,tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_fun(X2617,tc_HOL_Obool)),X2617),c_COMBC(X2617,tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2617,tc_prod(X2617,X2617)),tc_fun(X2617,tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool)),X2617),hAPP(c_COMBB(tc_prod(X2617,X2617),tc_fun(tc_fun(tc_prod(X2617,X2617),tc_HOL_Obool),tc_HOL_Obool),X2617),c_member(tc_prod(X2617,X2617)))),c_Product__Type_OPair(X2617,X2617)))),X2616),X2615,X2614) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).
fof(i_0_602,plain,
! [X2900,X2901,X2902,X2903] :
( ( ~ c_Predicate_ODomainP(X2903,X2902,hAPP(hAPP(c_COMBC(X2903,tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_fun(X2902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2902,tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_fun(X2902,tc_HOL_Obool)),X2903),c_COMBC(X2902,tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2902,tc_prod(X2903,X2902)),tc_fun(X2902,tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool)),X2903),hAPP(c_COMBB(tc_prod(X2903,X2902),tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool),X2902),c_member(tc_prod(X2903,X2902)))),c_Product__Type_OPair(X2903,X2902)))),X2901),X2900)
| hBOOL(hAPP(hAPP(c_member(X2903),X2900),c_Relation_ODomain(X2903,X2902,X2901))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2903),X2900),c_Relation_ODomain(X2903,X2902,X2901)))
| c_Predicate_ODomainP(X2903,X2902,hAPP(hAPP(c_COMBC(X2903,tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_fun(X2902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2902,tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_fun(X2902,tc_HOL_Obool)),X2903),c_COMBC(X2902,tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2902,tc_prod(X2903,X2902)),tc_fun(X2902,tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool)),X2903),hAPP(c_COMBB(tc_prod(X2903,X2902),tc_fun(tc_fun(tc_prod(X2903,X2902),tc_HOL_Obool),tc_HOL_Obool),X2902),c_member(tc_prod(X2903,X2902)))),c_Product__Type_OPair(X2903,X2902)))),X2901),X2900) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).
fof(i_0_603,plain,
! [X2896,X2897,X2898,X2899] :
( ( ~ c_Predicate_ORangeP(X2899,X2898,hAPP(hAPP(c_COMBC(X2899,tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_fun(X2898,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2898,tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_fun(X2898,tc_HOL_Obool)),X2899),c_COMBC(X2898,tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2898,tc_prod(X2899,X2898)),tc_fun(X2898,tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool)),X2899),hAPP(c_COMBB(tc_prod(X2899,X2898),tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool),X2898),c_member(tc_prod(X2899,X2898)))),c_Product__Type_OPair(X2899,X2898)))),X2897),X2896)
| hBOOL(hAPP(hAPP(c_member(X2898),X2896),c_Relation_ORange(X2899,X2898,X2897))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2898),X2896),c_Relation_ORange(X2899,X2898,X2897)))
| c_Predicate_ORangeP(X2899,X2898,hAPP(hAPP(c_COMBC(X2899,tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_fun(X2898,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2898,tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_fun(X2898,tc_HOL_Obool)),X2899),c_COMBC(X2898,tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2898,tc_prod(X2899,X2898)),tc_fun(X2898,tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool)),X2899),hAPP(c_COMBB(tc_prod(X2899,X2898),tc_fun(tc_fun(tc_prod(X2899,X2898),tc_HOL_Obool),tc_HOL_Obool),X2898),c_member(tc_prod(X2899,X2898)))),c_Product__Type_OPair(X2899,X2898)))),X2897),X2896) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).
fof(i_0_604,plain,
! [X2220,X2221,X2222,X2223] :
( ( hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223),c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223),hAPP(c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222),c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2221) != hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223),c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223),hAPP(c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222),c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2220)
| X2221 = X2220 )
& ( X2221 != X2220
| hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223),c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223),hAPP(c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222),c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2221) = hAPP(hAPP(c_COMBC(X2223,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_fun(X2222,tc_HOL_Obool)),X2223),c_COMBC(X2222,tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2222,tc_prod(X2223,X2222)),tc_fun(X2222,tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool)),X2223),hAPP(c_COMBB(tc_prod(X2223,X2222),tc_fun(tc_fun(tc_prod(X2223,X2222),tc_HOL_Obool),tc_HOL_Obool),X2222),c_member(tc_prod(X2223,X2222)))),c_Product__Type_OPair(X2223,X2222)))),X2220) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_605,plain,
! [X3389,X3390,X3391,X3392,X3393,X3394] :
( ( X3389 = hAPP(hAPP(c_Product__Type_OPair(X3392,X3391),esk84_6(X3389,X3390,X3391,X3392,X3393,X3394)),esk85_6(X3389,X3390,X3391,X3392,X3393,X3394))
| ~ hBOOL(hAPP(hAPP(c_member(X3394),X3393),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3392,X3391,tc_fun(X3394,tc_HOL_Obool)),X3390),X3389))) )
& ( hBOOL(hAPP(hAPP(c_member(X3394),X3393),hAPP(hAPP(X3390,esk84_6(X3389,X3390,X3391,X3392,X3393,X3394)),esk85_6(X3389,X3390,X3391,X3392,X3393,X3394))))
| ~ hBOOL(hAPP(hAPP(c_member(X3394),X3393),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3392,X3391,tc_fun(X3394,tc_HOL_Obool)),X3390),X3389))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_510])])])]) ).
fof(i_0_606,plain,
! [X3067,X3068,X3069,X3070,X3071] :
( ( X3070 = hAPP(hAPP(c_List_Olist_OCons(X3071),X3069),esk76_5(X3067,X3068,X3069,X3070,X3071))
| X3070 = hAPP(hAPP(c_List_Olist_OCons(X3071),esk75_5(X3067,X3068,X3069,X3070,X3071)),X3068)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071)),X3070),hAPP(hAPP(c_List_Olist_OCons(X3071),X3069),X3068))),c_List_Olistrel1(X3071,X3067))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071)),esk76_5(X3067,X3068,X3069,X3070,X3071)),X3068)),c_List_Olistrel1(X3071,X3067)))
| X3070 = hAPP(hAPP(c_List_Olist_OCons(X3071),esk75_5(X3067,X3068,X3069,X3070,X3071)),X3068)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071)),X3070),hAPP(hAPP(c_List_Olist_OCons(X3071),X3069),X3068))),c_List_Olistrel1(X3071,X3067))) )
& ( X3070 = hAPP(hAPP(c_List_Olist_OCons(X3071),X3069),esk76_5(X3067,X3068,X3069,X3070,X3071))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3071,X3071)),hAPP(hAPP(c_Product__Type_OPair(X3071,X3071),esk75_5(X3067,X3068,X3069,X3070,X3071)),X3069)),X3067))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071)),X3070),hAPP(hAPP(c_List_Olist_OCons(X3071),X3069),X3068))),c_List_Olistrel1(X3071,X3067))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071)),esk76_5(X3067,X3068,X3069,X3070,X3071)),X3068)),c_List_Olistrel1(X3071,X3067)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3071,X3071)),hAPP(hAPP(c_Product__Type_OPair(X3071,X3071),esk75_5(X3067,X3068,X3069,X3070,X3071)),X3069)),X3067))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071)),X3070),hAPP(hAPP(c_List_Olist_OCons(X3071),X3069),X3068))),c_List_Olistrel1(X3071,X3067))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_511])])])]) ).
fof(i_0_607,plain,
! [X3665,X3666,X3667,X3668] : c_Recdef_Oadm__wf(X3668,X3667,X3666,hAPP(hAPP(c_COMBC(tc_fun(X3668,X3667),tc_fun(X3668,X3668),tc_fun(X3668,X3667)),hAPP(hAPP(c_COMBB(tc_fun(X3668,tc_fun(X3668,X3667)),tc_fun(tc_fun(X3668,X3668),tc_fun(X3668,X3667)),tc_fun(X3668,X3667)),c_COMBS(X3668,X3668,X3667)),hAPP(hAPP(c_COMBB(tc_fun(X3668,tc_fun(X3668,X3667)),tc_fun(X3668,tc_fun(X3668,X3667)),tc_fun(X3668,X3667)),hAPP(c_COMBB(tc_fun(X3668,X3667),tc_fun(X3668,X3667),X3668),X3665)),hAPP(hAPP(c_COMBC(tc_fun(X3668,X3667),tc_fun(tc_prod(X3668,X3668),tc_HOL_Obool),tc_fun(X3668,tc_fun(X3668,X3667))),c_Recdef_Ocut(X3668,X3667)),X3666)))),c_COMBI(X3668))),
inference(variable_rename,[status(thm)],[fact_adm__lemma]) ).
fof(i_0_608,plain,
! [X2640,X2641,X2642,X2643,X2644] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2644),tc_List_Olist(X2644))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2644),tc_List_Olist(X2644)),hAPP(hAPP(c_List_Oappend(X2644),X2643),X2642)),hAPP(hAPP(c_List_Oappend(X2644),X2643),X2641))),c_List_Olexord(X2644,X2640)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2644,X2644)),hAPP(hAPP(c_Product__Type_OPair(X2644,X2644),esk42_5(X2640,X2641,X2642,X2643,X2644)),esk42_5(X2640,X2641,X2642,X2643,X2644))),X2640))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2644),tc_List_Olist(X2644))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2644),tc_List_Olist(X2644)),X2642),X2641)),c_List_Olexord(X2644,X2640))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_512])])]) ).
fof(i_0_609,plain,
! [X2385,X2386,X2387,X2388,X2389,X2390] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2388),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2387),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hBOOL(hAPP(hAPP(c_member(X2390),esk24_6(X2385,X2386,X2387,X2388,X2389,X2390)),X2389)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2387),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2388),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hBOOL(hAPP(hAPP(c_member(X2390),esk24_6(X2385,X2386,X2387,X2388,X2389,X2390)),X2389)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2388),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2387),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hAPP(X2388,esk24_6(X2385,X2386,X2387,X2388,X2389,X2390)) != hAPP(X2387,esk24_6(X2385,X2386,X2387,X2388,X2389,X2390)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2387),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2390,X2386)),X2388),c_FuncSet_OPi(X2390,X2386,X2389,X2385)))
| hAPP(X2388,esk24_6(X2385,X2386,X2387,X2388,X2389,X2390)) != hAPP(X2387,esk24_6(X2385,X2386,X2387,X2388,X2389,X2390)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__cong])])])]) ).
fof(i_0_610,plain,
! [X3525,X3526,X3527,X3528,X3529] :
( ( hBOOL(hAPP(hAPP(c_member(X3529),esk90_5(X3525,X3526,X3527,X3528,X3529)),X3528))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3529,X3527)),c_FuncSet_Orestrict(X3529,X3527,X3526,X3528)),c_FuncSet_OPi(X3529,X3527,X3528,X3525))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3527),hAPP(X3526,esk90_5(X3525,X3526,X3527,X3528,X3529))),hAPP(X3525,esk90_5(X3525,X3526,X3527,X3528,X3529))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3529,X3527)),c_FuncSet_Orestrict(X3529,X3527,X3526,X3528)),c_FuncSet_OPi(X3529,X3527,X3528,X3525))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrictI])])])]) ).
fof(i_0_611,plain,
! [X2379,X2380,X2381,X2382,X2383] :
( ( hBOOL(hAPP(hAPP(c_member(X2383),esk23_5(X2379,X2380,X2381,X2382,X2383)),X2382))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2383,X2381)),X2380),c_FuncSet_OPi(X2383,X2381,X2382,X2379))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2381),hAPP(X2380,esk23_5(X2379,X2380,X2381,X2382,X2383))),hAPP(X2379,esk23_5(X2379,X2380,X2381,X2382,X2383))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2383,X2381)),X2380),c_FuncSet_OPi(X2383,X2381,X2382,X2379))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I_H])])])]) ).
fof(i_0_612,plain,
! [X2305,X2306,X2307,X2308,X2309] :
( ( hBOOL(hAPP(hAPP(c_member(X2309),esk19_5(X2305,X2306,X2307,X2308,X2309)),X2308))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2309,X2307)),X2306),c_FuncSet_OPi(X2309,X2307,X2308,X2305))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2307),hAPP(X2306,esk19_5(X2305,X2306,X2307,X2308,X2309))),hAPP(X2305,esk19_5(X2305,X2306,X2307,X2308,X2309))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2309,X2307)),X2306),c_FuncSet_OPi(X2309,X2307,X2308,X2305))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_613,plain,
! [X2726,X2727,X2728,X2729,X2730] :
( ( X2727 = hAPP(hAPP(c_List_Olist_OCons(X2730),X2729),esk44_5(X2726,X2727,X2728,X2729,X2730))
| X2727 = hAPP(hAPP(c_List_Olist_OCons(X2730),esk43_5(X2726,X2727,X2728,X2729,X2730)),X2728)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),hAPP(hAPP(c_List_Olist_OCons(X2730),X2729),X2728)),X2727)),c_List_Olistrel1(X2730,X2726))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),X2728),esk44_5(X2726,X2727,X2728,X2729,X2730))),c_List_Olistrel1(X2730,X2726)))
| X2727 = hAPP(hAPP(c_List_Olist_OCons(X2730),esk43_5(X2726,X2727,X2728,X2729,X2730)),X2728)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),hAPP(hAPP(c_List_Olist_OCons(X2730),X2729),X2728)),X2727)),c_List_Olistrel1(X2730,X2726))) )
& ( X2727 = hAPP(hAPP(c_List_Olist_OCons(X2730),X2729),esk44_5(X2726,X2727,X2728,X2729,X2730))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2730,X2730)),hAPP(hAPP(c_Product__Type_OPair(X2730,X2730),X2729),esk43_5(X2726,X2727,X2728,X2729,X2730))),X2726))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),hAPP(hAPP(c_List_Olist_OCons(X2730),X2729),X2728)),X2727)),c_List_Olistrel1(X2730,X2726))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),X2728),esk44_5(X2726,X2727,X2728,X2729,X2730))),c_List_Olistrel1(X2730,X2726)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2730,X2730)),hAPP(hAPP(c_Product__Type_OPair(X2730,X2730),X2729),esk43_5(X2726,X2727,X2728,X2729,X2730))),X2726))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),hAPP(hAPP(c_List_Olist_OCons(X2730),X2729),X2728)),X2727)),c_List_Olistrel1(X2730,X2726))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_513])])])]) ).
fof(i_0_614,plain,
! [X2618,X2619,X2620,X2621,X2622] :
( ( X2621 = hAPP(hAPP(c_List_Olist_OCons(X2622),esk34_5(X2618,X2619,X2620,X2621,X2622)),esk35_5(X2618,X2619,X2620,X2621,X2622))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2622),tc_List_Olist(X2622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2622),tc_List_Olist(X2622)),X2621),hAPP(hAPP(c_List_Olist_OCons(X2622),X2620),X2619))),c_List_Olistrel(X2622,X2618))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2622,X2622)),hAPP(hAPP(c_Product__Type_OPair(X2622,X2622),esk34_5(X2618,X2619,X2620,X2621,X2622)),X2620)),X2618))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2622),tc_List_Olist(X2622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2622),tc_List_Olist(X2622)),X2621),hAPP(hAPP(c_List_Olist_OCons(X2622),X2620),X2619))),c_List_Olistrel(X2622,X2618))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2622),tc_List_Olist(X2622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2622),tc_List_Olist(X2622)),esk35_5(X2618,X2619,X2620,X2621,X2622)),X2619)),c_List_Olistrel(X2622,X2618)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2622),tc_List_Olist(X2622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2622),tc_List_Olist(X2622)),X2621),hAPP(hAPP(c_List_Olist_OCons(X2622),X2620),X2619))),c_List_Olistrel(X2622,X2618))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_514])])])]) ).
fof(i_0_615,plain,
! [X2292,X2293,X2294,X2295,X2296,X2298,X2303,X2304] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2293)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2294)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2293,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2294,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2294),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2293),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2292) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2294)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2293)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2293,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2294,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2294),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2293),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2292) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2293)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2294)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2293,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2294,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2294),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2293),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2292) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2294)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2292,X2293)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2293,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2295),X2296)),hAPP(X2294,esk14_5(X2292,X2293,X2294,X2295,X2296))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2294),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2293),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2292) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk15_1(X2298)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2298) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk16_1(X2298)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2298) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(esk15_1(X2298),X2303)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(esk16_1(X2298),X2303)))
| c_Arrow__Order__Mirabelle_OIIA(X2298) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(esk16_1(X2298),X2304)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(esk15_1(X2298),X2304)))
| c_Arrow__Order__Mirabelle_OIIA(X2298) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(X2298,esk15_1(X2298))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(X2298,esk16_1(X2298))))
| c_Arrow__Order__Mirabelle_OIIA(X2298) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(X2298,esk15_1(X2298))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X2298)),esk18_1(X2298))),hAPP(X2298,esk16_1(X2298))))
| c_Arrow__Order__Mirabelle_OIIA(X2298) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IIA__def])])])])])]) ).
fof(i_0_616,plain,
! [X3531,X3532,X3533,X3534,X3535] :
( ( hBOOL(hAPP(hAPP(c_member(X3535),esk91_5(X3531,X3532,X3533,X3534,X3535)),X3534))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3535,X3533)),c_FuncSet_Orestrict(X3535,X3533,X3532,X3534)),c_FuncSet_OPi(X3535,X3533,X3534,c_COMBK(tc_fun(X3533,tc_HOL_Obool),X3535,X3531)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3533),hAPP(X3532,esk91_5(X3531,X3532,X3533,X3534,X3535))),X3531))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3535,X3533)),c_FuncSet_Orestrict(X3535,X3533,X3532,X3534)),c_FuncSet_OPi(X3535,X3533,X3534,c_COMBK(tc_fun(X3533,tc_HOL_Obool),X3535,X3531)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_restrict__in__funcset])])])]) ).
fof(i_0_617,plain,
! [X2339,X2340,X2341,X2342,X2343] :
( ( hBOOL(hAPP(hAPP(c_member(X2343),esk21_5(X2339,X2340,X2341,X2342,X2343)),X2342))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2343,X2341)),X2340),c_FuncSet_OPi(X2343,X2341,X2342,c_COMBK(tc_fun(X2341,tc_HOL_Obool),X2343,X2339)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2341),hAPP(X2340,esk21_5(X2339,X2340,X2341,X2342,X2343))),X2339))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2343,X2341)),X2340),c_FuncSet_OPi(X2343,X2341,X2342,c_COMBK(tc_fun(X2341,tc_HOL_Obool),X2343,X2339)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcsetI])])])]) ).
fof(i_0_618,plain,
! [X3926,X3927,X3928,X3929] : c_Hilbert__Choice_OEps(tc_prod(X3929,X3928),hAPP(c_Product__Type_Oprod_Oprod__case(X3929,X3928,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3929,tc_fun(X3928,tc_HOL_Obool),tc_fun(X3928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3928,tc_HOL_Obool),tc_fun(X3928,tc_HOL_Obool)),X3929),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3928)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3929),c_fconj),hAPP(c_fequal,X3927)))),hAPP(c_fequal,X3926)))) = hAPP(hAPP(c_Product__Type_OPair(X3929,X3928),X3927),X3926),
inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).
fof(i_0_619,plain,
! [X3211,X3212] : c_Relation_OId__on(X3212,X3211) = hAPP(c_Product__Type_Oprod_Oprod__case(X3212,X3212,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X3212,tc_HOL_Obool,tc_fun(X3212,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3212,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X3212,tc_HOL_Obool)),X3212),c_COMBC(X3212,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3212,tc_HOL_Obool),tc_fun(X3212,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3212),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3212),c_fconj)),c_fequal))),X3211)),
inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).
fof(i_0_620,plain,
! [X2625,X2626,X2627,X2628,X2629] :
( ( X2626 = hAPP(hAPP(c_List_Olist_OCons(X2629),esk36_5(X2625,X2626,X2627,X2628,X2629)),esk37_5(X2625,X2626,X2627,X2628,X2629))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2629),tc_List_Olist(X2629))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2629),tc_List_Olist(X2629)),hAPP(hAPP(c_List_Olist_OCons(X2629),X2628),X2627)),X2626)),c_List_Olistrel(X2629,X2625))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2629,X2629)),hAPP(hAPP(c_Product__Type_OPair(X2629,X2629),X2628),esk36_5(X2625,X2626,X2627,X2628,X2629))),X2625))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2629),tc_List_Olist(X2629))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2629),tc_List_Olist(X2629)),hAPP(hAPP(c_List_Olist_OCons(X2629),X2628),X2627)),X2626)),c_List_Olistrel(X2629,X2625))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2629),tc_List_Olist(X2629))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2629),tc_List_Olist(X2629)),X2627),esk37_5(X2625,X2626,X2627,X2628,X2629))),c_List_Olistrel(X2629,X2625)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2629),tc_List_Olist(X2629))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2629),tc_List_Olist(X2629)),hAPP(hAPP(c_List_Olist_OCons(X2629),X2628),X2627)),X2626)),c_List_Olistrel(X2629,X2625))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_515])])])]) ).
fof(i_0_621,plain,
! [X2438,X2439,X2440,X2441] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2441,X2441)),hAPP(hAPP(c_Product__Type_OPair(X2441,X2441),esk28_4(X2438,X2439,X2440,X2441)),esk29_4(X2438,X2439,X2440,X2441))),X2440))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2441),tc_List_Olist(X2441))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2441),tc_List_Olist(X2441)),X2439),X2438)),c_List_Olexord(X2441,X2440)))
| X2439 = X2438
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2441),tc_List_Olist(X2441))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2441),tc_List_Olist(X2441)),X2438),X2439)),c_List_Olexord(X2441,X2440))) )
& ( esk28_4(X2438,X2439,X2440,X2441) != esk29_4(X2438,X2439,X2440,X2441)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2441),tc_List_Olist(X2441))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2441),tc_List_Olist(X2441)),X2439),X2438)),c_List_Olexord(X2441,X2440)))
| X2439 = X2438
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2441),tc_List_Olist(X2441))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2441),tc_List_Olist(X2441)),X2438),X2439)),c_List_Olexord(X2441,X2440))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2441,X2441)),hAPP(hAPP(c_Product__Type_OPair(X2441,X2441),esk29_4(X2438,X2439,X2440,X2441)),esk28_4(X2438,X2439,X2440,X2441))),X2440))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2441),tc_List_Olist(X2441))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2441),tc_List_Olist(X2441)),X2439),X2438)),c_List_Olexord(X2441,X2440)))
| X2439 = X2438
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2441),tc_List_Olist(X2441))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2441),tc_List_Olist(X2441)),X2438),X2439)),c_List_Olexord(X2441,X2440))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])]) ).
cnf(i_0_622,plain,
( c_FuncSet_Ocompose(X1,X6,X9,X4,X10,c_FuncSet_Ocompose(X1,X2,X6,X4,X7,X3)) = c_FuncSet_Ocompose(X1,X2,X9,X4,c_FuncSet_Ocompose(X2,X6,X9,X5,X10,X7),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X6)),X7),c_FuncSet_OPi(X2,X6,X5,c_COMBK(tc_fun(X6,tc_HOL_Obool),X2,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X9)),X10),c_FuncSet_OPi(X6,X9,X8,c_COMBK(tc_fun(X9,tc_HOL_Obool),X6,X11)))) ),
inference(split_conjunct,[status(thm)],[i_0_516]) ).
cnf(i_0_623,plain,
c_FuncSet_Ocompose(X1,X2,X3,X4,X5,X6) = c_FuncSet_Orestrict(X1,X3,hAPP(hAPP(c_COMBB(X2,X3,X1),X5),X6),X4),
inference(split_conjunct,[status(thm)],[i_0_517]) ).
fof(i_0_624,plain,
! [X3040,X3041,X3042,X3043] :
( ( hBOOL(hAPP(c_List_Olistsp(X3043,X3042),X3040))
| ~ hBOOL(hAPP(c_List_Olistsp(X3043,hAPP(hAPP(c_COMBS(X3043,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3043),c_fconj),X3042)),X3041)),X3040)) )
& ( hBOOL(hAPP(c_List_Olistsp(X3043,X3041),X3040))
| ~ hBOOL(hAPP(c_List_Olistsp(X3043,hAPP(hAPP(c_COMBS(X3043,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3043),c_fconj),X3042)),X3041)),X3040)) )
& ( ~ hBOOL(hAPP(c_List_Olistsp(X3043,X3042),X3040))
| ~ hBOOL(hAPP(c_List_Olistsp(X3043,X3041),X3040))
| hBOOL(hAPP(c_List_Olistsp(X3043,hAPP(hAPP(c_COMBS(X3043,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3043),c_fconj),X3042)),X3041)),X3040)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])]) ).
fof(i_0_625,plain,
! [X2590,X2591,X2592,X2593,X2594,X2595] :
( ( X2594 = X2592
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),X2594),X2592)),c_List_Olistrel1(X2595,X2590)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),hAPP(hAPP(c_List_Oappend(X2595),X2594),hAPP(hAPP(c_List_Olist_OCons(X2595),X2593),c_List_Olist_ONil(X2595)))),hAPP(hAPP(c_List_Oappend(X2595),X2592),hAPP(hAPP(c_List_Olist_OCons(X2595),X2591),c_List_Olist_ONil(X2595))))),c_List_Olistrel1(X2595,X2590))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2595,X2595)),hAPP(hAPP(c_Product__Type_OPair(X2595,X2595),X2593),X2591)),X2590))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),X2594),X2592)),c_List_Olistrel1(X2595,X2590)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),hAPP(hAPP(c_List_Oappend(X2595),X2594),hAPP(hAPP(c_List_Olist_OCons(X2595),X2593),c_List_Olist_ONil(X2595)))),hAPP(hAPP(c_List_Oappend(X2595),X2592),hAPP(hAPP(c_List_Olist_OCons(X2595),X2591),c_List_Olist_ONil(X2595))))),c_List_Olistrel1(X2595,X2590))) )
& ( X2594 = X2592
| X2593 = X2591
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),hAPP(hAPP(c_List_Oappend(X2595),X2594),hAPP(hAPP(c_List_Olist_OCons(X2595),X2593),c_List_Olist_ONil(X2595)))),hAPP(hAPP(c_List_Oappend(X2595),X2592),hAPP(hAPP(c_List_Olist_OCons(X2595),X2591),c_List_Olist_ONil(X2595))))),c_List_Olistrel1(X2595,X2590))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2595,X2595)),hAPP(hAPP(c_Product__Type_OPair(X2595,X2595),X2593),X2591)),X2590))
| X2593 = X2591
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),hAPP(hAPP(c_List_Oappend(X2595),X2594),hAPP(hAPP(c_List_Olist_OCons(X2595),X2593),c_List_Olist_ONil(X2595)))),hAPP(hAPP(c_List_Oappend(X2595),X2592),hAPP(hAPP(c_List_Olist_OCons(X2595),X2591),c_List_Olist_ONil(X2595))))),c_List_Olistrel1(X2595,X2590))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),X2594),X2592)),c_List_Olistrel1(X2595,X2590)))
| X2593 != X2591
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),hAPP(hAPP(c_List_Oappend(X2595),X2594),hAPP(hAPP(c_List_Olist_OCons(X2595),X2593),c_List_Olist_ONil(X2595)))),hAPP(hAPP(c_List_Oappend(X2595),X2592),hAPP(hAPP(c_List_Olist_OCons(X2595),X2591),c_List_Olist_ONil(X2595))))),c_List_Olistrel1(X2595,X2590))) )
& ( X2594 != X2592
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2595,X2595)),hAPP(hAPP(c_Product__Type_OPair(X2595,X2595),X2593),X2591)),X2590))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2595),tc_List_Olist(X2595))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2595),tc_List_Olist(X2595)),hAPP(hAPP(c_List_Oappend(X2595),X2594),hAPP(hAPP(c_List_Olist_OCons(X2595),X2593),c_List_Olist_ONil(X2595)))),hAPP(hAPP(c_List_Oappend(X2595),X2592),hAPP(hAPP(c_List_Olist_OCons(X2595),X2591),c_List_Olist_ONil(X2595))))),c_List_Olistrel1(X2595,X2590))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).
fof(i_0_626,plain,
! [X4035,X4036,X4037,X4038,X4039] :
( ( hBOOL(hAPP(hAPP(c_member(X4039),esk104_5(X4035,X4036,X4037,X4038,X4039)),X4038))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4039,X4037),tc_HOL_Obool),c_FuncSet_OPi(X4039,X4037,X4038,X4036),c_FuncSet_OPi(X4039,X4037,X4038,X4035)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4037,tc_HOL_Obool),hAPP(X4036,esk104_5(X4035,X4036,X4037,X4038,X4039)),hAPP(X4035,esk104_5(X4035,X4036,X4037,X4038,X4039)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4039,X4037),tc_HOL_Obool),c_FuncSet_OPi(X4039,X4037,X4038,X4036),c_FuncSet_OPi(X4039,X4037,X4038,X4035)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_627,plain,
! [X2354,X2355,X2356,X2357,X2358,X2359,X2360,X2361] :
( ( X2359 = X2357
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2359),X2357)),X2355))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2361,X2360),tc_prod(X2361,X2360))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2361,X2360),tc_prod(X2361,X2360)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2359),X2358)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2357),X2356))),c_Wellfounded_Olex__prod(X2361,X2360,X2355,X2354))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2360,X2360)),hAPP(hAPP(c_Product__Type_OPair(X2360,X2360),X2358),X2356)),X2354))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2359),X2357)),X2355))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2361,X2360),tc_prod(X2361,X2360))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2361,X2360),tc_prod(X2361,X2360)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2359),X2358)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2357),X2356))),c_Wellfounded_Olex__prod(X2361,X2360,X2355,X2354))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2361,X2361)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2361),X2359),X2357)),X2355))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2361,X2360),tc_prod(X2361,X2360))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2361,X2360),tc_prod(X2361,X2360)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2359),X2358)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2357),X2356))),c_Wellfounded_Olex__prod(X2361,X2360,X2355,X2354))) )
& ( X2359 != X2357
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2360,X2360)),hAPP(hAPP(c_Product__Type_OPair(X2360,X2360),X2358),X2356)),X2354))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2361,X2360),tc_prod(X2361,X2360))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2361,X2360),tc_prod(X2361,X2360)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2359),X2358)),hAPP(hAPP(c_Product__Type_OPair(X2361,X2360),X2357),X2356))),c_Wellfounded_Olex__prod(X2361,X2360,X2355,X2354))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_628,plain,
! [X2248,X2249] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk7_2(X2248,X2249)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2249,X2248)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2249),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
& ( esk8_2(X2248,X2249) != esk9_2(X2248,X2249)
| c_Arrow__Order__Mirabelle_Odictator(X2249,X2248)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2249),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk8_2(X2248,X2249)),esk9_2(X2248,X2249))),hAPP(esk7_2(X2248,X2249),X2248)))
| c_Arrow__Order__Mirabelle_Odictator(X2249,X2248)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2249),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk8_2(X2248,X2249)),esk9_2(X2248,X2249))),hAPP(X2249,esk7_2(X2248,X2249))))
| c_Arrow__Order__Mirabelle_Odictator(X2249,X2248)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2249),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dictatorI])])])]) ).
fof(i_0_629,plain,
! [X3708,X3709,X3710,X3711,X3712] : hAPP(c_Hilbert__Choice_Oinv__into(X3712,X3711,X3710,X3709),X3708) = c_Hilbert__Choice_OEps(X3712,hAPP(hAPP(c_COMBS(X3712,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3712),c_fconj),hAPP(hAPP(c_COMBC(X3712,tc_fun(X3712,tc_HOL_Obool),tc_HOL_Obool),c_member(X3712)),X3710))),hAPP(hAPP(c_COMBC(X3712,X3711,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3711,tc_fun(X3711,tc_HOL_Obool),X3712),c_fequal),X3709)),X3708))),
inference(variable_rename,[status(thm)],[fact_inv__into__def]) ).
fof(i_0_630,plain,
! [X2632,X2633,X2634,X2635] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2635,X2635)),hAPP(hAPP(c_Product__Type_OPair(X2635,X2635),esk38_4(X2632,X2633,X2634,X2635)),esk39_4(X2632,X2633,X2634,X2635))),X2632))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2635),tc_List_Olist(X2635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2635),tc_List_Olist(X2635)),X2634),X2633)),c_List_Olistrel1(X2635,X2632))) )
& ( X2634 = hAPP(hAPP(c_List_Oappend(X2635),esk40_4(X2632,X2633,X2634,X2635)),hAPP(hAPP(c_List_Olist_OCons(X2635),esk38_4(X2632,X2633,X2634,X2635)),esk41_4(X2632,X2633,X2634,X2635)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2635),tc_List_Olist(X2635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2635),tc_List_Olist(X2635)),X2634),X2633)),c_List_Olistrel1(X2635,X2632))) )
& ( X2633 = hAPP(hAPP(c_List_Oappend(X2635),esk40_4(X2632,X2633,X2634,X2635)),hAPP(hAPP(c_List_Olist_OCons(X2635),esk39_4(X2632,X2633,X2634,X2635)),esk41_4(X2632,X2633,X2634,X2635)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2635),tc_List_Olist(X2635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2635),tc_List_Olist(X2635)),X2634),X2633)),c_List_Olistrel1(X2635,X2632))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).
cnf(i_0_631,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X6)),c_FuncSet_Ocompose(X1,X2,X6,X4,X7,X3)),c_FuncSet_OPi(X1,X6,X4,c_COMBK(tc_fun(X6,tc_HOL_Obool),X1,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X6)),X7),c_FuncSet_OPi(X2,X6,X5,c_COMBK(tc_fun(X6,tc_HOL_Obool),X2,X8)))) ),
inference(split_conjunct,[status(thm)],[i_0_518]) ).
fof(i_0_632,plain,
! [X3063,X3064,X3065,X3066] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3066)),X3065),c_List_Olists(X3066,X3064)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3066)),X3065),c_List_Olists(X3066,X3063)))
| hBOOL(hAPP(c_List_Olistsp(X3066,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3066,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3066,tc_fun(X3066,tc_HOL_Obool),tc_HOL_Obool),c_member(X3066)),X3064),hAPP(hAPP(c_COMBC(X3066,tc_fun(X3066,tc_HOL_Obool),tc_HOL_Obool),c_member(X3066)),X3063))),X3065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__IntI])]) ).
fof(i_0_633,plain,
! [X3623,X3624,X3625,X3626,X3627] :
( ( hBOOL(hAPP(hAPP(c_member(X3627),esk92_5(X3623,X3624,X3625,X3626,X3627)),X3624))
| X3625 = X3623
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3627,X3626)),X3623),c_FuncSet_Oextensional(X3627,X3626,X3624)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3627,X3626)),X3625),c_FuncSet_Oextensional(X3627,X3626,X3624))) )
& ( hAPP(X3625,esk92_5(X3623,X3624,X3625,X3626,X3627)) != hAPP(X3623,esk92_5(X3623,X3624,X3625,X3626,X3627))
| X3625 = X3623
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3627,X3626)),X3623),c_FuncSet_Oextensional(X3627,X3626,X3624)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3627,X3626)),X3625),c_FuncSet_Oextensional(X3627,X3626,X3624))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensionalityI])])])]) ).
fof(i_0_634,plain,
! [X2456,X2457,X2458,X2459,X2460,X2461,X2462] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2462,X2462)),hAPP(hAPP(c_Product__Type_OPair(X2462,X2462),X2461),X2460)),X2459))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2462),tc_List_Olist(X2462))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2462),tc_List_Olist(X2462)),hAPP(hAPP(c_List_Oappend(X2462),X2458),hAPP(hAPP(c_List_Olist_OCons(X2462),X2461),X2457))),hAPP(hAPP(c_List_Oappend(X2462),X2458),hAPP(hAPP(c_List_Olist_OCons(X2462),X2460),X2456)))),c_List_Olexord(X2462,X2459))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).
fof(i_0_635,plain,
! [X2319,X2320,X2321,X2322,X2323,X2324,X2325] :
( ~ hBOOL(hAPP(X2325,X2324))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2323,X2323)),hAPP(hAPP(c_Product__Type_OPair(X2323,X2323),X2322),X2321)),hAPP(X2320,X2324)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2319,X2323),tc_prod(X2319,X2323))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2319,X2323),tc_prod(X2319,X2323)),hAPP(hAPP(c_Product__Type_OPair(X2319,X2323),X2324),X2322)),hAPP(hAPP(c_Product__Type_OPair(X2319,X2323),X2324),X2321))),c_Recdef_Osame__fst(X2319,X2323,X2325,X2320))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_636,plain,
! [X3153,X3154,X3155,X3156,X3157,X3158,X3159,X3160] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3160,X3159,X3158),X3157),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3156,X3155,tc_prod(X3160,X3159)),X3154),X3153)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3156,X3155,X3158),hAPP(hAPP(c_COMBB(tc_fun(X3155,tc_prod(X3160,X3159)),tc_fun(X3155,X3158),X3156),hAPP(c_COMBB(tc_prod(X3160,X3159),X3158,X3155),hAPP(c_Product__Type_Oprod_Oprod__case(X3160,X3159,X3158),X3157))),X3154)),X3153),
inference(variable_rename,[status(thm)],[fact_split__twice]) ).
fof(i_0_637,plain,
! [X2484,X2485,X2486,X2487,X2488,X2491,X2492,X2493,X2494,X2495,X2496,X2497] :
( ( hAPP(hAPP(c_List_Oappend(X2488),X2487),esk31_5(X2484,X2485,X2486,X2487,X2488)) = X2485
| X2487 = hAPP(hAPP(c_List_Oappend(X2488),X2485),esk30_5(X2484,X2485,X2486,X2487,X2488))
| hAPP(hAPP(c_List_Oappend(X2488),X2487),X2486) != hAPP(hAPP(c_List_Oappend(X2488),X2485),X2484) )
& ( X2486 = hAPP(hAPP(c_List_Oappend(X2488),esk31_5(X2484,X2485,X2486,X2487,X2488)),X2484)
| X2487 = hAPP(hAPP(c_List_Oappend(X2488),X2485),esk30_5(X2484,X2485,X2486,X2487,X2488))
| hAPP(hAPP(c_List_Oappend(X2488),X2487),X2486) != hAPP(hAPP(c_List_Oappend(X2488),X2485),X2484) )
& ( hAPP(hAPP(c_List_Oappend(X2488),X2487),esk31_5(X2484,X2485,X2486,X2487,X2488)) = X2485
| hAPP(hAPP(c_List_Oappend(X2488),esk30_5(X2484,X2485,X2486,X2487,X2488)),X2486) = X2484
| hAPP(hAPP(c_List_Oappend(X2488),X2487),X2486) != hAPP(hAPP(c_List_Oappend(X2488),X2485),X2484) )
& ( X2486 = hAPP(hAPP(c_List_Oappend(X2488),esk31_5(X2484,X2485,X2486,X2487,X2488)),X2484)
| hAPP(hAPP(c_List_Oappend(X2488),esk30_5(X2484,X2485,X2486,X2487,X2488)),X2486) = X2484
| hAPP(hAPP(c_List_Oappend(X2488),X2487),X2486) != hAPP(hAPP(c_List_Oappend(X2488),X2485),X2484) )
& ( X2494 != hAPP(hAPP(c_List_Oappend(X2495),X2492),X2496)
| hAPP(hAPP(c_List_Oappend(X2495),X2496),X2493) != X2491
| hAPP(hAPP(c_List_Oappend(X2495),X2494),X2493) = hAPP(hAPP(c_List_Oappend(X2495),X2492),X2491) )
& ( hAPP(hAPP(c_List_Oappend(X2495),X2494),X2497) != X2492
| X2493 != hAPP(hAPP(c_List_Oappend(X2495),X2497),X2491)
| hAPP(hAPP(c_List_Oappend(X2495),X2494),X2493) = hAPP(hAPP(c_List_Oappend(X2495),X2492),X2491) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2])])])])])]) ).
fof(i_0_638,plain,
! [X3146,X3147,X3148,X3149] :
( ( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3149,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3149,tc_fun(X3149,tc_HOL_Obool),tc_HOL_Obool),c_member(X3149)),X3148),hAPP(hAPP(c_COMBC(X3149,tc_fun(X3149,tc_HOL_Obool),tc_HOL_Obool),c_member(X3149)),X3147)),X3146))
| hBOOL(hAPP(hAPP(c_member(X3149),X3146),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3149,tc_HOL_Obool),X3148,X3147))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3149),X3146),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3149,tc_HOL_Obool),X3148,X3147)))
| hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3149,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3149,tc_fun(X3149,tc_HOL_Obool),tc_HOL_Obool),c_member(X3149)),X3148),hAPP(hAPP(c_COMBC(X3149,tc_fun(X3149,tc_HOL_Obool),tc_HOL_Obool),c_member(X3149)),X3147)),X3146)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).
fof(i_0_639,plain,
! [X2904,X2905,X2906,X2907] :
( ~ hBOOL(hAPP(hAPP(c_member(X2907),X2906),c_Relation_ORange(X2905,X2907,X2904)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2905,X2907)),hAPP(hAPP(c_Product__Type_OPair(X2905,X2907),esk55_4(X2904,X2905,X2906,X2907)),X2906)),X2904)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_519])])]) ).
fof(i_0_640,plain,
! [X2874,X2875,X2876,X2877,X2879,X2880,X2881,X2882,X2883] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2877),X2876),c_Relation_ORange(X2875,X2877,X2874)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2875,X2877)),hAPP(hAPP(c_Product__Type_OPair(X2875,X2877),esk53_4(X2874,X2875,X2876,X2877)),X2876)),X2874)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2880,X2882)),hAPP(hAPP(c_Product__Type_OPair(X2880,X2882),X2883),X2881)),X2879))
| hBOOL(hAPP(hAPP(c_member(X2882),X2881),c_Relation_ORange(X2880,X2882,X2879))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__iff])])])])]) ).
fof(i_0_641,plain,
! [X2468,X2469,X2470,X2471,X2472,X2473] :
( ( X2472 = X2470
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2472),X2470)),X2468))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2472),X2471)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2470),X2469))),c_List_Olistrel1(X2473,X2468))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),X2471),X2469)),c_List_Olistrel1(X2473,X2468)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2472),X2470)),X2468))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2472),X2471)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2470),X2469))),c_List_Olistrel1(X2473,X2468))) )
& ( X2472 = X2470
| X2471 = X2469
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2472),X2471)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2470),X2469))),c_List_Olistrel1(X2473,X2468))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),X2471),X2469)),c_List_Olistrel1(X2473,X2468)))
| X2471 = X2469
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2472),X2471)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2470),X2469))),c_List_Olistrel1(X2473,X2468))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2472),X2470)),X2468))
| X2471 != X2469
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2472),X2471)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2470),X2469))),c_List_Olistrel1(X2473,X2468))) )
& ( X2472 != X2470
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),X2471),X2469)),c_List_Olistrel1(X2473,X2468)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2473),tc_List_Olist(X2473))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2473),tc_List_Olist(X2473)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2472),X2471)),hAPP(hAPP(c_List_Olist_OCons(X2473),X2470),X2469))),c_List_Olistrel1(X2473,X2468))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).
fof(i_0_642,plain,
! [X2652,X2653,X2654,X2655,X2656,X2657] :
( ( X2656 = X2654
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2657,X2657)),hAPP(hAPP(c_Product__Type_OPair(X2657,X2657),X2656),X2654)),X2652))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2656),X2655)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2654),X2653))),c_List_Olex(X2657,X2652))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),X2655),X2653)),c_List_Olex(X2657,X2652)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2657,X2657)),hAPP(hAPP(c_Product__Type_OPair(X2657,X2657),X2656),X2654)),X2652))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2656),X2655)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2654),X2653))),c_List_Olex(X2657,X2652))) )
& ( X2656 = X2654
| c_Nat_Osize__class_Osize(tc_List_Olist(X2657),X2655) = c_Nat_Osize__class_Osize(tc_List_Olist(X2657),X2653)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2656),X2655)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2654),X2653))),c_List_Olex(X2657,X2652))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),X2655),X2653)),c_List_Olex(X2657,X2652)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2657),X2655) = c_Nat_Osize__class_Osize(tc_List_Olist(X2657),X2653)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2656),X2655)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2654),X2653))),c_List_Olex(X2657,X2652))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2657,X2657)),hAPP(hAPP(c_Product__Type_OPair(X2657,X2657),X2656),X2654)),X2652))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2657),X2655) != c_Nat_Osize__class_Osize(tc_List_Olist(X2657),X2653)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2656),X2655)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2654),X2653))),c_List_Olex(X2657,X2652))) )
& ( X2656 != X2654
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),X2655),X2653)),c_List_Olex(X2657,X2652)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2657),tc_List_Olist(X2657))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2657),tc_List_Olist(X2657)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2656),X2655)),hAPP(hAPP(c_List_Olist_OCons(X2657),X2654),X2653))),c_List_Olex(X2657,X2652))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).
fof(i_0_643,plain,
! [X2362,X2363,X2364,X2365,X2366,X2367] :
( ( X2366 = X2364
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2367,X2367)),hAPP(hAPP(c_Product__Type_OPair(X2367,X2367),X2366),X2364)),X2362))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2367),tc_List_Olist(X2367))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2367),tc_List_Olist(X2367)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2366),X2365)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2364),X2363))),c_List_Olexord(X2367,X2362))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2367),tc_List_Olist(X2367))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2367),tc_List_Olist(X2367)),X2365),X2363)),c_List_Olexord(X2367,X2362)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2367,X2367)),hAPP(hAPP(c_Product__Type_OPair(X2367,X2367),X2366),X2364)),X2362))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2367),tc_List_Olist(X2367))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2367),tc_List_Olist(X2367)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2366),X2365)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2364),X2363))),c_List_Olexord(X2367,X2362))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2367,X2367)),hAPP(hAPP(c_Product__Type_OPair(X2367,X2367),X2366),X2364)),X2362))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2367),tc_List_Olist(X2367))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2367),tc_List_Olist(X2367)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2366),X2365)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2364),X2363))),c_List_Olexord(X2367,X2362))) )
& ( X2366 != X2364
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2367),tc_List_Olist(X2367))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2367),tc_List_Olist(X2367)),X2365),X2363)),c_List_Olexord(X2367,X2362)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2367),tc_List_Olist(X2367))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2367),tc_List_Olist(X2367)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2366),X2365)),hAPP(hAPP(c_List_Olist_OCons(X2367),X2364),X2363))),c_List_Olexord(X2367,X2362))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).
fof(i_0_644,plain,
! [X2746,X2747,X2748,X2749,X2750,X2751] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2751,X2751)),hAPP(hAPP(c_Product__Type_OPair(X2751,X2751),X2750),X2749)),c_Transitive__Closure_Ortrancl(X2751,X2748)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2751),tc_List_Olist(X2751))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2751),tc_List_Olist(X2751)),X2747),X2746)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2751),c_List_Olistrel1(X2751,X2748))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2751),tc_List_Olist(X2751))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2751),tc_List_Olist(X2751)),hAPP(hAPP(c_List_Olist_OCons(X2751),X2750),X2747)),hAPP(hAPP(c_List_Olist_OCons(X2751),X2749),X2746))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2751),c_List_Olistrel1(X2751,X2748)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).
fof(i_0_645,plain,
! [X2450,X2451,X2452,X2453,X2454,X2455] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2455,X2455)),hAPP(hAPP(c_Product__Type_OPair(X2455,X2455),X2454),X2453)),X2452))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2455),tc_List_Olist(X2455))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2455),tc_List_Olist(X2455)),X2451),X2450)),c_List_Olistrel(X2455,X2452)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2455),tc_List_Olist(X2455))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2455),tc_List_Olist(X2455)),hAPP(hAPP(c_List_Olist_OCons(X2455),X2454),X2451)),hAPP(hAPP(c_List_Olist_OCons(X2455),X2453),X2450))),c_List_Olistrel(X2455,X2452))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).
fof(i_0_646,plain,
! [X3553,X3554,X3555,X3556,X3557] :
( c_Set_Oimage(X3557,X3556,X3555,X3554) != X3553
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3556,X3557)),c_FuncSet_Orestrict(X3556,X3557,c_Hilbert__Choice_Oinv__into(X3557,X3556,X3554,X3555),X3553)),c_FuncSet_OPi(X3556,X3557,X3553,c_COMBK(tc_fun(X3557,tc_HOL_Obool),X3556,X3554)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__funcset])]) ).
fof(i_0_647,plain,
! [X2282,X2283,X2284,X2285,X2287,X2291] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2282)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2283),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2284),X2285)),hAPP(X2283,esk10_4(X2282,X2283,X2284,X2285))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2284),X2285)),hAPP(X2282,X2283))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk11_1(X2287)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2287) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X2287)),esk13_1(X2287))),hAPP(esk11_1(X2287),X2291)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2287) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X2287)),esk13_1(X2287))),hAPP(X2287,esk11_1(X2287))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2287) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unanimity__def])])])])])]) ).
fof(i_0_648,plain,
! [X2755,X2756,X2757,X2758,X2759] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2759),tc_List_Olist(X2759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2759),tc_List_Olist(X2759)),X2758),X2757)),c_List_Olistrel(X2759,c_Transitive__Closure_Ortrancl(X2759,X2756))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2759),tc_List_Olist(X2759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2759),tc_List_Olist(X2759)),X2757),X2755)),c_List_Olistrel(X2759,c_Transitive__Closure_Ortrancl(X2759,X2756))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2759),tc_List_Olist(X2759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2759),tc_List_Olist(X2759)),X2758),X2755)),c_List_Olistrel(X2759,c_Transitive__Closure_Ortrancl(X2759,X2756)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).
fof(i_0_649,plain,
! [X2760,X2761,X2762,X2763,X2764] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2764),tc_List_Olist(X2764))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2764),tc_List_Olist(X2764)),X2763),X2762)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2764),c_List_Olistrel1(X2764,X2761))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2764),tc_List_Olist(X2764))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2764),tc_List_Olist(X2764)),hAPP(hAPP(c_List_Olist_OCons(X2764),X2760),X2763)),hAPP(hAPP(c_List_Olist_OCons(X2764),X2760),X2762))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2764),c_List_Olistrel1(X2764,X2761)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).
fof(i_0_650,plain,
! [X2713,X2714,X2715,X2716,X2717] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2717),tc_List_Olist(X2717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2717),tc_List_Olist(X2717)),X2716),X2715)),c_List_Olexord(X2717,X2714)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2717),tc_List_Olist(X2717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2717),tc_List_Olist(X2717)),X2715),X2713)),c_List_Olexord(X2717,X2714)))
| ~ c_Relation_Otrans(X2717,X2714)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2717),tc_List_Olist(X2717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2717),tc_List_Olist(X2717)),X2716),X2713)),c_List_Olexord(X2717,X2714))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__trans])]) ).
fof(i_0_651,plain,
! [X2547,X2548,X2549,X2550,X2551,X2552] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2552),tc_List_Olist(X2552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2552),tc_List_Olist(X2552)),X2551),X2550)),c_List_Olistrel1(X2552,X2549)))
| X2548 != X2547
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2552),tc_List_Olist(X2552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2552),tc_List_Olist(X2552)),hAPP(hAPP(c_List_Oappend(X2552),X2551),X2548)),hAPP(hAPP(c_List_Oappend(X2552),X2550),X2547))),c_List_Olistrel1(X2552,X2549))) )
& ( X2551 != X2550
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2552),tc_List_Olist(X2552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2552),tc_List_Olist(X2552)),X2548),X2547)),c_List_Olistrel1(X2552,X2549)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2552),tc_List_Olist(X2552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2552),tc_List_Olist(X2552)),hAPP(hAPP(c_List_Oappend(X2552),X2551),X2548)),hAPP(hAPP(c_List_Oappend(X2552),X2550),X2547))),c_List_Olistrel1(X2552,X2549))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).
fof(i_0_652,plain,
! [X2596,X2597,X2598,X2599,X2600] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2600),tc_List_Olist(X2600))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2600),tc_List_Olist(X2600)),X2599),X2598)),c_List_Olexord(X2600,X2597)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2600),tc_List_Olist(X2600))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2600),tc_List_Olist(X2600)),hAPP(hAPP(c_List_Oappend(X2600),X2596),X2599)),hAPP(hAPP(c_List_Oappend(X2600),X2596),X2598))),c_List_Olexord(X2600,X2597))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).
fof(i_0_653,plain,
! [X2601,X2602,X2603,X2604,X2605] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2605),tc_List_Olist(X2605))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2605),tc_List_Olist(X2605)),X2604),X2603)),c_List_Olistrel1(X2605,X2602)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2605),tc_List_Olist(X2605))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2605),tc_List_Olist(X2605)),hAPP(hAPP(c_List_Olist_OCons(X2605),X2601),X2604)),hAPP(hAPP(c_List_Olist_OCons(X2605),X2601),X2603))),c_List_Olistrel1(X2605,X2602))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).
cnf(i_0_654,plain,
( c_FuncSet_Ocompose(X1,X2,X2,X4,c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_520]) ).
cnf(i_0_655,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_FuncSet_Ocompose(X1,X3,X2,X4,X5,X6)),c_FuncSet_Oextensional(X1,X2,X4))),
inference(split_conjunct,[status(thm)],[i_0_521]) ).
fof(i_0_656,plain,
! [X2224,X2225,X2226,X2227,X2228] :
( ( X2225 != X2224
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2224 != X2228
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 != X2228
| X2224 = X2227
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2224)),X2226))
| X2224 = X2228
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 = X2228
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),X2226))
| X2224 = X2228
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2224 != X2228
| X2224 = X2228
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 != X2228
| X2225 = X2228
| X2224 = X2228
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),X2226))
| X2225 = X2228
| X2224 = X2228
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 != X2228
| X2224 != X2227
| X2224 = X2228
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),X2226))
| X2224 != X2227
| X2224 = X2228
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 != X2228
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2224)),X2226))
| X2224 = X2228
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),X2226))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2224)),X2226))
| X2224 = X2228
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2224 != X2228
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 != X2228
| X2225 = X2228
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),X2226))
| X2225 = X2228
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 != X2228
| X2224 != X2227
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),X2226))
| X2224 != X2227
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( X2225 != X2228
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2224)),X2226))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),X2226))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2224)),X2226))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2227)),X2226))
| X2225 = X2224
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2226),X2228),X2227)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2226),c_Arrow__Order__Mirabelle_OLin))
| X2228 = X2227 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_657,plain,
! [X2243,X2244,X2245,X2246,X2247] :
( ( X2244 != X2243
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2244 != X2246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 != X2246
| X2244 = X2247
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2247)),X2245))
| X2244 = X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 = X2246
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),X2245))
| X2244 = X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2244 != X2246
| X2244 = X2246
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 != X2246
| X2243 = X2246
| X2244 = X2246
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),X2245))
| X2243 = X2246
| X2244 = X2246
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 != X2246
| X2244 != X2247
| X2244 = X2246
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),X2245))
| X2244 != X2247
| X2244 = X2246
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 != X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2247)),X2245))
| X2244 = X2246
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),X2245))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2247)),X2245))
| X2244 = X2246
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2244 != X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 != X2246
| X2243 = X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),X2245))
| X2243 = X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 != X2246
| X2244 != X2247
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),X2245))
| X2244 != X2247
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( X2243 != X2246
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2247)),X2245))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),X2245))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2247)),X2245))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2247),X2243)),X2245))
| X2244 = X2243
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),c_Arrow__Order__Mirabelle_Oabove(X2245,X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2245),c_Arrow__Order__Mirabelle_OLin))
| X2247 = X2246 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_658,plain,
! [X2434,X2435,X2436] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2436,X2436)),hAPP(hAPP(c_Product__Type_OPair(X2436,X2436),esk27_3(X2434,X2435,X2436)),esk27_3(X2434,X2435,X2436))),X2435))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2436),tc_List_Olist(X2436))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2436),tc_List_Olist(X2436)),X2434),X2434)),c_List_Olexord(X2436,X2435))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_522])])]) ).
fof(i_0_659,plain,
! [X3680,X3681,X3682,X3683,X3684,X3685] :
( ~ hBOOL(hAPP(hAPP(c_member(X3685),X3684),X3683))
| c_Fun_Ooverride__on(X3685,X3682,X3681,X3680,X3683,X3684) = hAPP(X3680,X3684) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_override__on__apply__in])]) ).
fof(i_0_660,plain,
! [X3674,X3675,X3676,X3677,X3678,X3679] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3679),X3678),X3677))
| c_Fun_Ooverride__on(X3679,X3676,X3675,X3674,X3677,X3678) = hAPP(X3674,X3678) )
& ( hBOOL(hAPP(hAPP(c_member(X3679),X3678),X3677))
| c_Fun_Ooverride__on(X3679,X3676,X3675,X3674,X3677,X3678) = hAPP(X3675,X3678) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])]) ).
fof(i_0_661,plain,
! [X3686,X3687,X3688,X3689,X3690,X3691] :
( hBOOL(hAPP(hAPP(c_member(X3691),X3690),X3689))
| c_Fun_Ooverride__on(X3691,X3688,X3687,X3686,X3689,X3690) = hAPP(X3687,X3690) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).
fof(i_0_662,plain,
! [X3600,X3601,X3602,X3603,X3604] :
( ~ hBOOL(hAPP(hAPP(c_member(X3604),X3603),c_Set_Oimage(X3602,X3604,X3601,X3600)))
| hBOOL(hAPP(hAPP(c_member(X3602),hAPP(c_Hilbert__Choice_Oinv__into(X3602,X3604,X3600,X3601),X3603)),X3600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
fof(i_0_663,plain,
! [X2463,X2464,X2465,X2466,X2467] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2467,X2467)),hAPP(hAPP(c_Product__Type_OPair(X2467,X2467),X2466),X2465)),X2464))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2467),tc_List_Olist(X2467))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2467),tc_List_Olist(X2467)),hAPP(hAPP(c_List_Olist_OCons(X2467),X2466),X2463)),hAPP(hAPP(c_List_Olist_OCons(X2467),X2465),X2463))),c_List_Olistrel1(X2467,X2464))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).
fof(i_0_664,plain,
! [X3923,X3924,X3925] : c_Hilbert__Choice_OEps(tc_prod(X3925,X3924),X3923) = c_Hilbert__Choice_OEps(tc_prod(X3925,X3924),hAPP(c_Product__Type_Oprod_Oprod__case(X3925,X3924,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3924,tc_prod(X3925,X3924)),tc_fun(X3924,tc_HOL_Obool),X3925),hAPP(c_COMBB(tc_prod(X3925,X3924),tc_HOL_Obool,X3924),X3923)),c_Product__Type_OPair(X3925,X3924)))),
inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).
fof(i_0_665,plain,
! [X2823,X2824,X2825,X2826,X2827] :
( ~ c_Relation_Osingle__valued(X2827,X2827,X2826)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2827,X2827)),hAPP(hAPP(c_Product__Type_OPair(X2827,X2827),X2825),X2824)),c_Transitive__Closure_Ortrancl(X2827,X2826)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2827,X2827)),hAPP(hAPP(c_Product__Type_OPair(X2827,X2827),X2825),X2823)),c_Transitive__Closure_Ortrancl(X2827,X2826)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2827,X2827)),hAPP(hAPP(c_Product__Type_OPair(X2827,X2827),X2824),X2823)),c_Transitive__Closure_Ortrancl(X2827,X2826)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2827,X2827)),hAPP(hAPP(c_Product__Type_OPair(X2827,X2827),X2823),X2824)),c_Transitive__Closure_Ortrancl(X2827,X2826))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).
cnf(i_0_666,plain,
( c_FuncSet_Ocompose(X1,X1,X2,X4,X3,c_FuncSet_Orestrict(X1,X1,c_COMBI(X1),X4)) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_525]) ).
fof(i_0_667,plain,
! [X2909,X2910,X2911,X2912] :
( ~ hBOOL(hAPP(hAPP(c_member(X2912),X2911),c_Relation_ODomain(X2912,X2910,X2909)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2912,X2910)),hAPP(hAPP(c_Product__Type_OPair(X2912,X2910),X2911),esk56_4(X2909,X2910,X2911,X2912))),X2909)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])])]) ).
fof(i_0_668,plain,
! [X2864,X2865,X2866,X2867,X2869,X2870,X2871,X2872,X2873] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2867),X2866),c_Relation_ODomain(X2867,X2865,X2864)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2867,X2865)),hAPP(hAPP(c_Product__Type_OPair(X2867,X2865),X2866),esk52_4(X2864,X2865,X2866,X2867))),X2864)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2872,X2870)),hAPP(hAPP(c_Product__Type_OPair(X2872,X2870),X2871),X2873)),X2869))
| hBOOL(hAPP(hAPP(c_member(X2872),X2871),c_Relation_ODomain(X2872,X2870,X2869))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__iff])])])])]) ).
fof(i_0_669,plain,
! [X2558,X2559,X2560,X2561,X2562,X2564,X2565,X2566,X2567,X2568,X2569] :
( ( hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),esk32_5(X2558,X2559,X2560,X2561,X2562)) = X2559
| X2559 = c_List_Olist_ONil(X2562)
| hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),X2560) != hAPP(hAPP(c_List_Oappend(X2562),X2559),X2558) )
& ( X2560 = hAPP(hAPP(c_List_Oappend(X2562),esk32_5(X2558,X2559,X2560,X2561,X2562)),X2558)
| X2559 = c_List_Olist_ONil(X2562)
| hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),X2560) != hAPP(hAPP(c_List_Oappend(X2562),X2559),X2558) )
& ( hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),esk32_5(X2558,X2559,X2560,X2561,X2562)) = X2559
| hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),X2560) = X2558
| hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),X2560) != hAPP(hAPP(c_List_Oappend(X2562),X2559),X2558) )
& ( X2560 = hAPP(hAPP(c_List_Oappend(X2562),esk32_5(X2558,X2559,X2560,X2561,X2562)),X2558)
| hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),X2560) = X2558
| hAPP(hAPP(c_List_Olist_OCons(X2562),X2561),X2560) != hAPP(hAPP(c_List_Oappend(X2562),X2559),X2558) )
& ( X2565 != c_List_Olist_ONil(X2568)
| hAPP(hAPP(c_List_Olist_OCons(X2568),X2567),X2566) != X2564
| hAPP(hAPP(c_List_Olist_OCons(X2568),X2567),X2566) = hAPP(hAPP(c_List_Oappend(X2568),X2565),X2564) )
& ( hAPP(hAPP(c_List_Olist_OCons(X2568),X2567),X2569) != X2565
| X2566 != hAPP(hAPP(c_List_Oappend(X2568),X2569),X2564)
| hAPP(hAPP(c_List_Olist_OCons(X2568),X2567),X2566) = hAPP(hAPP(c_List_Oappend(X2568),X2565),X2564) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__append__conv])])])])])]) ).
fof(i_0_670,plain,
! [X2570,X2571,X2572,X2573,X2574,X2576,X2577,X2578,X2579,X2580,X2581] :
( ( X2573 = hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),esk33_5(X2570,X2571,X2572,X2573,X2574))
| X2573 = c_List_Olist_ONil(X2574)
| hAPP(hAPP(c_List_Oappend(X2574),X2573),X2572) != hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),X2570) )
& ( hAPP(hAPP(c_List_Oappend(X2574),esk33_5(X2570,X2571,X2572,X2573,X2574)),X2572) = X2570
| X2573 = c_List_Olist_ONil(X2574)
| hAPP(hAPP(c_List_Oappend(X2574),X2573),X2572) != hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),X2570) )
& ( X2573 = hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),esk33_5(X2570,X2571,X2572,X2573,X2574))
| X2572 = hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),X2570)
| hAPP(hAPP(c_List_Oappend(X2574),X2573),X2572) != hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),X2570) )
& ( hAPP(hAPP(c_List_Oappend(X2574),esk33_5(X2570,X2571,X2572,X2573,X2574)),X2572) = X2570
| X2572 = hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),X2570)
| hAPP(hAPP(c_List_Oappend(X2574),X2573),X2572) != hAPP(hAPP(c_List_Olist_OCons(X2574),X2571),X2570) )
& ( X2579 != c_List_Olist_ONil(X2580)
| X2578 != hAPP(hAPP(c_List_Olist_OCons(X2580),X2577),X2576)
| hAPP(hAPP(c_List_Oappend(X2580),X2579),X2578) = hAPP(hAPP(c_List_Olist_OCons(X2580),X2577),X2576) )
& ( X2579 != hAPP(hAPP(c_List_Olist_OCons(X2580),X2577),X2581)
| hAPP(hAPP(c_List_Oappend(X2580),X2581),X2578) != X2576
| hAPP(hAPP(c_List_Oappend(X2580),X2579),X2578) = hAPP(hAPP(c_List_Olist_OCons(X2580),X2577),X2576) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__Cons__conv])])])])])]) ).
fof(i_0_671,plain,
! [X3605,X3606,X3607,X3608,X3609,X3610] :
( hAPP(c_Hilbert__Choice_Oinv__into(X3610,X3609,X3608,X3607),X3606) != hAPP(c_Hilbert__Choice_Oinv__into(X3610,X3609,X3608,X3607),X3605)
| ~ hBOOL(hAPP(hAPP(c_member(X3609),X3606),c_Set_Oimage(X3610,X3609,X3607,X3608)))
| ~ hBOOL(hAPP(hAPP(c_member(X3609),X3605),c_Set_Oimage(X3610,X3609,X3607,X3608)))
| X3606 = X3605 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
fof(i_0_672,plain,
! [X3150,X3151,X3152] : c_List_Olistsp(X3152,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3152,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3152,tc_fun(X3152,tc_HOL_Obool),tc_HOL_Obool),c_member(X3152)),X3151),hAPP(hAPP(c_COMBC(X3152,tc_fun(X3152,tc_HOL_Obool),tc_HOL_Obool),c_member(X3152)),X3150))) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X3152),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X3152),tc_fun(tc_List_Olist(X3152),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X3152))),c_List_Olists(X3152,X3151)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3152),tc_fun(tc_List_Olist(X3152),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X3152))),c_List_Olists(X3152,X3150))),
inference(variable_rename,[status(thm)],[fact_lists__Int__eq]) ).
fof(i_0_673,plain,
! [X2658,X2659] : c_List_Orotate1(X2659,X2658) = c_List_Olist_Olist__case(tc_List_Olist(X2659),X2659,c_List_Olist_ONil(X2659),hAPP(hAPP(c_COMBB(tc_List_Olist(X2659),tc_fun(tc_List_Olist(X2659),tc_List_Olist(X2659)),X2659),hAPP(c_COMBC(tc_List_Olist(X2659),tc_List_Olist(X2659),tc_List_Olist(X2659)),c_List_Oappend(X2659))),hAPP(hAPP(c_COMBC(X2659,tc_List_Olist(X2659),tc_List_Olist(X2659)),c_List_Olist_OCons(X2659)),c_List_Olist_ONil(X2659))),X2658),
inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).
fof(i_0_674,plain,
! [X3011,X3012,X3013] :
( ( ~ hBOOL(hAPP(c_List_Olistsp(X3013,hAPP(hAPP(c_COMBC(X3013,tc_fun(X3013,tc_HOL_Obool),tc_HOL_Obool),c_member(X3013)),X3012)),X3011))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3013)),X3011),c_List_Olists(X3013,X3012))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3013)),X3011),c_List_Olists(X3013,X3012)))
| hBOOL(hAPP(c_List_Olistsp(X3013,hAPP(hAPP(c_COMBC(X3013,tc_fun(X3013,tc_HOL_Obool),tc_HOL_Obool),c_member(X3013)),X3012)),X3011)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])]) ).
fof(i_0_675,plain,
! [X4058,X4059,X4060,X4061,X4062] :
( ( hAPP(X4059,X4061) = hAPP(X4059,X4060)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4059,X4061),hAPP(X4059,X4060))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4062,X4062)),hAPP(hAPP(c_Product__Type_OPair(X4062,X4062),X4061),X4060)),c_List_Omeasures(X4062,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4062,tc_Nat_Onat)),X4059),X4058)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4062,X4062)),hAPP(hAPP(c_Product__Type_OPair(X4062,X4062),X4061),X4060)),c_List_Omeasures(X4062,X4058)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4059,X4061),hAPP(X4059,X4060))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4062,X4062)),hAPP(hAPP(c_Product__Type_OPair(X4062,X4062),X4061),X4060)),c_List_Omeasures(X4062,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4062,tc_Nat_Onat)),X4059),X4058)))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4059,X4061),hAPP(X4059,X4060))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4062,X4062)),hAPP(hAPP(c_Product__Type_OPair(X4062,X4062),X4061),X4060)),c_List_Omeasures(X4062,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4062,tc_Nat_Onat)),X4059),X4058)))) )
& ( hAPP(X4059,X4061) != hAPP(X4059,X4060)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4062,X4062)),hAPP(hAPP(c_Product__Type_OPair(X4062,X4062),X4061),X4060)),c_List_Omeasures(X4062,X4058)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4062,X4062)),hAPP(hAPP(c_Product__Type_OPair(X4062,X4062),X4061),X4060)),c_List_Omeasures(X4062,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4062,tc_Nat_Onat)),X4059),X4058)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).
fof(i_0_676,plain,
! [X2804,X2805,X2806,X2807,X2808] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2807),X2806)),c_Transitive__Closure_Ortrancl(X2808,X2805)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2806),X2804)),c_Transitive__Closure_Ortrancl(X2808,X2805)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2808,X2808)),hAPP(hAPP(c_Product__Type_OPair(X2808,X2808),X2807),X2804)),c_Transitive__Closure_Ortrancl(X2808,X2805))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).
fof(i_0_677,plain,
! [X2790,X2791,X2792,X2793,X2794] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2794,X2794)),hAPP(hAPP(c_Product__Type_OPair(X2794,X2794),X2793),X2792)),X2791))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2794,X2794)),hAPP(hAPP(c_Product__Type_OPair(X2794,X2794),X2792),X2790)),c_Transitive__Closure_Ortrancl(X2794,X2791)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2794,X2794)),hAPP(hAPP(c_Product__Type_OPair(X2794,X2794),X2793),X2790)),c_Transitive__Closure_Ortrancl(X2794,X2791))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).
fof(i_0_678,plain,
! [X2795,X2796,X2797,X2798,X2799] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2799,X2799)),hAPP(hAPP(c_Product__Type_OPair(X2799,X2799),X2798),X2797)),c_Transitive__Closure_Ortrancl(X2799,X2796)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2799,X2799)),hAPP(hAPP(c_Product__Type_OPair(X2799,X2799),X2797),X2795)),X2796))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2799,X2799)),hAPP(hAPP(c_Product__Type_OPair(X2799,X2799),X2798),X2795)),c_Transitive__Closure_Ortrancl(X2799,X2796))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).
fof(i_0_679,plain,
! [X2718,X2719,X2720,X2721] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2721),tc_List_Olist(X2721))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2721),tc_List_Olist(X2721)),X2720),X2719)),c_List_Olistrel(X2721,X2718)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2721),tc_List_Olist(X2721))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2721),tc_List_Olist(X2721)),X2720),X2719)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2721),c_List_Olistrel1(X2721,X2718)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).
fof(i_0_680,plain,
! [X2722,X2723,X2724,X2725] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2725),tc_List_Olist(X2725))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2725),tc_List_Olist(X2725)),X2724),X2723)),c_List_Olistrel1(X2725,X2722)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2725),tc_List_Olist(X2725))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2725),tc_List_Olist(X2725)),X2724),X2723)),c_List_Olistrel(X2725,c_Transitive__Closure_Ortrancl(X2725,X2722)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).
fof(i_0_681,plain,
! [X2693,X2694,X2695,X2696] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2695),X2694)),c_List_Olexord(X2696,X2693)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2695),X2694)),c_List_Olex(X2696,X2693))) )
& ( c_Nat_Osize__class_Osize(tc_List_Olist(X2696),X2695) = c_Nat_Osize__class_Osize(tc_List_Olist(X2696),X2694)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2695),X2694)),c_List_Olex(X2696,X2693))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2695),X2694)),c_List_Olexord(X2696,X2693)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2696),X2695) != c_Nat_Osize__class_Osize(tc_List_Olist(X2696),X2694)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2695),X2694)),c_List_Olex(X2696,X2693))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).
cnf(i_0_682,plain,
( c_FuncSet_Ocompose(X2,X1,X2,X5,X3,c_FuncSet_Orestrict(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5)) = c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5)
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_527]) ).
fof(i_0_683,plain,
! [X2785,X2786,X2787,X2788,X2789] :
( ~ c_Relation_Otrans(X2789,X2788)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2789,X2789)),hAPP(hAPP(c_Product__Type_OPair(X2789,X2789),X2787),X2786)),X2788))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2789,X2789)),hAPP(hAPP(c_Product__Type_OPair(X2789,X2789),X2786),X2785)),X2788))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2789,X2789)),hAPP(hAPP(c_Product__Type_OPair(X2789,X2789),X2787),X2785)),X2788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transD])]) ).
fof(i_0_684,plain,
! [X2775,X2776,X2777,X2778,X2779,X2780,X2781] :
( ( ~ c_Relation_Otrans(X2776,X2775)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2776,X2776)),hAPP(hAPP(c_Product__Type_OPair(X2776,X2776),X2777),X2778)),X2775))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2776,X2776)),hAPP(hAPP(c_Product__Type_OPair(X2776,X2776),X2778),X2779)),X2775))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2776,X2776)),hAPP(hAPP(c_Product__Type_OPair(X2776,X2776),X2777),X2779)),X2775)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2781,X2781)),hAPP(hAPP(c_Product__Type_OPair(X2781,X2781),esk45_2(X2780,X2781)),esk46_2(X2780,X2781))),X2780))
| c_Relation_Otrans(X2781,X2780) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2781,X2781)),hAPP(hAPP(c_Product__Type_OPair(X2781,X2781),esk46_2(X2780,X2781)),esk47_2(X2780,X2781))),X2780))
| c_Relation_Otrans(X2781,X2780) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2781,X2781)),hAPP(hAPP(c_Product__Type_OPair(X2781,X2781),esk45_2(X2780,X2781)),esk47_2(X2780,X2781))),X2780))
| c_Relation_Otrans(X2781,X2780) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__def])])])])])]) ).
fof(i_0_685,plain,
! [X4020,X4021,X4022,X4023,X4024] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4024,X4023),hAPP(X4024,X4022))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4021,X4021)),hAPP(hAPP(c_Product__Type_OPair(X4021,X4021),X4023),X4022)),c_List_Omeasures(X4021,X4020)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4021,X4021)),hAPP(hAPP(c_Product__Type_OPair(X4021,X4021),X4023),X4022)),c_List_Omeasures(X4021,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4021,tc_Nat_Onat)),X4024),X4020)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).
fof(i_0_686,plain,
! [X3309,X3310,X3311,X3312,X3313,X3314,X3315] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3315,X3314)),hAPP(hAPP(c_Product__Type_OPair(X3315,X3314),X3313),X3312)),X3311))
| hBOOL(hAPP(hAPP(c_member(X3310),hAPP(hAPP(X3309,X3313),X3312)),c_Set_Oimage(tc_prod(X3315,X3314),X3310,hAPP(c_Product__Type_Oprod_Oprod__case(X3315,X3314,X3310),X3309),X3311))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).
fof(i_0_687,plain,
! [X2582,X2583,X2584,X2585,X2586,X2587,X2588,X2589] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2589,X2589)),hAPP(hAPP(c_Product__Type_OPair(X2589,X2589),X2588),X2587)),X2586))
| X2585 != hAPP(hAPP(c_List_Oappend(X2589),X2584),hAPP(hAPP(c_List_Olist_OCons(X2589),X2588),X2583))
| X2582 != hAPP(hAPP(c_List_Oappend(X2589),X2584),hAPP(hAPP(c_List_Olist_OCons(X2589),X2587),X2583))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2589),tc_List_Olist(X2589))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2589),tc_List_Olist(X2589)),X2585),X2582)),c_List_Olistrel1(X2589,X2586))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).
fof(i_0_688,plain,
! [X3360,X3361,X3362,X3363,X3364,X3366,X3367,X3368,X3369,X3370,X3371] :
( ( hBOOL(hAPP(hAPP(c_member(X3362),esk83_4(X3360,X3361,X3362,X3363)),X3360))
| ~ hBOOL(hAPP(hAPP(c_member(X3364),X3363),c_Set_Oimage(X3362,X3364,X3361,X3360))) )
& ( X3363 = hAPP(X3361,esk83_4(X3360,X3361,X3362,X3363))
| ~ hBOOL(hAPP(hAPP(c_member(X3364),X3363),c_Set_Oimage(X3362,X3364,X3361,X3360))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3368),X3370),X3366))
| X3369 != hAPP(X3367,X3370)
| hBOOL(hAPP(hAPP(c_member(X3371),X3369),c_Set_Oimage(X3368,X3371,X3367,X3366))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__iff])])])])])]) ).
fof(i_0_689,plain,
! [X2214,X2215,X2216] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2214)),X2216))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2215)),X2216))
| X2215 = X2214
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2216),c_Arrow__Order__Mirabelle_OLin)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2215)),X2216))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2215),X2214)),X2216))
| X2215 = X2214
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2216),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).
fof(i_0_690,plain,
! [X2217,X2218,X2219] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2219),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2218),X2217)),X2219))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2217),X2218)),X2219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])]) ).
fof(i_0_691,plain,
! [X3078,X3079,X3080] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3080,X3079)),hAPP(hAPP(c_Product__Type_OPair(X3080,X3079),esk77_3(X3078,X3079,X3080)),esk78_3(X3078,X3079,X3080))),X3078))
| c_Relation_Osingle__valued(X3080,X3079,X3078) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3080,X3079)),hAPP(hAPP(c_Product__Type_OPair(X3080,X3079),esk77_3(X3078,X3079,X3080)),esk79_3(X3078,X3079,X3080))),X3078))
| c_Relation_Osingle__valued(X3080,X3079,X3078) )
& ( esk78_3(X3078,X3079,X3080) != esk79_3(X3078,X3079,X3080)
| c_Relation_Osingle__valued(X3080,X3079,X3078) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedI])])])]) ).
fof(i_0_692,plain,
! [X2846,X2847,X2848,X2849,X2850,X2851,X2852,X2853,X2854] :
( ( ~ c_Relation_Osingle__valued(X2848,X2847,X2846)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2848,X2847)),hAPP(hAPP(c_Product__Type_OPair(X2848,X2847),X2849),X2850)),X2846))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2848,X2847)),hAPP(hAPP(c_Product__Type_OPair(X2848,X2847),X2849),X2851)),X2846))
| X2850 = X2851 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2854,X2853)),hAPP(hAPP(c_Product__Type_OPair(X2854,X2853),esk49_3(X2852,X2853,X2854)),esk50_3(X2852,X2853,X2854))),X2852))
| c_Relation_Osingle__valued(X2854,X2853,X2852) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2854,X2853)),hAPP(hAPP(c_Product__Type_OPair(X2854,X2853),esk49_3(X2852,X2853,X2854)),esk51_3(X2852,X2853,X2854))),X2852))
| c_Relation_Osingle__valued(X2854,X2853,X2852) )
& ( esk50_3(X2852,X2853,X2854) != esk51_3(X2852,X2853,X2854)
| c_Relation_Osingle__valued(X2854,X2853,X2852) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__def])])])])])]) ).
fof(i_0_693,plain,
! [X3423,X3424,X3425,X3426,X3427] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X3427,X3426,tc_HOL_Obool,X3425),X3424),X3423))
| hBOOL(hAPP(X3425,hAPP(hAPP(c_Product__Type_OPair(X3427,X3426),X3424),X3423))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryD])]) ).
fof(i_0_694,plain,
! [X3418,X3419,X3420,X3421,X3422] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X3422,X3421,tc_HOL_Obool,X3420),X3419),X3418))
| hBOOL(hAPP(X3420,hAPP(hAPP(c_Product__Type_OPair(X3422,X3421),X3419),X3418))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryE])]) ).
fof(i_0_695,plain,
! [X3938,X3939,X3940,X3941,X3942] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3942,X3941)),X3940),c_FuncSet_OPi(X3942,X3941,X3939,c_COMBK(tc_fun(X3941,tc_HOL_Obool),X3942,X3938))))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3941,tc_HOL_Obool),c_Set_Oimage(X3942,X3941,X3940,X3939),X3938) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_696,plain,
! [X3895,X3896,X3897,X3898,X3899,X3901,X3902,X3903,X3904,X3905,X3906] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3897,tc_HOL_Obool),esk102_5(X3895,X3896,X3897,X3898,X3899),X3895)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3899,tc_HOL_Obool),X3898,c_Set_Oimage(X3897,X3899,X3896,X3895)) )
& ( X3898 = c_Set_Oimage(X3897,X3899,X3896,esk102_5(X3895,X3896,X3897,X3898,X3899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3899,tc_HOL_Obool),X3898,c_Set_Oimage(X3897,X3899,X3896,X3895)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3903,tc_HOL_Obool),X3906,X3901)
| X3904 != c_Set_Oimage(X3903,X3905,X3902,X3906)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3905,tc_HOL_Obool),X3904,c_Set_Oimage(X3903,X3905,X3902,X3901)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__image__iff])])])])])]) ).
fof(i_0_697,plain,
! [X3204,X3205,X3206,X3207,X3208,X3209,X3210] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3210,X3209,tc_fun(X3208,tc_HOL_Obool)),X3207),hAPP(hAPP(c_Product__Type_OPair(X3210,X3209),X3206),X3205)),X3204))
| hBOOL(hAPP(hAPP(hAPP(X3207,X3206),X3205),X3204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).
fof(i_0_698,plain,
! [X2253,X2254,X2255,X2256,X2257,X2258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2258,X2257)),X2256),c_FuncSet_OPi(X2258,X2257,X2255,c_COMBK(tc_fun(X2257,tc_HOL_Obool),X2258,X2254))))
| ~ hBOOL(hAPP(hAPP(c_member(X2258),X2253),X2255))
| hBOOL(hAPP(hAPP(c_member(X2257),hAPP(X2256,X2253)),X2254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_699,plain,
! [X2858,X2859,X2860,X2861,X2862,X2863] :
( ~ c_Relation_Osingle__valued(X2863,X2862,X2861)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2863,X2862)),hAPP(hAPP(c_Product__Type_OPair(X2863,X2862),X2860),X2859)),X2861))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2863,X2862)),hAPP(hAPP(c_Product__Type_OPair(X2863,X2862),X2860),X2858)),X2861))
| X2859 = X2858 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).
fof(i_0_700,plain,
! [X3947,X3948,X3949,X3950,X3951] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3949,X3950),X3948,X3947)
| c_Orderings_Oord__class_Oless__eq(X3950,hAPP(X3948,X3951),hAPP(X3947,X3951))
| ~ class_Orderings_Oord(X3950) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3950,hAPP(X3948,esk103_4(X3947,X3948,X3949,X3950)),hAPP(X3947,esk103_4(X3947,X3948,X3949,X3950)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3949,X3950),X3948,X3947)
| ~ class_Orderings_Oord(X3950) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__fun__def])])])])]) ).
fof(i_0_701,plain,
! [X2424,X2425,X2426,X2429,X2430,X2431,X2432,X2433] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2426),tc_List_Olist(X2426))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2426),tc_List_Olist(X2426)),c_List_Olist_ONil(X2426)),X2425)),c_List_Olexord(X2426,X2424)))
| X2425 = hAPP(hAPP(c_List_Olist_OCons(X2426),esk25_3(X2424,X2425,X2426)),esk26_3(X2424,X2425,X2426)) )
& ( X2430 != hAPP(hAPP(c_List_Olist_OCons(X2431),X2432),X2433)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2431),tc_List_Olist(X2431))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2431),tc_List_Olist(X2431)),c_List_Olist_ONil(X2431)),X2430)),c_List_Olexord(X2431,X2429))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__Nil__left])])])])]) ).
fof(i_0_702,plain,
! [X2193] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2193),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,X2193)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_703,plain,
! [X4030,X4031,X4032,X4033,X4034] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4034,X4033),hAPP(X4034,X4032))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4031,X4031)),hAPP(hAPP(c_Product__Type_OPair(X4031,X4031),X4033),X4032)),X4030))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4031,X4031)),hAPP(hAPP(c_Product__Type_OPair(X4031,X4031),X4033),X4032)),c_Wellfounded_Omlex__prod(X4031,X4034,X4030))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_704,plain,
! [X3907,X3908,X3909,X3910,X3911] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3911,tc_HOL_Obool),c_Set_Oimage(X3910,X3911,X3909,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3910,tc_HOL_Obool),X3908,X3907)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3911,tc_HOL_Obool),c_Set_Oimage(X3910,X3911,X3909,X3908),c_Set_Oimage(X3910,X3911,X3909,X3907))),
inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).
fof(i_0_705,plain,
! [X2311,X2312,X2313,X2314,X2315] :
( ( ~ c_FunDef_Oin__rel(X2315,X2314,X2313,X2312,X2311)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2315,X2314)),hAPP(hAPP(c_Product__Type_OPair(X2315,X2314),X2312),X2311)),X2313)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2315,X2314)),hAPP(hAPP(c_Product__Type_OPair(X2315,X2314),X2312),X2311)),X2313))
| c_FunDef_Oin__rel(X2315,X2314,X2313,X2312,X2311) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_706,plain,
! [X2701,X2702,X2703,X2704,X2705] :
( ( c_Nat_Osize__class_Osize(tc_List_Olist(X2705),X2704) = X2701
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2705),tc_List_Olist(X2705))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2705),tc_List_Olist(X2705)),X2704),X2703)),c_List_Olexn(X2705,X2702,X2701))) )
& ( c_Nat_Osize__class_Osize(tc_List_Olist(X2705),X2703) = X2701
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2705),tc_List_Olist(X2705))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2705),tc_List_Olist(X2705)),X2704),X2703)),c_List_Olexn(X2705,X2702,X2701))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).
fof(i_0_707,plain,
! [X2967,X2968,X2969] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2969,X2969)),hAPP(hAPP(c_Product__Type_OPair(X2969,X2969),esk61_3(X2967,X2968,X2969)),X2968)),X2967))
| hBOOL(hAPP(hAPP(c_member(X2969),X2968),c_Wellfounded_Oacc(X2969,X2967))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2969),esk61_3(X2967,X2968,X2969)),c_Wellfounded_Oacc(X2969,X2967)))
| hBOOL(hAPP(hAPP(c_member(X2969),X2968),c_Wellfounded_Oacc(X2969,X2967))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])])])]) ).
fof(i_0_708,plain,
! [X2917,X2918,X2919] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2919,X2919)),hAPP(hAPP(c_Product__Type_OPair(X2919,X2919),esk57_3(X2917,X2918,X2919)),X2918)),X2917))
| hBOOL(hAPP(hAPP(c_member(X2919),X2918),c_Wellfounded_Oacc(X2919,X2917))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2919),esk57_3(X2917,X2918,X2919)),c_Wellfounded_Oacc(X2919,X2917)))
| hBOOL(hAPP(hAPP(c_member(X2919),X2918),c_Wellfounded_Oacc(X2919,X2917))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).
fof(i_0_709,plain,
! [X2884,X2885,X2886,X2887,X2888,X2889,X2890] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2886),X2885),c_Wellfounded_Oacc(X2886,X2884)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2886,X2886)),hAPP(hAPP(c_Product__Type_OPair(X2886,X2886),X2887),X2885)),X2884))
| hBOOL(hAPP(hAPP(c_member(X2886),X2887),c_Wellfounded_Oacc(X2886,X2884))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2890,X2890)),hAPP(hAPP(c_Product__Type_OPair(X2890,X2890),esk54_3(X2888,X2889,X2890)),X2889)),X2888))
| hBOOL(hAPP(hAPP(c_member(X2890),X2889),c_Wellfounded_Oacc(X2890,X2888))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2890),esk54_3(X2888,X2889,X2890)),c_Wellfounded_Oacc(X2890,X2888)))
| hBOOL(hAPP(hAPP(c_member(X2890),X2889),c_Wellfounded_Oacc(X2890,X2888))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_Osimps])])])])])]) ).
fof(i_0_710,plain,
! [X3161,X3162,X3163,X3164] : hAPP(c_Product__Type_Oprod_Oprod__case(X3164,X3163,X3162),hAPP(hAPP(c_COMBB(tc_fun(X3163,tc_prod(X3164,X3163)),tc_fun(X3163,X3162),X3164),hAPP(c_COMBB(tc_prod(X3164,X3163),X3162,X3163),X3161)),c_Product__Type_OPair(X3164,X3163))) = X3161,
inference(variable_rename,[status(thm)],[fact_split__eta]) ).
fof(i_0_711,plain,
! [X2765,X2766,X2767,X2768] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2768),tc_List_Olist(X2768))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2768),tc_List_Olist(X2768)),X2767),X2766)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2768),c_List_Olistrel1(X2768,X2765))))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2768),X2767) = c_Nat_Osize__class_Osize(tc_List_Olist(X2768),X2766) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).
fof(i_0_712,plain,
! [X2474,X2475,X2476] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2476),tc_List_Olist(X2476))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2476),tc_List_Olist(X2476)),c_List_Olist_ONil(X2476)),X2475)),c_List_Olistrel(X2476,X2474)))
| X2475 = c_List_Olist_ONil(X2476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).
fof(i_0_713,plain,
! [X2606,X2607,X2608] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2608),tc_List_Olist(X2608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2608),tc_List_Olist(X2608)),c_List_Olist_ONil(X2608)),X2607)),c_List_Olistrel1(X2608,X2606))),
inference(variable_rename,[status(thm)],[i_0_531]) ).
fof(i_0_714,plain,
! [X2447,X2448,X2449] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2449),tc_List_Olist(X2449))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2449),tc_List_Olist(X2449)),c_List_Olist_ONil(X2449)),X2448)),c_List_Olex(X2449,X2447))),
inference(variable_rename,[status(thm)],[i_0_532]) ).
fof(i_0_715,plain,
! [X3595,X3596,X3597,X3598,X3599] :
( ~ hBOOL(hAPP(hAPP(c_member(X3599),X3598),c_Set_Oimage(X3597,X3599,X3596,X3595)))
| hAPP(X3596,hAPP(c_Hilbert__Choice_Oinv__into(X3597,X3599,X3595,X3596),X3598)) = X3598 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
fof(i_0_716,plain,
! [X2477,X2478,X2479] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2479),tc_List_Olist(X2479))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2479),tc_List_Olist(X2479)),X2478),c_List_Olist_ONil(X2479))),c_List_Olistrel(X2479,X2477)))
| X2478 = c_List_Olist_ONil(X2479) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).
fof(i_0_717,plain,
! [X2609,X2610,X2611] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2611),tc_List_Olist(X2611))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2611),tc_List_Olist(X2611)),X2610),c_List_Olist_ONil(X2611))),c_List_Olistrel1(X2611,X2609))),
inference(variable_rename,[status(thm)],[i_0_533]) ).
fof(i_0_718,plain,
! [X2444,X2445,X2446] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2446),tc_List_Olist(X2446))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2446),tc_List_Olist(X2446)),X2445),c_List_Olist_ONil(X2446))),c_List_Olex(X2446,X2444))),
inference(variable_rename,[status(thm)],[i_0_534]) ).
fof(i_0_719,plain,
! [X2418,X2419,X2420] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2420),tc_List_Olist(X2420))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2420),tc_List_Olist(X2420)),X2419),c_List_Olist_ONil(X2420))),c_List_Olexord(X2420,X2418))),
inference(variable_rename,[status(thm)],[i_0_535]) ).
fof(i_0_720,plain,
! [X2685,X2686,X2687,X2688] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2688),tc_List_Olist(X2688))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2688),tc_List_Olist(X2688)),X2687),X2686)),c_List_Olistrel1(X2688,X2685)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2688),X2687) = c_Nat_Osize__class_Osize(tc_List_Olist(X2688),X2686) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).
fof(i_0_721,plain,
! [X2689,X2690,X2691,X2692] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2692),tc_List_Olist(X2692))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2692),tc_List_Olist(X2692)),X2691),X2690)),c_List_Olistrel(X2692,X2689)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2692),X2691) = c_Nat_Osize__class_Osize(tc_List_Olist(X2692),X2690) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).
fof(i_0_722,plain,
! [X3219,X3220,X3221,X3223,X3224,X3225,X3226,X3227,X3230] :
( ( ~ hBOOL(hAPP(X3221,esk80_3(X3219,X3220,X3221)))
| hBOOL(hAPP(X3221,hAPP(hAPP(c_Product__Type_OPair(X3220,X3219),X3223),X3224))) )
& ( ~ hBOOL(hAPP(X3227,hAPP(hAPP(c_Product__Type_OPair(X3226,X3225),esk81_3(X3225,X3226,X3227)),esk82_3(X3225,X3226,X3227))))
| hBOOL(hAPP(X3227,X3230)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__paired__All])])])])]) ).
fof(i_0_723,plain,
! [X3413,X3414,X3415,X3416,X3417] :
( ~ hBOOL(hAPP(X3417,hAPP(hAPP(c_Product__Type_OPair(X3416,X3415),X3414),X3413)))
| hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X3416,X3415,tc_HOL_Obool,X3417),X3414),X3413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).
fof(i_0_724,plain,
! [X3669,X3670] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3670,X3670)),hAPP(hAPP(c_Product__Type_OPair(X3670,X3670),esk94_2(X3669,X3670)),esk95_2(X3669,X3670))),X3669))
| c_Relation_Otrans(X3670,X3669) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3670,X3670)),hAPP(hAPP(c_Product__Type_OPair(X3670,X3670),esk95_2(X3669,X3670)),esk96_2(X3669,X3670))),X3669))
| c_Relation_Otrans(X3670,X3669) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3670,X3670)),hAPP(hAPP(c_Product__Type_OPair(X3670,X3670),esk94_2(X3669,X3670)),esk96_2(X3669,X3670))),X3669))
| c_Relation_Otrans(X3670,X3669) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transI])])])]) ).
fof(i_0_725,plain,
! [X2370,X2371,X2372,X2373,X2374] :
( ( ~ c_Nitpick_Orefl_H(X2371,X2370)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2371,X2371)),hAPP(hAPP(c_Product__Type_OPair(X2371,X2371),X2372),X2372)),X2370)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2374,X2374)),hAPP(hAPP(c_Product__Type_OPair(X2374,X2374),esk22_2(X2373,X2374)),esk22_2(X2373,X2374))),X2373))
| c_Nitpick_Orefl_H(X2374,X2373) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def])])])])]) ).
fof(i_0_726,plain,
! [X3192,X3193,X3194,X3195,X3196,X3197,X3198] :
( ~ hBOOL(hAPP(hAPP(c_member(X3198),X3197),hAPP(hAPP(X3196,X3195),X3194)))
| hBOOL(hAPP(hAPP(c_member(X3198),X3197),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3193,X3192,tc_fun(X3198,tc_HOL_Obool)),X3196),hAPP(hAPP(c_Product__Type_OPair(X3193,X3192),X3195),X3194)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).
fof(i_0_727,plain,
! [X2646,X2647,X2648,X2649,X2650,X2651] :
( X2649 != hAPP(hAPP(c_List_Olist_OCons(X2648),X2650),X2651)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2648),tc_List_Olist(X2648))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2648),tc_List_Olist(X2648)),X2647),hAPP(hAPP(c_List_Oappend(X2648),X2647),X2649))),c_List_Olexord(X2648,X2646))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).
cnf(i_0_728,plain,
( c_Set_Oimage(X1,X6,c_FuncSet_Ocompose(X1,X2,X6,X4,X7,X3),X4) = X8
| c_Set_Oimage(X1,X2,X3,X4) != X5
| c_Set_Oimage(X2,X6,X7,X5) != X8 ),
inference(split_conjunct,[status(thm)],[i_0_536]) ).
fof(i_0_729,plain,
! [X3514,X3515,X3516,X3517] : hBOOL(hAPP(hAPP(c_member(tc_fun(X3517,X3516)),c_FuncSet_Orestrict(X3517,X3516,X3515,X3514)),c_FuncSet_Oextensional(X3517,X3516,X3514))),
inference(variable_rename,[status(thm)],[fact_restrict__extensional]) ).
fof(i_0_730,plain,
! [X2259,X2260,X2261,X2262,X2263,X2264] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2264,X2263)),X2262),c_FuncSet_OPi(X2264,X2263,X2261,X2260)))
| ~ hBOOL(hAPP(hAPP(c_member(X2264),X2259),X2261))
| hBOOL(hAPP(hAPP(c_member(X2263),hAPP(X2262,X2259)),hAPP(X2260,X2259))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_731,plain,
! [X2237,X2238,X2239,X2240,X2241,X2242] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2242,X2241)),X2240),c_FuncSet_OPi(X2242,X2241,X2239,X2238)))
| hBOOL(hAPP(hAPP(c_member(X2241),hAPP(X2240,X2237)),hAPP(X2238,X2237)))
| ~ hBOOL(hAPP(hAPP(c_member(X2242),X2237),X2239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_537])]) ).
fof(i_0_732,plain,
! [X3629,X3630,X3631,X3632,X3633,X3634] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3634,X3633)),X3632),c_FuncSet_Oextensional__funcset(X3634,X3633,X3631,X3630)))
| ~ hBOOL(hAPP(hAPP(c_member(X3634),X3629),X3631))
| hBOOL(hAPP(hAPP(c_member(X3633),hAPP(X3632,X3629)),X3630)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__mem])]) ).
fof(i_0_733,plain,
! [X3816,X3817,X3818] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3818,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3818,tc_fun(X3818,tc_HOL_Obool),tc_HOL_Obool),c_member(X3818)),X3817),hAPP(hAPP(c_COMBC(X3818,tc_fun(X3818,tc_HOL_Obool),tc_HOL_Obool),c_member(X3818)),X3816))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3818,tc_HOL_Obool),X3817,X3816) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3818,tc_HOL_Obool),X3817,X3816)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3818,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3818,tc_fun(X3818,tc_HOL_Obool),tc_HOL_Obool),c_member(X3818)),X3817),hAPP(hAPP(c_COMBC(X3818,tc_fun(X3818,tc_HOL_Obool),tc_HOL_Obool),c_member(X3818)),X3816)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_734,plain,
! [X4053,X4054,X4055,X4056,X4057] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4057,X4056),hAPP(X4057,X4055))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4054,X4054)),hAPP(hAPP(c_Product__Type_OPair(X4054,X4054),X4056),X4055)),c_List_Omeasures(X4054,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4054,tc_Nat_Onat)),X4057),X4053)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).
fof(i_0_735,plain,
! [X2274,X2275,X2276,X2277] :
( ( X2276 != X2274
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),c_Arrow__Order__Mirabelle_Omkbot(X2275,X2274))) )
& ( X2277 != X2274
| X2277 != X2276
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),c_Arrow__Order__Mirabelle_Omkbot(X2275,X2274))) )
& ( X2277 = X2274
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),X2275))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),c_Arrow__Order__Mirabelle_Omkbot(X2275,X2274))) )
& ( X2277 != X2274
| X2277 = X2274
| X2276 = X2274
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),c_Arrow__Order__Mirabelle_Omkbot(X2275,X2274))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),X2275))
| X2277 = X2274
| X2276 = X2274
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),c_Arrow__Order__Mirabelle_Omkbot(X2275,X2274))) )
& ( X2277 != X2274
| X2277 = X2276
| X2276 = X2274
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),c_Arrow__Order__Mirabelle_Omkbot(X2275,X2274))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),X2275))
| X2277 = X2276
| X2276 = X2274
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2277),X2276)),c_Arrow__Order__Mirabelle_Omkbot(X2275,X2274))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_736,plain,
! [X2278,X2279,X2280,X2281] :
( ( X2281 != X2278
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),c_Arrow__Order__Mirabelle_Omktop(X2279,X2278))) )
& ( X2280 != X2278
| X2281 != X2280
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),c_Arrow__Order__Mirabelle_Omktop(X2279,X2278))) )
& ( X2280 = X2278
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),X2279))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),c_Arrow__Order__Mirabelle_Omktop(X2279,X2278))) )
& ( X2280 != X2278
| X2280 = X2278
| X2281 = X2278
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),c_Arrow__Order__Mirabelle_Omktop(X2279,X2278))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),X2279))
| X2280 = X2278
| X2281 = X2278
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),c_Arrow__Order__Mirabelle_Omktop(X2279,X2278))) )
& ( X2280 != X2278
| X2281 = X2280
| X2281 = X2278
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),c_Arrow__Order__Mirabelle_Omktop(X2279,X2278))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),X2279))
| X2281 = X2280
| X2281 = X2278
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2281),X2280)),c_Arrow__Order__Mirabelle_Omktop(X2279,X2278))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_737,plain,
! [X2169] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X2169)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,X2169))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,X2169)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X2169))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iff])]) ).
fof(i_0_738,plain,
! [X3912,X3913,X3914,X3915,X3916,X3917] :
( c_Set_Oimage(X3917,X3916,X3915,X3914) != X3913
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3916,tc_HOL_Obool),X3912,X3913)
| c_Set_Oimage(X3917,X3916,X3915,c_Set_Oimage(X3916,X3917,c_Hilbert__Choice_Oinv__into(X3917,X3916,X3914,X3915),X3912)) = X3912 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_739,plain,
! [X2229,X2230,X2231] :
( X2231 = X2230
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2229),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2229),X2231),X2230)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_740,plain,
! [X3617,X3618,X3619,X3620,X3621,X3622] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3622,X3621)),X3620),c_FuncSet_Oextensional__funcset(X3622,X3621,X3619,X3618)))
| hBOOL(hAPP(hAPP(c_member(X3622),X3617),X3619))
| hAPP(X3620,X3617) = c_HOL_Oundefined(X3621) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])]) ).
fof(i_0_741,plain,
! [X2819,X2820,X2821,X2822] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2822,X2822)),hAPP(hAPP(c_Product__Type_OPair(X2822,X2822),X2821),X2820)),c_Transitive__Closure_Ortrancl(X2822,X2819)))
| ~ hBOOL(hAPP(hAPP(c_member(X2822),X2820),c_Wellfounded_Oacc(X2822,X2819)))
| hBOOL(hAPP(hAPP(c_member(X2822),X2821),c_Wellfounded_Oacc(X2822,X2819))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).
fof(i_0_742,plain,
! [X2815,X2816,X2817,X2818] :
( ~ hBOOL(hAPP(hAPP(c_member(X2818),X2817),c_Wellfounded_Oacc(X2818,X2816)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2818,X2818)),hAPP(hAPP(c_Product__Type_OPair(X2818,X2818),X2815),X2817)),c_Transitive__Closure_Ortrancl(X2818,X2816)))
| hBOOL(hAPP(hAPP(c_member(X2818),X2815),c_Wellfounded_Oacc(X2818,X2816))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).
fof(i_0_743,plain,
! [X2154,X2155,X2156,X2157,X2158] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2155,X2154)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2156),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2155,X2156) = hAPP(X2156,X2154) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk2_2(X2157,X2158)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2158,X2157) )
& ( hAPP(X2158,esk2_2(X2157,X2158)) != hAPP(esk2_2(X2157,X2158),X2157)
| c_Arrow__Order__Mirabelle_Odictator(X2158,X2157) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dictator__def])])])])])]) ).
fof(i_0_744,plain,
! [X3655,X3656,X3657,X3658,X3659,X3660] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3658,X3658)),hAPP(hAPP(c_Product__Type_OPair(X3658,X3658),X3657),X3656)),X3660))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3658,X3655),X3659),X3660),X3656),X3657) = hAPP(X3659,X3657) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__cut__apply])]) ).
fof(i_0_745,plain,
! [X3635,X3636,X3637,X3638,X3639,X3640] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3640,X3640)),hAPP(hAPP(c_Product__Type_OPair(X3640,X3640),X3639),X3638)),X3637))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3640,X3636),X3635),X3637),X3638),X3639) = hAPP(X3635,X3639) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut__apply])]) ).
fof(i_0_746,plain,
! [X3611,X3612,X3613,X3614,X3615,X3616] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3616,X3616)),hAPP(hAPP(c_Product__Type_OPair(X3616,X3616),X3615),X3614)),X3613))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3616,X3612),X3611),X3613),X3614),X3615) = hAPP(X3611,X3615) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3616,X3616)),hAPP(hAPP(c_Product__Type_OPair(X3616,X3616),X3615),X3614)),X3613))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3616,X3612),X3611),X3613),X3614),X3615) = c_HOL_Oundefined(X3612) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])]) ).
fof(i_0_747,plain,
! [X2892,X2893,X2894,X2895] :
( ~ hBOOL(hAPP(hAPP(c_member(X2895),X2894),c_Wellfounded_Oacc(X2895,X2893)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2895,X2895)),hAPP(hAPP(c_Product__Type_OPair(X2895,X2895),X2892),X2894)),X2893))
| hBOOL(hAPP(hAPP(c_member(X2895),X2892),c_Wellfounded_Oacc(X2895,X2893))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).
fof(i_0_748,plain,
! [X2376,X2377,X2378] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2378,X2378)),hAPP(hAPP(c_Product__Type_OPair(X2378,X2378),X2377),X2376)),c_List_Omeasures(X2378,c_List_Olist_ONil(tc_fun(X2378,tc_Nat_Onat))))),
inference(variable_rename,[status(thm)],[i_0_540]) ).
fof(i_0_749,plain,
! [X2828,X2829,X2830,X2831] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2831,X2831)),hAPP(hAPP(c_Product__Type_OPair(X2831,X2831),X2830),X2828)),c_Transitive__Closure_Ortrancl(X2831,X2829)))
| X2830 = X2828
| hBOOL(hAPP(hAPP(c_member(X2831),X2830),c_Relation_ODomain(X2831,X2831,X2829))) )
& ( X2830 != X2828
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2831,X2831)),hAPP(hAPP(c_Product__Type_OPair(X2831,X2831),X2830),X2828)),c_Transitive__Closure_Ortrancl(X2831,X2829)))
| hBOOL(hAPP(hAPP(c_member(X2831),X2830),c_Relation_ODomain(X2831,X2831,X2829))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])])]) ).
fof(i_0_750,plain,
! [X2267,X2268,X2269] :
( X2269 = X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2267),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(X2267,X2269,X2268)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_751,plain,
! [X2837,X2838,X2839,X2840,X2841] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2841,X2840)),hAPP(hAPP(c_Product__Type_OPair(X2841,X2840),X2839),X2838)),X2837))
| hBOOL(hAPP(hAPP(c_member(X2841),X2839),c_Relation_ODomain(X2841,X2840,X2837))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).
fof(i_0_752,plain,
! [X2832,X2833,X2834,X2835,X2836] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2836,X2835)),hAPP(hAPP(c_Product__Type_OPair(X2836,X2835),X2834),X2833)),X2832))
| hBOOL(hAPP(hAPP(c_member(X2835),X2833),c_Relation_ORange(X2836,X2835,X2832))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).
fof(i_0_753,plain,
! [X2265,X2266] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2266,X2266)),c_COMBI(X2266)),c_FuncSet_OPi(X2266,X2266,X2265,c_COMBK(tc_fun(X2266,tc_HOL_Obool),X2266,X2265)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_754,plain,
! [X2612,X2613] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2613),tc_List_Olist(X2613))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2613),tc_List_Olist(X2613)),c_List_Olist_ONil(X2613)),c_List_Olist_ONil(X2613))),c_List_Olistrel(X2613,X2612))),
inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).
fof(i_0_755,plain,
! [X2975,X2976,X2977,X2978] :
( ( X2977 = X2976
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2978,X2978)),hAPP(hAPP(c_Product__Type_OPair(X2978,X2978),X2977),X2976)),c_Relation_OId__on(X2978,X2975))) )
& ( hBOOL(hAPP(hAPP(c_member(X2978),X2977),X2975))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2978,X2978)),hAPP(hAPP(c_Product__Type_OPair(X2978,X2978),X2977),X2976)),c_Relation_OId__on(X2978,X2975))) )
& ( X2977 != X2976
| ~ hBOOL(hAPP(hAPP(c_member(X2978),X2977),X2975))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2978,X2978)),hAPP(hAPP(c_Product__Type_OPair(X2978,X2978),X2977),X2976)),c_Relation_OId__on(X2978,X2975))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).
fof(i_0_756,plain,
! [X4213,X4214,X4215,X4216] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4216,X4216)),hAPP(hAPP(c_Product__Type_OPair(X4216,X4216),X4215),X4214)),c_Wellfounded_Omeasure(X4216,X4213)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4213,X4215),hAPP(X4213,X4214)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4213,X4215),hAPP(X4213,X4214))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4216,X4216)),hAPP(hAPP(c_Product__Type_OPair(X4216,X4216),X4215),X4214)),c_Wellfounded_Omeasure(X4216,X4213))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_757,plain,
! [X3328,X3329,X3330,X3331,X3332,X3333] :
( ( hBOOL(hAPP(hAPP(X3331,X3329),X3328))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3333,tc_fun(X3332,tc_HOL_Obool)),X3331,X3330),X3329),X3328)) )
& ( hBOOL(hAPP(hAPP(X3330,X3329),X3328))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3333,tc_fun(X3332,tc_HOL_Obool)),X3331,X3330),X3329),X3328)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])])]) ).
fof(i_0_758,plain,
! [X3340,X3341,X3342,X3343,X3344,X3345] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3345,tc_fun(X3344,tc_HOL_Obool)),X3343,X3342),X3341),X3340))
| hBOOL(hAPP(hAPP(X3343,X3341),X3340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).
fof(i_0_759,plain,
! [X3346,X3347,X3348,X3349,X3350,X3351] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3351,tc_fun(X3350,tc_HOL_Obool)),X3349,X3348),X3347),X3346))
| hBOOL(hAPP(hAPP(X3348,X3347),X3346)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).
fof(i_0_760,plain,
! [X2737,X2738,X2739] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2739),tc_List_Olist(X2739))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2739),tc_List_Olist(X2739)),X2738),X2738)),c_List_Olistrel(X2739,c_Transitive__Closure_Ortrancl(X2739,X2737)))),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).
cnf(i_0_761,plain,
( hAPP(c_FuncSet_Ocompose(X1,X4,X5,X3,X6,X7),X2) = hAPP(X6,hAPP(X7,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_543]) ).
fof(i_0_762,plain,
! [X2809,X2810,X2811,X2812,X2813] :
( ( ~ c_Relation_Oirrefl(X2810,X2809)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2810,X2810)),hAPP(hAPP(c_Product__Type_OPair(X2810,X2810),X2811),X2811)),X2809)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2813,X2813)),hAPP(hAPP(c_Product__Type_OPair(X2813,X2813),esk48_2(X2812,X2813)),esk48_2(X2812,X2813))),X2812))
| c_Relation_Oirrefl(X2813,X2812) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])])])])]) ).
fof(i_0_763,plain,
! [X2272,X2273] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2273),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(X2273,X2272)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_764,plain,
! [X2270,X2271] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2271),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(X2271,X2270)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_765,plain,
! [X3537,X3538] :
( X3538 = c_List_Olist_ONil(X3537)
| ~ c_List_Odistinct(X3537,X3538)
| c_List_OtakeWhile(X3537,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3537),c_fNot),hAPP(hAPP(c_COMBC(X3537,X3537,tc_HOL_Obool),c_fequal),c_List_Olast(X3537,X3538))),X3538) = c_List_Obutlast(X3537,X3538) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last])]) ).
fof(i_0_766,plain,
! [X2842,X2843,X2844,X2845] :
( ~ hBOOL(hAPP(hAPP(c_member(X2845),X2844),c_Wellfounded_Oacc(X2845,X2843)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2845)),X2842),c_Wellfounded_Oacc(tc_List_Olist(X2845),c_List_Olistrel1(X2845,X2843))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2845)),hAPP(hAPP(c_List_Olist_OCons(X2845),X2844),X2842)),c_Wellfounded_Oacc(tc_List_Olist(X2845),c_List_Olistrel1(X2845,X2843)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).
fof(i_0_767,plain,
! [X3383,X3384,X3385,X3386,X3387,X3388] : c_Set_Oimage(X3388,X3387,X3386,c_Set_Oimage(X3385,X3388,X3384,X3383)) = c_Set_Oimage(X3385,X3387,hAPP(hAPP(c_COMBB(X3388,X3387,X3385),X3386),X3384),X3383),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_768,plain,
! [X3918,X3919,X3920,X3921,X3922] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3922,X3921)),X3920),c_FuncSet_Oextensional(X3922,X3921,X3919)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3922,tc_HOL_Obool),X3919,X3918)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3922,X3921)),X3920),c_FuncSet_Oextensional(X3922,X3921,X3918))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__subset])]) ).
fof(i_0_769,plain,
! [X3199,X3200,X3201,X3202,X3203] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3203,X3202,tc_HOL_Obool),X3201),hAPP(hAPP(c_Product__Type_OPair(X3203,X3202),X3200),X3199)))
| hBOOL(hAPP(hAPP(X3201,X3200),X3199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).
fof(i_0_770,plain,
! [X3300,X3301,X3302,X3303,X3304,X3305] : c_Product__Type_Oprod_Oprod__rec(X3305,X3304,X3303,X3302,hAPP(hAPP(c_Product__Type_OPair(X3305,X3304),X3301),X3300)) = hAPP(hAPP(X3302,X3301),X3300),
inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).
fof(i_0_771,plain,
! [X4208,X4209,X4210,X4211,X4212] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4212,X4211),hAPP(X4212,X4210))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4209,X4209)),hAPP(hAPP(c_Product__Type_OPair(X4209,X4209),X4211),X4210)),c_Wellfounded_Omlex__prod(X4209,X4212,X4208))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_772,plain,
! [X3372,X3373,X3374,X3375,X3376] :
( ~ hBOOL(hAPP(hAPP(c_member(X3376),X3375),X3374))
| hBOOL(hAPP(hAPP(c_member(X3373),hAPP(X3372,X3375)),c_Set_Oimage(X3376,X3373,X3372,X3374))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_773,plain,
! [X2330,X2331,X2332,X2333,X2334,X2335] : c_List_Olist_Olist__case(X2335,X2334,X2333,X2332,hAPP(hAPP(c_List_Olist_OCons(X2334),X2331),X2330)) = hAPP(hAPP(X2332,X2331),X2330),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).
fof(i_0_774,plain,
! [X3322,X3323,X3324,X3325,X3326,X3327] :
( ~ hBOOL(hAPP(hAPP(X3327,X3326),X3325))
| ~ hBOOL(hAPP(hAPP(X3324,X3326),X3325))
| hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3323,tc_fun(X3322,tc_HOL_Obool)),X3327,X3324),X3326),X3325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).
fof(i_0_775,plain,
! [X3334,X3335,X3336,X3337,X3338,X3339] :
( X3339 != hAPP(X3338,X3337)
| ~ hBOOL(hAPP(hAPP(c_member(X3336),X3337),X3335))
| hBOOL(hAPP(hAPP(c_member(X3334),X3339),c_Set_Oimage(X3336,X3334,X3338,X3335))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_776,plain,
! [X3377,X3378,X3379,X3380,X3381,X3382] :
( ~ hBOOL(hAPP(hAPP(c_member(X3382),X3381),X3380))
| X3379 != hAPP(X3378,X3381)
| hBOOL(hAPP(hAPP(c_member(X3377),X3379),c_Set_Oimage(X3382,X3377,X3378,X3380))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_777,plain,
! [X3661,X3662,X3663,X3664] : c_FuncSet_Oextensional__funcset(X3664,X3663,X3662,X3661) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X3664,X3663),tc_HOL_Obool),c_FuncSet_OPi(X3664,X3663,X3662,c_COMBK(tc_fun(X3663,tc_HOL_Obool),X3664,X3661)),c_FuncSet_Oextensional(X3664,X3663,X3662)),
inference(variable_rename,[status(thm)],[fact_extensional__funcset__def]) ).
fof(i_0_778,plain,
! [X3934,X3935,X3936,X3937] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3937,tc_HOL_Obool),c_Relation_ORange(X3936,X3937,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3936,X3937),tc_HOL_Obool),X3935,X3934)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3937,tc_HOL_Obool),c_Relation_ORange(X3936,X3937,X3935),c_Relation_ORange(X3936,X3937,X3934))),
inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).
fof(i_0_779,plain,
! [X3930,X3931,X3932,X3933] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3933,tc_HOL_Obool),c_Relation_ODomain(X3933,X3932,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3933,X3932),tc_HOL_Obool),X3931,X3930)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3933,tc_HOL_Obool),c_Relation_ODomain(X3933,X3932,X3931),c_Relation_ODomain(X3933,X3932,X3930))),
inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).
fof(i_0_780,plain,
! [X2989,X2990,X2991,X2992] :
( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),X2991),c_List_Olists(X2992,X2989)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),hAPP(hAPP(c_List_Oappend(X2992),X2991),X2990)),c_List_Olists(X2992,X2989))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),X2990),c_List_Olists(X2992,X2989)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),hAPP(hAPP(c_List_Oappend(X2992),X2991),X2990)),c_List_Olists(X2992,X2989))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),X2991),c_List_Olists(X2992,X2989)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),X2990),c_List_Olists(X2992,X2989)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),hAPP(hAPP(c_List_Oappend(X2992),X2991),X2990)),c_List_Olists(X2992,X2989))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).
fof(i_0_781,plain,
! [X2971,X2972,X2973,X2974] :
( X2974 != X2973
| ~ hBOOL(hAPP(hAPP(c_member(X2972),X2974),X2971))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2972,X2972)),hAPP(hAPP(c_Product__Type_OPair(X2972,X2972),X2974),X2973)),c_Relation_OId__on(X2972,X2971))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).
fof(i_0_782,plain,
! [X3853,X3854,X3855,X3856,X3857] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3857,tc_HOL_Obool),X3856,X3855)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3857,X3854),tc_HOL_Obool),c_FuncSet_OPi(X3857,X3854,X3855,X3853),c_FuncSet_OPi(X3857,X3854,X3856,X3853)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_783,plain,
! [X3428,X3429,X3430,X3431,X3432,X3433] : hAPP(hAPP(c_Product__Type_Ocurry(X3433,X3432,X3431,X3430),X3429),X3428) = hAPP(X3430,hAPP(hAPP(c_Product__Type_OPair(X3433,X3432),X3429),X3428)),
inference(variable_rename,[status(thm)],[fact_curry__conv]) ).
fof(i_0_784,plain,
! [X3407,X3408,X3409,X3410,X3411,X3412] : hAPP(hAPP(c_Product__Type_Ocurry(X3412,X3411,X3410,X3409),X3408),X3407) = hAPP(X3409,hAPP(hAPP(c_Product__Type_OPair(X3412,X3411),X3408),X3407)),
inference(variable_rename,[status(thm)],[fact_curry__def]) ).
fof(i_0_785,plain,
! [X2326,X2327,X2328,X2329] : c_List_Olist_Olist__case(X2329,X2328,X2327,X2326,c_List_Olist_ONil(X2328)) = X2327,
inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).
fof(i_0_786,plain,
! [X3890,X3891,X3892,X3893,X3894] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3894,tc_HOL_Obool),X3893,X3892)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3891,tc_HOL_Obool),c_Set_Oimage(X3894,X3891,X3890,X3893),c_Set_Oimage(X3894,X3891,X3890,X3892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_787,plain,
! [X2993,X2994,X2995,X2996] :
( ( hBOOL(hAPP(hAPP(c_member(X2996),X2995),X2993))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2996)),hAPP(hAPP(c_List_Olist_OCons(X2996),X2995),X2994)),c_List_Olists(X2996,X2993))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2996)),X2994),c_List_Olists(X2996,X2993)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2996)),hAPP(hAPP(c_List_Olist_OCons(X2996),X2995),X2994)),c_List_Olists(X2996,X2993))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2996),X2995),X2993))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2996)),X2994),c_List_Olists(X2996,X2993)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2996)),hAPP(hAPP(c_List_Olist_OCons(X2996),X2995),X2994)),c_List_Olists(X2996,X2993))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).
fof(i_0_788,plain,
! [X3007,X3008,X3009] :
( ( hBOOL(hAPP(hAPP(c_member(X3009),esk64_3(X3007,X3008,X3009)),X3007))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3009,X3009)),X3008),c_Relation_OId__on(X3009,X3007))) )
& ( X3008 = hAPP(hAPP(c_Product__Type_OPair(X3009,X3009),esk64_3(X3007,X3008,X3009)),esk64_3(X3007,X3008,X3009))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3009,X3009)),X3008),c_Relation_OId__on(X3009,X3007))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).
fof(i_0_789,plain,
! [X2160,X2161,X2162] :
( ( hAPP(hAPP(c_COMBC(X2162,tc_fun(X2162,tc_HOL_Obool),tc_HOL_Obool),c_member(X2162)),X2161) != hAPP(hAPP(c_COMBC(X2162,tc_fun(X2162,tc_HOL_Obool),tc_HOL_Obool),c_member(X2162)),X2160)
| X2161 = X2160 )
& ( X2161 != X2160
| hAPP(hAPP(c_COMBC(X2162,tc_fun(X2162,tc_HOL_Obool),tc_HOL_Obool),c_member(X2162)),X2161) = hAPP(hAPP(c_COMBC(X2162,tc_fun(X2162,tc_HOL_Obool),tc_HOL_Obool),c_member(X2162)),X2160) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_790,plain,
! [X2769,X2770,X2771] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2771,X2771)),hAPP(hAPP(c_Product__Type_OPair(X2771,X2771),X2770),X2770)),c_Transitive__Closure_Ortrancl(X2771,X2769))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
fof(i_0_791,plain,
! [X2190,X2191] :
( X2191 = X2190
| c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X2191),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X2190),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),esk4_2(X2190,X2191)),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_third__alt])])]) ).
fof(i_0_792,plain,
! [X3510,X3511,X3512,X3513] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3513,X3512)),X3511),c_FuncSet_Oextensional(X3513,X3512,X3510)))
| c_FuncSet_Orestrict(X3513,X3512,X3511,X3510) = X3511 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__restrict])]) ).
fof(i_0_793,plain,
! [X3187,X3188,X3189,X3190,X3191] :
( ~ hBOOL(hAPP(hAPP(X3191,X3190),X3189))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3188,X3187,tc_HOL_Obool),X3191),hAPP(hAPP(c_Product__Type_OPair(X3188,X3187),X3190),X3189))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).
fof(i_0_794,plain,
! [X3182,X3183,X3184,X3185,X3186] :
( ~ hBOOL(hAPP(hAPP(X3186,X3185),X3184))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3183,X3182,tc_HOL_Obool),X3186),hAPP(hAPP(c_Product__Type_OPair(X3183,X3182),X3185),X3184))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).
fof(i_0_795,plain,
! [X3492,X3493,X3494,X3495] : c_Set_Oimage(X3495,X3494,c_FuncSet_Orestrict(X3495,X3494,X3493,X3492),X3492) = c_Set_Oimage(X3495,X3494,X3493,X3492),
inference(variable_rename,[status(thm)],[fact_image__restrict__eq]) ).
fof(i_0_796,plain,
! [X2675,X2676,X2677,X2678,X2679,X2680] :
( ~ hBOOL(hAPP(hAPP(X2680,X2679),X2678))
| ~ c_List_Olistrelp(X2677,X2680,X2676,X2675)
| c_List_Olistrelp(X2677,X2680,hAPP(hAPP(c_List_Olist_OCons(X2677),X2679),X2676),hAPP(hAPP(c_List_Olist_OCons(X2677),X2678),X2675)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).
fof(i_0_797,plain,
! [X2669,X2670,X2671,X2672,X2673,X2674] :
( ( hBOOL(hAPP(hAPP(X2673,X2672),X2670))
| ~ c_List_Olistrelp(X2674,X2673,hAPP(hAPP(c_List_Olist_OCons(X2674),X2672),X2671),hAPP(hAPP(c_List_Olist_OCons(X2674),X2670),X2669)) )
& ( c_List_Olistrelp(X2674,X2673,X2671,X2669)
| ~ c_List_Olistrelp(X2674,X2673,hAPP(hAPP(c_List_Olist_OCons(X2674),X2672),X2671),hAPP(hAPP(c_List_Olist_OCons(X2674),X2670),X2669)) )
& ( ~ hBOOL(hAPP(hAPP(X2673,X2672),X2670))
| ~ c_List_Olistrelp(X2674,X2673,X2671,X2669)
| c_List_Olistrelp(X2674,X2673,hAPP(hAPP(c_List_Olist_OCons(X2674),X2672),X2671),hAPP(hAPP(c_List_Olist_OCons(X2674),X2670),X2669)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).
fof(i_0_798,plain,
! [X2997,X2998,X2999,X3002,X3003,X3004,X3005,X3006] :
( ( X2998 = hAPP(hAPP(c_List_Olist_OCons(X2999),esk62_3(X2997,X2998,X2999)),esk63_3(X2997,X2998,X2999))
| X2998 = c_List_Olist_ONil(X2999)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2999)),X2998),c_List_Olists(X2999,X2997))) )
& ( hBOOL(hAPP(hAPP(c_member(X2999),esk62_3(X2997,X2998,X2999)),X2997))
| X2998 = c_List_Olist_ONil(X2999)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2999)),X2998),c_List_Olists(X2999,X2997))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2999)),esk63_3(X2997,X2998,X2999)),c_List_Olists(X2999,X2997)))
| X2998 = c_List_Olist_ONil(X2999)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2999)),X2998),c_List_Olists(X2999,X2997))) )
& ( X3003 != c_List_Olist_ONil(X3004)
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3004)),X3003),c_List_Olists(X3004,X3002))) )
& ( X3003 != hAPP(hAPP(c_List_Olist_OCons(X3004),X3005),X3006)
| ~ hBOOL(hAPP(hAPP(c_member(X3004),X3005),X3002))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3004)),X3006),c_List_Olists(X3004,X3002)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3004)),X3003),c_List_Olists(X3004,X3002))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists_Osimps])])])])])]) ).
fof(i_0_799,plain,
! [X3563,X3564,X3565,X3566,X3567] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3567,X3566)),X3565),c_FuncSet_Oextensional(X3567,X3566,X3564)))
| hBOOL(hAPP(hAPP(c_member(X3567),X3563),X3564))
| hAPP(X3565,X3563) = c_HOL_Oundefined(X3566) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])]) ).
fof(i_0_800,plain,
! [X3142,X3143,X3144,X3145] :
( ~ hBOOL(hAPP(c_List_Olistsp(X3145,X3144),X3143))
| ~ hBOOL(hAPP(c_List_Olistsp(X3145,X3142),X3143))
| hBOOL(hAPP(c_List_Olistsp(X3145,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3145,tc_HOL_Obool),X3144,X3142)),X3143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])]) ).
fof(i_0_801,plain,
! [X2336,X2337] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk20_2(X2336,X2337)),c_Arrow__Order__Mirabelle_OLin))
| X2337 = X2336 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2337),X2336)),esk20_2(X2336,X2337)))
| X2337 = X2336 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_complete__Lin])])])]) ).
fof(i_0_802,plain,
! [X2706,X2707,X2708,X2709,X2710] : c_List_Omaps(X2710,X2709,X2708,hAPP(hAPP(c_List_Olist_OCons(X2710),X2707),X2706)) = hAPP(hAPP(c_List_Oappend(X2709),hAPP(X2708,X2707)),c_List_Omaps(X2710,X2709,X2708,X2706)),
inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J]) ).
fof(i_0_803,plain,
! [X2772,X2773,X2774] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2774,X2774)),X2773),X2772))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2774,X2774)),X2773),c_Transitive__Closure_Ortrancl(X2774,X2772))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).
fof(i_0_804,plain,
! [X2964,X2965,X2966] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2966)),X2965),c_Wellfounded_Oacc(tc_List_Olist(X2966),c_List_Olistrel1(X2966,X2964))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2966)),X2965),c_List_Olists(X2966,c_Wellfounded_Oacc(X2966,X2964)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).
fof(i_0_805,plain,
! [X2961,X2962,X2963] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2963)),X2962),c_List_Olists(X2963,c_Wellfounded_Oacc(X2963,X2961))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2963)),X2962),c_Wellfounded_Oacc(tc_List_Olist(X2963),c_List_Olistrel1(X2963,X2961)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).
fof(i_0_806,plain,
! [X3135,X3136,X3137,X3138] :
( ( hBOOL(hAPP(hAPP(c_member(X3138),X3137),X3136))
| ~ hBOOL(hAPP(hAPP(c_member(X3138),X3137),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3138,tc_HOL_Obool),X3136,X3135))) )
& ( hBOOL(hAPP(hAPP(c_member(X3138),X3137),X3135))
| ~ hBOOL(hAPP(hAPP(c_member(X3138),X3137),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3138,tc_HOL_Obool),X3136,X3135))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3138),X3137),X3136))
| ~ hBOOL(hAPP(hAPP(c_member(X3138),X3137),X3135))
| hBOOL(hAPP(hAPP(c_member(X3138),X3137),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3138,tc_HOL_Obool),X3136,X3135))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).
fof(i_0_807,plain,
! [X3131,X3132,X3133,X3134] :
( ~ hBOOL(hAPP(hAPP(c_member(X3134),X3133),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3134,tc_HOL_Obool),X3132,X3131)))
| hBOOL(hAPP(hAPP(c_member(X3134),X3133),X3132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).
fof(i_0_808,plain,
! [X3096,X3097,X3098,X3099] :
( ( hBOOL(hAPP(hAPP(c_member(X3099),X3098),X3097))
| ~ hBOOL(hAPP(hAPP(c_member(X3099),X3098),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3099,tc_HOL_Obool),X3097,X3096))) )
& ( hBOOL(hAPP(hAPP(c_member(X3099),X3098),X3096))
| ~ hBOOL(hAPP(hAPP(c_member(X3099),X3098),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3099,tc_HOL_Obool),X3097,X3096))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])])]) ).
fof(i_0_809,plain,
! [X3127,X3128,X3129,X3130] :
( ~ hBOOL(hAPP(hAPP(c_member(X3130),X3129),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3130,tc_HOL_Obool),X3128,X3127)))
| hBOOL(hAPP(hAPP(c_member(X3130),X3129),X3127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).
fof(i_0_810,plain,
! [X3092,X3093,X3094,X3095] :
( ~ hBOOL(hAPP(hAPP(c_member(X3095),X3094),X3093))
| ~ hBOOL(hAPP(hAPP(c_member(X3095),X3094),X3092))
| hBOOL(hAPP(hAPP(c_member(X3095),X3094),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3095,tc_HOL_Obool),X3093,X3092))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).
fof(i_0_811,plain,
! [X3558,X3559,X3560,X3561,X3562] :
( ( X3560 = hAPP(hAPP(c_List_Oappend(X3562),c_List_OtakeWhile(X3562,X3561,X3560)),hAPP(hAPP(c_List_Olist_OCons(X3562),X3559),X3558))
| c_List_OdropWhile(X3562,X3561,X3560) != hAPP(hAPP(c_List_Olist_OCons(X3562),X3559),X3558) )
& ( ~ hBOOL(hAPP(X3561,X3559))
| c_List_OdropWhile(X3562,X3561,X3560) != hAPP(hAPP(c_List_Olist_OCons(X3562),X3559),X3558) )
& ( X3560 != hAPP(hAPP(c_List_Oappend(X3562),c_List_OtakeWhile(X3562,X3561,X3560)),hAPP(hAPP(c_List_Olist_OCons(X3562),X3559),X3558))
| hBOOL(hAPP(X3561,X3559))
| c_List_OdropWhile(X3562,X3561,X3560) = hAPP(hAPP(c_List_Olist_OCons(X3562),X3559),X3558) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])])]) ).
fof(i_0_812,plain,
! [X3585,X3586,X3587,X3588,X3589] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3589),X3588),X3587))
| hAPP(c_FuncSet_Orestrict(X3589,X3586,X3585,X3587),X3588) = hAPP(X3585,X3588) )
& ( hBOOL(hAPP(hAPP(c_member(X3589),X3588),X3587))
| hAPP(c_FuncSet_Orestrict(X3589,X3586,X3585,X3587),X3588) = c_HOL_Oundefined(X3586) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])]) ).
fof(i_0_813,plain,
! [X3580,X3581,X3582,X3583,X3584] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3584),X3583),X3582))
| hAPP(c_FuncSet_Orestrict(X3584,X3581,X3580,X3582),X3583) = hAPP(X3580,X3583) )
& ( hBOOL(hAPP(hAPP(c_member(X3584),X3583),X3582))
| hAPP(c_FuncSet_Orestrict(X3584,X3581,X3580,X3582),X3583) = c_HOL_Oundefined(X3581) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])]) ).
fof(i_0_814,plain,
! [X3772,X3773,X3774,X3775,X3776] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3776,tc_HOL_Obool),X3775,X3774)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3776,tc_HOL_Obool),X3773,X3772)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3776,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3776,tc_HOL_Obool),X3775,X3773),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3776,tc_HOL_Obool),X3774,X3772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).
fof(i_0_815,plain,
! [X2345,X2346,X2347,X2348,X2349] : c_List_Osplice(X2349,hAPP(hAPP(c_List_Olist_OCons(X2349),X2348),X2347),hAPP(hAPP(c_List_Olist_OCons(X2349),X2346),X2345)) = hAPP(hAPP(c_List_Olist_OCons(X2349),X2348),hAPP(hAPP(c_List_Olist_OCons(X2349),X2346),c_List_Osplice(X2349,X2347,X2345))),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).
fof(i_0_816,plain,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),esk3_0),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])])]) ).
fof(i_0_817,plain,
! [X3434,X3435,X3436,X3437] : hAPP(c_Product__Type_Oprod_Oprod__case(X3437,X3436,X3435),c_Product__Type_Ocurry(X3437,X3436,X3435,X3434)) = X3434,
inference(variable_rename,[status(thm)],[fact_split__curry]) ).
fof(i_0_818,plain,
! [X2953,X2954,X2955,X2956,X2957,X2958,X2959] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2955,X2954),X2953))
| ~ hBOOL(hAPP(hAPP(X2954,X2956),X2953))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2955,X2954),X2956)) )
& ( hBOOL(hAPP(hAPP(X2958,esk60_3(X2957,X2958,X2959)),X2957))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2959,X2958),X2957)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2959,X2958),esk60_3(X2957,X2958,X2959)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2959,X2958),X2957)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp_Osimps])])])])])]) ).
fof(i_0_819,plain,
! [X2945,X2946,X2947,X2948,X2949,X2950,X2951] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2947,X2946),X2945))
| ~ hBOOL(hAPP(hAPP(X2946,X2948),X2945))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2947,X2946),X2948)) )
& ( hBOOL(hAPP(hAPP(X2950,esk59_3(X2949,X2950,X2951)),X2949))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2951,X2950),X2949)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2951,X2950),esk59_3(X2949,X2950,X2951)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2951,X2950),X2949)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp_Oequations])])])])])]) ).
fof(i_0_820,plain,
! [X4290,X4291,X4292,X4293,X4294,X4295] : hAPP(hAPP(hAPP(c_COMBS(X4295,X4294,X4293),X4292),X4291),X4290) = hAPP(hAPP(X4292,X4290),hAPP(X4291,X4290)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_821,plain,
! [X2733,X2734,X2735,X2736] :
( ~ c_Relation_Otrans(X2736,X2735)
| ~ c_Relation_Otrans(X2734,X2733)
| c_Relation_Otrans(tc_prod(X2736,X2734),c_Wellfounded_Olex__prod(X2736,X2734,X2735,X2733)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__lex__prod])]) ).
fof(i_0_822,plain,
! [X2931,X2932,X2933,X2934,X2936,X2937,X2938,X2939,X2940] :
( ( ~ c_Predicate_ORangeP(X2934,X2933,X2932,X2931)
| hBOOL(hAPP(hAPP(X2932,esk58_2(X2931,X2932)),X2931)) )
& ( ~ hBOOL(hAPP(hAPP(X2937,X2938),X2936))
| c_Predicate_ORangeP(X2940,X2939,X2937,X2936) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations])])])])]) ).
fof(i_0_823,plain,
! [X4284,X4285,X4286,X4287,X4288,X4289] : hAPP(hAPP(hAPP(c_COMBC(X4289,X4288,X4287),X4286),X4285),X4284) = hAPP(hAPP(X4286,X4284),X4285),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_824,plain,
! [X4278,X4279,X4280,X4281,X4282,X4283] : hAPP(hAPP(hAPP(c_COMBB(X4283,X4282,X4281),X4280),X4279),X4278) = hAPP(X4280,hAPP(X4279,X4278)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_825,plain,
! [X3088,X3089,X3090,X3091] :
( ( hBOOL(hAPP(X3090,X3088))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3091,tc_HOL_Obool),X3090,X3089),X3088)) )
& ( hBOOL(hAPP(X3089,X3088))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3091,tc_HOL_Obool),X3090,X3089),X3088)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).
fof(i_0_826,plain,
! [X3119,X3120,X3121,X3122] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3122,tc_HOL_Obool),X3121,X3120),X3119))
| hBOOL(hAPP(X3121,X3119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).
fof(i_0_827,plain,
! [X3123,X3124,X3125,X3126] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3126,tc_HOL_Obool),X3125,X3124),X3123))
| hBOOL(hAPP(X3124,X3123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).
fof(i_0_828,plain,
! [X3050,X3051,X3052,X3053] :
( ( hBOOL(hAPP(c_List_Olistsp(X3053,X3052),X3051))
| ~ hBOOL(hAPP(c_List_Olistsp(X3053,X3052),hAPP(hAPP(c_List_Oappend(X3053),X3051),X3050))) )
& ( hBOOL(hAPP(c_List_Olistsp(X3053,X3052),X3050))
| ~ hBOOL(hAPP(c_List_Olistsp(X3053,X3052),hAPP(hAPP(c_List_Oappend(X3053),X3051),X3050))) )
& ( ~ hBOOL(hAPP(c_List_Olistsp(X3053,X3052),X3051))
| ~ hBOOL(hAPP(c_List_Olistsp(X3053,X3052),X3050))
| hBOOL(hAPP(c_List_Olistsp(X3053,X3052),hAPP(hAPP(c_List_Oappend(X3053),X3051),X3050))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])]) ).
fof(i_0_829,plain,
! [X3044,X3045,X3046,X3047] :
( ( hBOOL(hAPP(X3046,X3045))
| ~ hBOOL(hAPP(c_List_Olistsp(X3047,X3046),hAPP(hAPP(c_List_Olist_OCons(X3047),X3045),X3044))) )
& ( hBOOL(hAPP(c_List_Olistsp(X3047,X3046),X3044))
| ~ hBOOL(hAPP(c_List_Olistsp(X3047,X3046),hAPP(hAPP(c_List_Olist_OCons(X3047),X3045),X3044))) )
& ( ~ hBOOL(hAPP(X3046,X3045))
| ~ hBOOL(hAPP(c_List_Olistsp(X3047,X3046),X3044))
| hBOOL(hAPP(c_List_Olistsp(X3047,X3046),hAPP(hAPP(c_List_Olist_OCons(X3047),X3045),X3044))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])]) ).
fof(i_0_830,plain,
! [X2553,X2554,X2555,X2556,X2557] :
( ( X2556 = X2554
| hAPP(hAPP(c_List_Oappend(X2557),X2556),hAPP(hAPP(c_List_Olist_OCons(X2557),X2555),c_List_Olist_ONil(X2557))) != hAPP(hAPP(c_List_Oappend(X2557),X2554),hAPP(hAPP(c_List_Olist_OCons(X2557),X2553),c_List_Olist_ONil(X2557))) )
& ( X2555 = X2553
| hAPP(hAPP(c_List_Oappend(X2557),X2556),hAPP(hAPP(c_List_Olist_OCons(X2557),X2555),c_List_Olist_ONil(X2557))) != hAPP(hAPP(c_List_Oappend(X2557),X2554),hAPP(hAPP(c_List_Olist_OCons(X2557),X2553),c_List_Olist_ONil(X2557))) )
& ( X2556 != X2554
| X2555 != X2553
| hAPP(hAPP(c_List_Oappend(X2557),X2556),hAPP(hAPP(c_List_Olist_OCons(X2557),X2555),c_List_Olist_ONil(X2557))) = hAPP(hAPP(c_List_Oappend(X2557),X2554),hAPP(hAPP(c_List_Olist_OCons(X2557),X2553),c_List_Olist_ONil(X2557))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).
fof(i_0_831,plain,
! [X3442,X3443,X3444,X3447,X3448,X3449,X3450,X3451] :
( ( X3442 = hAPP(hAPP(c_List_Olist_OCons(X3444),esk88_3(X3442,X3443,X3444)),esk89_3(X3442,X3443,X3444))
| X3442 = c_List_Olist_ONil(X3444)
| ~ hBOOL(hAPP(c_List_Olistsp(X3444,X3443),X3442)) )
& ( hBOOL(hAPP(X3443,esk88_3(X3442,X3443,X3444)))
| X3442 = c_List_Olist_ONil(X3444)
| ~ hBOOL(hAPP(c_List_Olistsp(X3444,X3443),X3442)) )
& ( hBOOL(hAPP(c_List_Olistsp(X3444,X3443),esk89_3(X3442,X3443,X3444)))
| X3442 = c_List_Olist_ONil(X3444)
| ~ hBOOL(hAPP(c_List_Olistsp(X3444,X3443),X3442)) )
& ( X3447 != c_List_Olist_ONil(X3449)
| hBOOL(hAPP(c_List_Olistsp(X3449,X3448),X3447)) )
& ( X3447 != hAPP(hAPP(c_List_Olist_OCons(X3449),X3450),X3451)
| ~ hBOOL(hAPP(X3448,X3450))
| ~ hBOOL(hAPP(c_List_Olistsp(X3449,X3448),X3451))
| hBOOL(hAPP(c_List_Olistsp(X3449,X3448),X3447)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Osimps])])])])])]) ).
fof(i_0_832,plain,
! [X3801,X3802] : c_Hilbert__Choice_OEps(X3802,hAPP(hAPP(c_COMBC(X3802,X3802,tc_HOL_Obool),c_fequal),X3801)) = X3801,
inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).
fof(i_0_833,plain,
! [X3843,X3844,X3845,X3846] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3846,X3845),tc_HOL_Obool),X3844,X3843)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3846,tc_HOL_Obool),c_Relation_ODomain(X3846,X3845,X3844),c_Relation_ODomain(X3846,X3845,X3843)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).
fof(i_0_834,plain,
! [X3438,X3439,X3440,X3441] : c_Product__Type_Ocurry(X3441,X3440,X3439,hAPP(c_Product__Type_Oprod_Oprod__case(X3441,X3440,X3439),X3438)) = X3438,
inference(variable_rename,[status(thm)],[fact_curry__split]) ).
fof(i_0_835,plain,
! [X3822,X3823,X3824] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3824,X3824),tc_HOL_Obool),X3823,X3822)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3824,X3824),tc_HOL_Obool),X3822,c_Transitive__Closure_Ortrancl(X3824,X3823))
| c_Transitive__Closure_Ortrancl(X3824,X3822) = c_Transitive__Closure_Ortrancl(X3824,X3823) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).
cnf(i_0_836,plain,
hAPP(hAPP(c_Product__Type_Ointernal__split(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_552]) ).
cnf(i_0_837,plain,
c_Product__Type_Ointernal__split(X1,X2,X3) = c_Product__Type_Oprod_Oprod__case(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_553]) ).
fof(i_0_838,plain,
! [X3176,X3177,X3178,X3179,X3180,X3181] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3181,X3180,X3179),X3178),hAPP(hAPP(c_Product__Type_OPair(X3181,X3180),X3177),X3176)) = hAPP(hAPP(X3178,X3177),X3176),
inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(i_0_839,plain,
! [X3170,X3171,X3172,X3173,X3174,X3175] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3175,X3174,X3173),X3172),hAPP(hAPP(c_Product__Type_OPair(X3175,X3174),X3171),X3170)) = hAPP(hAPP(X3172,X3171),X3170),
inference(variable_rename,[status(thm)],[fact_split__conv]) ).
fof(i_0_840,plain,
! [X3777,X3778,X3779,X3780] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3780,tc_HOL_Obool),X3779,X3778)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3780,tc_HOL_Obool),X3779,X3777)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3780,tc_HOL_Obool),X3779,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3780,tc_HOL_Obool),X3778,X3777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).
fof(i_0_841,plain,
! [X3115,X3116,X3117,X3118] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool),X3117,X3116),X3115) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool),X3117,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3118,tc_HOL_Obool),X3116,X3115)),
inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).
fof(i_0_842,plain,
! [X3111,X3112,X3113,X3114] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3114,tc_HOL_Obool),X3113,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3114,tc_HOL_Obool),X3112,X3111)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3114,tc_HOL_Obool),X3112,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3114,tc_HOL_Obool),X3113,X3111)),
inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).
fof(i_0_843,plain,
! [X3763,X3764,X3765,X3766,X3767] :
( ~ class_Lattices_Osemilattice__inf(X3767)
| ~ c_Orderings_Oord__class_Oless__eq(X3767,X3766,X3765)
| ~ c_Orderings_Oord__class_Oless__eq(X3767,X3764,X3763)
| c_Orderings_Oord__class_Oless__eq(X3767,c_Lattices_Osemilattice__inf__class_Oinf(X3767,X3766,X3764),c_Lattices_Osemilattice__inf__class_Oinf(X3767,X3765,X3763)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).
fof(i_0_844,plain,
! [X3548,X3549,X3550,X3551,X3552] :
( hBOOL(hAPP(X3552,X3551))
| c_List_OtakeWhile(X3550,X3552,hAPP(hAPP(c_List_Oappend(X3550),X3549),hAPP(hAPP(c_List_Olist_OCons(X3550),X3551),X3548))) = c_List_OtakeWhile(X3550,X3552,X3549) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])]) ).
fof(i_0_845,plain,
! [X3850,X3851,X3852] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3852,X3852),tc_HOL_Obool),X3851,X3850)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3852),tc_List_Olist(X3852)),tc_HOL_Obool),c_List_Olistrel1(X3852,X3851),c_List_Olistrel1(X3852,X3850)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).
fof(i_0_846,plain,
! [X3847,X3848,X3849] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3849,X3849),tc_HOL_Obool),X3848,X3847)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3849),tc_List_Olist(X3849)),tc_HOL_Obool),c_List_Olistrel(X3849,X3848),c_List_Olistrel(X3849,X3847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).
fof(i_0_847,plain,
! [X3084,X3085,X3086,X3087] :
( ~ hBOOL(hAPP(X3087,X3086))
| ~ hBOOL(hAPP(X3085,X3086))
| hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3084,tc_HOL_Obool),X3087,X3085),X3086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).
fof(i_0_848,plain,
! [X3825,X3826,X3827] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3827,X3827),tc_HOL_Obool),X3826,c_Transitive__Closure_Ortrancl(X3827,X3825))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3827,X3827),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3827,X3826),c_Transitive__Closure_Ortrancl(X3827,X3825)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).
fof(i_0_849,plain,
! [X2480,X2481,X2482,X2483] : hAPP(hAPP(c_List_Oappend(X2483),hAPP(hAPP(c_List_Oappend(X2483),X2482),X2481)),X2480) = hAPP(hAPP(c_List_Oappend(X2483),X2482),hAPP(hAPP(c_List_Oappend(X2483),X2481),X2480)),
inference(variable_rename,[status(thm)],[fact_append__assoc]) ).
fof(i_0_850,plain,
! [X2518,X2519,X2520,X2521] : hAPP(hAPP(c_List_Oappend(X2521),hAPP(hAPP(c_List_Olist_OCons(X2521),X2520),X2519)),X2518) = hAPP(hAPP(c_List_Olist_OCons(X2521),X2520),hAPP(hAPP(c_List_Oappend(X2521),X2519),X2518)),
inference(variable_rename,[status(thm)],[fact_append__Cons]) ).
fof(i_0_851,plain,
! [X4047,X4048,X4049,X4050,X4051,X4052] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4052,tc_fun(X4051,tc_HOL_Obool)),X4050,X4049)
| ~ hBOOL(hAPP(hAPP(X4050,X4048),X4047))
| hBOOL(hAPP(hAPP(X4049,X4048),X4047)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_852,plain,
! [X4041,X4042,X4043,X4044,X4045,X4046] :
( ~ hBOOL(hAPP(hAPP(X4046,X4045),X4044))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4043,tc_fun(X4042,tc_HOL_Obool)),X4046,X4041)
| hBOOL(hAPP(hAPP(X4041,X4045),X4044)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_853,plain,
! [X3835,X3836,X3837,X3838] :
( ~ hBOOL(hAPP(hAPP(c_member(X3838),X3837),X3836))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3838,tc_HOL_Obool),X3836,X3835)
| hBOOL(hAPP(hAPP(c_member(X3838),X3837),X3835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_854,plain,
! [X4240,X4241,X4242,X4243] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X4243,tc_HOL_Obool),X4242,X4241)
| ~ hBOOL(hAPP(hAPP(c_member(X4243),X4240),X4242))
| hBOOL(hAPP(hAPP(c_member(X4243),X4240),X4241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_855,plain,
! [X3839,X3840,X3841,X3842] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3842,tc_HOL_Obool),X3841,X3840)
| ~ hBOOL(hAPP(hAPP(c_member(X3842),X3839),X3841))
| hBOOL(hAPP(hAPP(c_member(X3842),X3839),X3840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_856,plain,
! [X3831,X3832,X3833,X3834] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3834,tc_HOL_Obool),X3833,X3832)
| ~ hBOOL(hAPP(hAPP(c_member(X3834),X3831),X3833))
| hBOOL(hAPP(hAPP(c_member(X3834),X3831),X3832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_857,plain,
! [X3718,X3719,X3720,X3721] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3721,tc_HOL_Obool),X3720,X3719)
| ~ hBOOL(hAPP(hAPP(c_member(X3721),X3718),X3720))
| hBOOL(hAPP(hAPP(c_member(X3721),X3718),X3719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_858,plain,
! [X3819,X3820,X3821] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3821,X3821),tc_HOL_Obool),X3820,X3819)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3821,X3821),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3821,X3820),c_Transitive__Closure_Ortrancl(X3821,X3819)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).
fof(i_0_859,plain,
! [X2921,X2922,X2923,X2924,X2925] :
( ~ hBOOL(hAPP(hAPP(X2925,X2924),X2923))
| c_Predicate_ODomainP(X2922,X2921,X2925,X2924) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).
fof(i_0_860,plain,
! [X2926,X2927,X2928,X2929,X2930] :
( ~ hBOOL(hAPP(hAPP(X2930,X2929),X2928))
| c_Predicate_ORangeP(X2927,X2926,X2930,X2928) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).
fof(i_0_861,plain,
! [X3577,X3578,X3579] : hAPP(hAPP(c_List_Oappend(X3579),c_List_OtakeWhile(X3579,X3578,X3577)),c_List_OdropWhile(X3579,X3578,X3577)) = X3577,
inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id]) ).
fof(i_0_862,plain,
! [X3544,X3545,X3546,X3547] :
( ( ~ hBOOL(hAPP(X3547,X3546))
| c_List_OtakeWhile(X3545,X3547,hAPP(hAPP(c_List_Olist_OCons(X3545),X3546),X3544)) = hAPP(hAPP(c_List_Olist_OCons(X3545),X3546),c_List_OtakeWhile(X3545,X3547,X3544)) )
& ( hBOOL(hAPP(X3547,X3546))
| c_List_OtakeWhile(X3545,X3547,hAPP(hAPP(c_List_Olist_OCons(X3545),X3546),X3544)) = c_List_Olist_ONil(X3545) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).
fof(i_0_863,plain,
! [X3943,X3944] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3944),tc_List_Olist(X3944)),tc_HOL_Obool),c_List_Olistrel1(X3944,c_Transitive__Closure_Ortrancl(X3944,X3943)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X3944),c_List_Olistrel1(X3944,X3943))),
inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).
fof(i_0_864,plain,
! [X3518,X3519,X3520] : c_List_Obutlast(X3520,hAPP(hAPP(c_List_Oappend(X3520),X3519),hAPP(hAPP(c_List_Olist_OCons(X3520),X3518),c_List_Olist_ONil(X3520)))) = X3519,
inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).
fof(i_0_865,plain,
! [X3452,X3453,X3454] : c_List_Olast(X3454,hAPP(hAPP(c_List_Oappend(X3454),X3453),hAPP(hAPP(c_List_Olist_OCons(X3454),X3452),c_List_Olist_ONil(X3454)))) = X3452,
inference(variable_rename,[status(thm)],[fact_last__snoc]) ).
fof(i_0_866,plain,
! [X3812,X3813,X3814,X3815] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3815,X3814),tc_HOL_Obool),X3813,X3812)
| ~ c_Relation_Osingle__valued(X3815,X3814,X3812)
| c_Relation_Osingle__valued(X3815,X3814,X3813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).
fof(i_0_867,plain,
! [X3968,X3969,X3970] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3970),c_List_OdropWhile(X3970,X3969,X3968)),c_Nat_Osize__class_Osize(tc_List_Olist(X3970),X3968)),
inference(variable_rename,[status(thm)],[fact_length__dropWhile__le]) ).
fof(i_0_868,plain,
! [X3965,X3966,X3967] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3967),c_List_OtakeWhile(X3967,X3966,X3965)),c_Nat_Osize__class_Osize(tc_List_Olist(X3967),X3965)),
inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).
fof(i_0_869,plain,
! [X3759,X3760,X3761,X3762] :
( ~ class_Lattices_Osemilattice__inf(X3762)
| ~ c_Orderings_Oord__class_Oless__eq(X3762,X3761,X3760)
| ~ c_Orderings_Oord__class_Oless__eq(X3762,X3761,X3759)
| c_Orderings_Oord__class_Oless__eq(X3762,X3761,c_Lattices_Osemilattice__inf__class_Oinf(X3762,X3760,X3759)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).
fof(i_0_870,plain,
! [X3755,X3756,X3757,X3758] :
( ~ class_Lattices_Osemilattice__inf(X3758)
| ~ c_Orderings_Oord__class_Oless__eq(X3758,X3757,X3756)
| ~ c_Orderings_Oord__class_Oless__eq(X3758,X3757,X3755)
| c_Orderings_Oord__class_Oless__eq(X3758,X3757,c_Lattices_Osemilattice__inf__class_Oinf(X3758,X3756,X3755)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).
fof(i_0_871,plain,
! [X3737,X3738,X3739,X3740] :
( ( c_Orderings_Oord__class_Oless__eq(X3740,X3739,X3738)
| ~ c_Orderings_Oord__class_Oless__eq(X3740,X3739,c_Lattices_Osemilattice__inf__class_Oinf(X3740,X3738,X3737))
| ~ class_Lattices_Osemilattice__inf(X3740) )
& ( c_Orderings_Oord__class_Oless__eq(X3740,X3739,X3737)
| ~ c_Orderings_Oord__class_Oless__eq(X3740,X3739,c_Lattices_Osemilattice__inf__class_Oinf(X3740,X3738,X3737))
| ~ class_Lattices_Osemilattice__inf(X3740) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3740,X3739,X3738)
| ~ c_Orderings_Oord__class_Oless__eq(X3740,X3739,X3737)
| c_Orderings_Oord__class_Oless__eq(X3740,X3739,c_Lattices_Osemilattice__inf__class_Oinf(X3740,X3738,X3737))
| ~ class_Lattices_Osemilattice__inf(X3740) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).
fof(i_0_872,plain,
! [X2941,X2942,X2943,X2944] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2944,X2943),X2942))
| ~ hBOOL(hAPP(hAPP(X2943,X2941),X2942))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2944,X2943),X2941)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).
fof(i_0_873,plain,
! [X3884,X3885,X3886] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3886,X3886),tc_HOL_Obool),X3885,X3884)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3886,tc_HOL_Obool),c_Wellfounded_Oacc(X3886,X3884),c_Wellfounded_Oacc(X3886,X3885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).
fof(i_0_874,plain,
! [X3285,X3286,X3287,X3288] :
( ~ class_Lattices_Osemilattice__inf(X3288)
| c_Lattices_Osemilattice__inf__class_Oinf(X3288,c_Lattices_Osemilattice__inf__class_Oinf(X3288,X3287,X3286),X3285) = c_Lattices_Osemilattice__inf__class_Oinf(X3288,X3287,c_Lattices_Osemilattice__inf__class_Oinf(X3288,X3286,X3285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).
fof(i_0_875,plain,
! [X3277,X3278,X3279,X3280] :
( ~ class_Lattices_Osemilattice__inf(X3280)
| c_Lattices_Osemilattice__inf__class_Oinf(X3280,c_Lattices_Osemilattice__inf__class_Oinf(X3280,X3279,X3278),X3277) = c_Lattices_Osemilattice__inf__class_Oinf(X3280,X3279,c_Lattices_Osemilattice__inf__class_Oinf(X3280,X3278,X3277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).
fof(i_0_876,plain,
! [X3281,X3282,X3283,X3284] :
( ~ class_Lattices_Olattice(X3284)
| c_Lattices_Osemilattice__inf__class_Oinf(X3284,c_Lattices_Osemilattice__inf__class_Oinf(X3284,X3283,X3282),X3281) = c_Lattices_Osemilattice__inf__class_Oinf(X3284,X3283,c_Lattices_Osemilattice__inf__class_Oinf(X3284,X3282,X3281)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).
fof(i_0_877,plain,
! [X3273,X3274,X3275,X3276] :
( ~ class_Lattices_Osemilattice__inf(X3276)
| c_Lattices_Osemilattice__inf__class_Oinf(X3276,X3275,c_Lattices_Osemilattice__inf__class_Oinf(X3276,X3274,X3273)) = c_Lattices_Osemilattice__inf__class_Oinf(X3276,X3274,c_Lattices_Osemilattice__inf__class_Oinf(X3276,X3275,X3273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).
fof(i_0_878,plain,
! [X3265,X3266,X3267,X3268] :
( ~ class_Lattices_Osemilattice__inf(X3268)
| c_Lattices_Osemilattice__inf__class_Oinf(X3268,X3267,c_Lattices_Osemilattice__inf__class_Oinf(X3268,X3266,X3265)) = c_Lattices_Osemilattice__inf__class_Oinf(X3268,X3266,c_Lattices_Osemilattice__inf__class_Oinf(X3268,X3267,X3265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).
fof(i_0_879,plain,
! [X3269,X3270,X3271,X3272] :
( ~ class_Lattices_Olattice(X3272)
| c_Lattices_Osemilattice__inf__class_Oinf(X3272,X3271,c_Lattices_Osemilattice__inf__class_Oinf(X3272,X3270,X3269)) = c_Lattices_Osemilattice__inf__class_Oinf(X3272,X3270,c_Lattices_Osemilattice__inf__class_Oinf(X3272,X3271,X3269)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).
fof(i_0_880,plain,
! [X3489,X3490] :
( X3490 = c_List_Olist_ONil(X3489)
| hAPP(hAPP(c_List_Oappend(X3489),c_List_Obutlast(X3489,X3490)),hAPP(hAPP(c_List_Olist_OCons(X3489),c_List_Olast(X3489,X3490)),c_List_Olist_ONil(X3489))) = X3490 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).
fof(i_0_881,plain,
! [X3958,X3959,X3960] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3960,tc_fun(X3960,tc_HOL_Obool)),X3959,X3958)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3960,tc_HOL_Obool),c_Wellfounded_Oaccp(X3960,X3958),c_Wellfounded_Oaccp(X3960,X3959)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).
fof(i_0_882,plain,
! [X4223,X4224,X4225,X4226] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4226,tc_HOL_Obool),X4225,X4224)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4226,tc_HOL_Obool),X4224,X4223)
| c_Orderings_Oord__class_Oless(tc_fun(X4226,tc_HOL_Obool),X4225,X4223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_883,plain,
! [X4227,X4228,X4229,X4230] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X4230,tc_HOL_Obool),X4229,X4228)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4230,tc_HOL_Obool),X4228,X4227)
| c_Orderings_Oord__class_Oless(tc_fun(X4230,tc_HOL_Obool),X4229,X4227) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_884,plain,
! [X3861,X3862,X3863,X3864] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3864,tc_HOL_Obool),X3863,X3862)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3864,tc_HOL_Obool),X3862,X3861)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3864,tc_HOL_Obool),X3863,X3861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_885,plain,
! [X3139,X3140,X3141] :
( ~ c_Relation_Otrans(X3141,X3140)
| ~ c_Relation_Otrans(X3141,X3139)
| c_Relation_Otrans(X3141,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3141,X3141),tc_HOL_Obool),X3140,X3139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__Int])]) ).
fof(i_0_886,plain,
! [X3768,X3769,X3770,X3771] :
( ( c_Orderings_Oord__class_Oless__eq(X3771,X3770,X3769)
| ~ c_Orderings_Oord__class_Oless__eq(X3771,X3770,c_Lattices_Osemilattice__inf__class_Oinf(X3771,X3769,X3768))
| ~ class_Lattices_Osemilattice__inf(X3771) )
& ( c_Orderings_Oord__class_Oless__eq(X3771,X3770,X3768)
| ~ c_Orderings_Oord__class_Oless__eq(X3771,X3770,c_Lattices_Osemilattice__inf__class_Oinf(X3771,X3769,X3768))
| ~ class_Lattices_Osemilattice__inf(X3771) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).
fof(i_0_887,plain,
! [X3100,X3101,X3102] : c_List_Olistsp(X3102,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3102,tc_HOL_Obool),X3101,X3100)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X3102),tc_HOL_Obool),c_List_Olistsp(X3102,X3101),c_List_Olistsp(X3102,X3100)),
inference(variable_rename,[status(thm)],[fact_listsp__inf__eq]) ).
fof(i_0_888,plain,
! [X3108,X3109,X3110] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3110,tc_HOL_Obool),X3109,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3110,tc_HOL_Obool),X3109,X3108)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3110,tc_HOL_Obool),X3109,X3108),
inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).
fof(i_0_889,plain,
! [X4219,X4220,X4221,X4222] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4221,X4222),X4220,X4219)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4221,X4222),X4220,X4219)
| ~ class_Orderings_Oord(X4222) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4221,X4222),X4219,X4220)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4221,X4222),X4220,X4219)
| ~ class_Orderings_Oord(X4222) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4221,X4222),X4220,X4219)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4221,X4222),X4219,X4220)
| c_Orderings_Oord__class_Oless(tc_fun(X4221,X4222),X4220,X4219)
| ~ class_Orderings_Oord(X4222) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])])]) ).
fof(i_0_890,plain,
! [X3713,X3714] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3714),tc_List_Olist(X3714)),tc_HOL_Obool),c_List_Olistrel(X3714,X3713),c_Transitive__Closure_Ortrancl(tc_List_Olist(X3714),c_List_Olistrel1(X3714,X3713))),
inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).
fof(i_0_891,plain,
! [X3237,X3238,X3239,X3240,X3241,X3242] :
( ( X3240 = X3238
| hAPP(hAPP(c_Product__Type_OPair(X3242,X3241),X3240),X3239) != hAPP(hAPP(c_Product__Type_OPair(X3242,X3241),X3238),X3237) )
& ( X3239 = X3237
| hAPP(hAPP(c_Product__Type_OPair(X3242,X3241),X3240),X3239) != hAPP(hAPP(c_Product__Type_OPair(X3242,X3241),X3238),X3237) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).
fof(i_0_892,plain,
! [X3231,X3232,X3233,X3234,X3235,X3236] :
( ( X3234 = X3232
| hAPP(hAPP(c_Product__Type_OPair(X3236,X3235),X3234),X3233) != hAPP(hAPP(c_Product__Type_OPair(X3236,X3235),X3232),X3231) )
& ( X3233 = X3231
| hAPP(hAPP(c_Product__Type_OPair(X3236,X3235),X3234),X3233) != hAPP(hAPP(c_Product__Type_OPair(X3236,X3235),X3232),X3231) )
& ( X3234 != X3232
| X3233 != X3231
| hAPP(hAPP(c_Product__Type_OPair(X3236,X3235),X3234),X3233) = hAPP(hAPP(c_Product__Type_OPair(X3236,X3235),X3232),X3231) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).
fof(i_0_893,plain,
! [X3961,X3962,X3963,X3964] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3964),X3963),c_Nat_Osize__class_Osize(tc_List_Olist(X3964),X3962))
| X3963 != hAPP(hAPP(c_List_Olist_OCons(X3964),X3961),X3962) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).
fof(i_0_894,plain,
! [X3295,X3296,X3297,X3298,X3299] :
( ~ class_Lattices_Olattice(X3299)
| hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3298,X3299),X3297,X3296),X3295) = c_Lattices_Osemilattice__inf__class_Oinf(X3299,hAPP(X3297,X3295),hAPP(X3296,X3295)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).
fof(i_0_895,plain,
! [X3165,X3166,X3167,X3168,X3169] :
( ~ class_Lattices_Olattice(X3169)
| hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3168,X3169),X3167,X3166),X3165) = c_Lattices_Osemilattice__inf__class_Oinf(X3169,hAPP(X3167,X3165),hAPP(X3166,X3165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).
fof(i_0_896,plain,
! [X2697,X2698,X2699,X2700] :
( c_List_Orotate1(X2700,c_List_Olist_ONil(X2700)) = c_List_Olist_ONil(X2700)
& c_List_Orotate1(X2699,hAPP(hAPP(c_List_Olist_OCons(X2699),X2698),X2697)) = hAPP(hAPP(c_List_Oappend(X2699),X2697),hAPP(hAPP(c_List_Olist_OCons(X2699),X2698),c_List_Olist_ONil(X2699))) ),
inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).
fof(i_0_897,plain,
! [X3521,X3522,X3523,X3524] :
( ( X3521 != c_List_Olist_ONil(X3524)
| hAPP(hAPP(c_List_Oappend(X3524),X3523),hAPP(hAPP(c_List_Olist_OCons(X3524),X3522),c_List_Olist_ONil(X3524))) != X3521 )
& ( c_List_Obutlast(X3524,X3521) = X3523
| hAPP(hAPP(c_List_Oappend(X3524),X3523),hAPP(hAPP(c_List_Olist_OCons(X3524),X3522),c_List_Olist_ONil(X3524))) != X3521 )
& ( c_List_Olast(X3524,X3521) = X3522
| hAPP(hAPP(c_List_Oappend(X3524),X3523),hAPP(hAPP(c_List_Olist_OCons(X3524),X3522),c_List_Olist_ONil(X3524))) != X3521 )
& ( X3521 = c_List_Olist_ONil(X3524)
| c_List_Obutlast(X3524,X3521) != X3523
| c_List_Olast(X3524,X3521) != X3522
| hAPP(hAPP(c_List_Oappend(X3524),X3523),hAPP(hAPP(c_List_Olist_OCons(X3524),X3522),c_List_Olist_ONil(X3524))) = X3521 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).
fof(i_0_898,plain,
! [X2506,X2507,X2508,X2509,X2510,X2511] :
( hAPP(hAPP(c_List_Oappend(X2511),X2510),X2509) != X2508
| X2507 != hAPP(hAPP(c_List_Oappend(X2511),X2509),X2506)
| hAPP(hAPP(c_List_Oappend(X2511),X2510),X2507) = hAPP(hAPP(c_List_Oappend(X2511),X2508),X2506) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).
fof(i_0_899,plain,
! [X2512,X2513,X2514,X2515,X2516,X2517] :
( hAPP(hAPP(c_List_Olist_OCons(X2517),X2516),X2515) != X2514
| X2513 != hAPP(hAPP(c_List_Oappend(X2517),X2515),X2512)
| hAPP(hAPP(c_List_Olist_OCons(X2517),X2516),X2513) = hAPP(hAPP(c_List_Oappend(X2517),X2514),X2512) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).
fof(i_0_900,plain,
! [X3887,X3888,X3889] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3889,tc_HOL_Obool),X3888,X3887)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X3889),tc_HOL_Obool),c_List_Olistsp(X3889,X3888),c_List_Olistsp(X3889,X3887)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])]) ).
fof(i_0_901,plain,
! [X3828,X3829,X3830] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3830,tc_HOL_Obool),X3829,X3828)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X3830),tc_HOL_Obool),c_List_Olists(X3830,X3829),c_List_Olists(X3830,X3828)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).
fof(i_0_902,plain,
! [X2683,X2684] : c_List_Olistrelp(X2684,X2683,c_List_Olist_ONil(X2684),c_List_Olist_ONil(X2684)),
inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).
fof(i_0_903,plain,
! [X2681,X2682] : c_List_Olistrelp(X2682,X2681,c_List_Olist_ONil(X2682),c_List_Olist_ONil(X2682)),
inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).
fof(i_0_904,plain,
! [X3568,X3569,X3570,X3571] :
( ( ~ hBOOL(hAPP(X3571,X3570))
| c_List_OdropWhile(X3569,X3571,hAPP(hAPP(c_List_Olist_OCons(X3569),X3570),X3568)) = c_List_OdropWhile(X3569,X3571,X3568) )
& ( hBOOL(hAPP(X3571,X3570))
| c_List_OdropWhile(X3569,X3571,hAPP(hAPP(c_List_Olist_OCons(X3569),X3570),X3568)) = hAPP(hAPP(c_List_Olist_OCons(X3569),X3570),X3568) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_905,plain,
! [X2752,X2753,X2754] : c_List_Omaps(X2754,X2753,X2752,c_List_Olist_ONil(X2754)) = c_List_Olist_ONil(X2753),
inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J]) ).
fof(i_0_906,plain,
! [X4136,X4137,X4138,X4139] :
( ~ class_Lattices_Osemilattice__inf(X4139)
| ~ c_Orderings_Oord__class_Oless(X4139,X4138,X4137)
| c_Orderings_Oord__class_Oless(X4139,c_Lattices_Osemilattice__inf__class_Oinf(X4139,X4138,X4136),X4137) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).
fof(i_0_907,plain,
! [X4132,X4133,X4134,X4135] :
( ~ class_Lattices_Osemilattice__inf(X4135)
| ~ c_Orderings_Oord__class_Oless(X4135,X4134,X4133)
| c_Orderings_Oord__class_Oless(X4135,c_Lattices_Osemilattice__inf__class_Oinf(X4135,X4132,X4134),X4133) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).
fof(i_0_908,plain,
! [X3741,X3742,X3743,X3744] :
( ~ class_Lattices_Osemilattice__inf(X3744)
| ~ c_Orderings_Oord__class_Oless__eq(X3744,X3743,X3742)
| c_Orderings_Oord__class_Oless__eq(X3744,c_Lattices_Osemilattice__inf__class_Oinf(X3744,X3743,X3741),X3742) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).
fof(i_0_909,plain,
! [X3745,X3746,X3747,X3748] :
( ~ class_Lattices_Osemilattice__inf(X3748)
| ~ c_Orderings_Oord__class_Oless__eq(X3748,X3747,X3746)
| c_Orderings_Oord__class_Oless__eq(X3748,c_Lattices_Osemilattice__inf__class_Oinf(X3748,X3745,X3747),X3746) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).
fof(i_0_910,plain,
! [X3405,X3406] : c_Set_Oimage(X3406,X3406,c_COMBI(X3406),X3405) = X3405,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_911,plain,
! [X3879,X3880,X3881] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3879,tc_HOL_Obool),X3881,X3880)
| X3881 != X3880 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3879,tc_HOL_Obool),X3880,X3881)
| X3881 != X3880 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3879,tc_HOL_Obool),X3881,X3880)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3879,tc_HOL_Obool),X3880,X3881)
| X3881 = X3880 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_912,plain,
! [X3715,X3716,X3717] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3717,tc_HOL_Obool),X3716,X3715)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3717,tc_HOL_Obool),X3715,X3716)
| X3716 = X3715 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_913,plain,
! [X2166,X2167,X2168] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2168),X2167),hAPP(c_fequal,X2166)))
| X2167 = X2166 )
& ( X2167 != X2166
| hBOOL(hAPP(hAPP(c_member(X2168),X2167),hAPP(c_fequal,X2166))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_914,plain,
! [X4025,X4026,X4027,X4028,X4029] :
( ~ class_Orderings_Oord(X4029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4028,X4029),X4027,X4026)
| c_Orderings_Oord__class_Oless__eq(X4029,hAPP(X4027,X4025),hAPP(X4026,X4025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_915,plain,
! [X3953,X3954,X3955,X3956,X3957] :
( ~ class_Orderings_Oord(X3957)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3956,X3957),X3955,X3954)
| c_Orderings_Oord__class_Oless__eq(X3957,hAPP(X3955,X3953),hAPP(X3954,X3953)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_916,plain,
! [X4194,X4195,X4196,X4197] :
( ~ class_Orderings_Opreorder(X4197)
| ~ c_Orderings_Oord__class_Oless(X4197,X4196,X4195)
| ~ c_Orderings_Oord__class_Oless(X4197,X4195,X4194)
| c_Orderings_Oord__class_Oless(X4197,X4196,X4194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_917,plain,
! [X4124,X4125,X4126,X4127] :
( ~ class_Orderings_Opreorder(X4127)
| ~ c_Orderings_Oord__class_Oless__eq(X4127,X4126,X4125)
| ~ c_Orderings_Oord__class_Oless(X4127,X4125,X4124)
| c_Orderings_Oord__class_Oless(X4127,X4126,X4124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_918,plain,
! [X4116,X4117,X4118,X4119] :
( ~ class_Orderings_Opreorder(X4119)
| ~ c_Orderings_Oord__class_Oless(X4119,X4118,X4117)
| ~ c_Orderings_Oord__class_Oless__eq(X4119,X4117,X4116)
| c_Orderings_Oord__class_Oless(X4119,X4118,X4116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_919,plain,
! [X4198,X4199,X4200,X4201] :
( ~ class_Orderings_Oorder(X4201)
| ~ c_Orderings_Oord__class_Oless(X4201,X4200,X4199)
| ~ c_Orderings_Oord__class_Oless(X4201,X4198,X4200)
| c_Orderings_Oord__class_Oless(X4201,X4198,X4199) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_920,plain,
! [X4128,X4129,X4130,X4131] :
( ~ class_Orderings_Oorder(X4131)
| ~ c_Orderings_Oord__class_Oless__eq(X4131,X4130,X4129)
| ~ c_Orderings_Oord__class_Oless(X4131,X4128,X4130)
| c_Orderings_Oord__class_Oless(X4131,X4128,X4129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_921,plain,
! [X4120,X4121,X4122,X4123] :
( ~ class_Orderings_Oorder(X4123)
| ~ c_Orderings_Oord__class_Oless(X4123,X4122,X4121)
| ~ c_Orderings_Oord__class_Oless__eq(X4123,X4120,X4122)
| c_Orderings_Oord__class_Oless(X4123,X4120,X4121) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_922,plain,
! [X3981,X3982,X3983,X3984] :
( ~ class_Orderings_Opreorder(X3984)
| ~ c_Orderings_Oord__class_Oless__eq(X3984,X3983,X3982)
| ~ c_Orderings_Oord__class_Oless__eq(X3984,X3982,X3981)
| c_Orderings_Oord__class_Oless__eq(X3984,X3983,X3981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_923,plain,
! [X3974,X3975,X3976,X3977] :
( ~ class_Orderings_Oorder(X3977)
| ~ c_Orderings_Oord__class_Oless__eq(X3977,X3976,X3975)
| ~ c_Orderings_Oord__class_Oless__eq(X3977,X3974,X3976)
| c_Orderings_Oord__class_Oless__eq(X3977,X3974,X3975) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_924,plain,
! [X2979,X2980] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2980)),c_List_Olist_ONil(X2980)),c_List_Olists(X2980,X2979))),
inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).
fof(i_0_925,plain,
! [X3790,X3791,X3792] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3792,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3792,tc_HOL_Obool),X3791,X3790),X3791),
inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).
fof(i_0_926,plain,
! [X3787,X3788,X3789] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3789,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3789,tc_HOL_Obool),X3788,X3787),X3787),
inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).
fof(i_0_927,plain,
! [X3262,X3263,X3264] :
( ~ class_Lattices_Osemilattice__inf(X3264)
| c_Lattices_Osemilattice__inf__class_Oinf(X3264,X3263,c_Lattices_Osemilattice__inf__class_Oinf(X3264,X3263,X3262)) = c_Lattices_Osemilattice__inf__class_Oinf(X3264,X3263,X3262) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).
fof(i_0_928,plain,
! [X3256,X3257,X3258] :
( ~ class_Lattices_Osemilattice__inf(X3258)
| c_Lattices_Osemilattice__inf__class_Oinf(X3258,X3257,c_Lattices_Osemilattice__inf__class_Oinf(X3258,X3257,X3256)) = c_Lattices_Osemilattice__inf__class_Oinf(X3258,X3257,X3256) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).
fof(i_0_929,plain,
! [X3259,X3260,X3261] :
( ~ class_Lattices_Olattice(X3261)
| c_Lattices_Osemilattice__inf__class_Oinf(X3261,X3260,c_Lattices_Osemilattice__inf__class_Oinf(X3261,X3260,X3259)) = c_Lattices_Osemilattice__inf__class_Oinf(X3261,X3260,X3259) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).
fof(i_0_930,plain,
! [X2711,X2712] : c_List_Opartition(X2712,X2711,c_List_Olist_ONil(X2712)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2712),tc_List_Olist(X2712)),c_List_Olist_ONil(X2712)),c_List_Olist_ONil(X2712)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).
fof(i_0_931,plain,
! [X2316,X2317,X2318] : c_List_Osplice(X2318,hAPP(hAPP(c_List_Olist_OCons(X2318),X2317),X2316),c_List_Olist_ONil(X2318)) = hAPP(hAPP(c_List_Olist_OCons(X2318),X2317),X2316),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).
fof(i_0_932,plain,
! [X3803,X3804,X3806,X3807,X3808] :
( ( ~ hBOOL(hAPP(X3804,c_Hilbert__Choice_OEps(X3803,X3804)))
| hBOOL(hAPP(X3804,esk101_2(X3803,X3804))) )
& ( ~ hBOOL(hAPP(X3807,X3808))
| hBOOL(hAPP(X3807,c_Hilbert__Choice_OEps(X3806,X3807))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_some__eq__ex])])])])]) ).
fof(i_0_933,plain,
! [X4077,X4078,X4079] :
( ( c_Orderings_Oord__class_Oless__eq(X4079,X4078,X4077)
| ~ c_Orderings_Oord__class_Oless(X4079,X4078,X4077)
| ~ class_Orderings_Opreorder(X4079) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4079,X4077,X4078)
| ~ c_Orderings_Oord__class_Oless(X4079,X4078,X4077)
| ~ class_Orderings_Opreorder(X4079) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4079,X4078,X4077)
| c_Orderings_Oord__class_Oless__eq(X4079,X4077,X4078)
| c_Orderings_Oord__class_Oless(X4079,X4078,X4077)
| ~ class_Orderings_Opreorder(X4079) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])])]) ).
fof(i_0_934,plain,
! [X4237,X4238,X4239] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4239,tc_HOL_Obool),X4238,X4237)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4239,tc_HOL_Obool),X4238,X4237) )
& ( X4238 != X4237
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4239,tc_HOL_Obool),X4238,X4237) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4239,tc_HOL_Obool),X4238,X4237)
| X4238 = X4237
| c_Orderings_Oord__class_Oless(tc_fun(X4239,tc_HOL_Obool),X4238,X4237) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_935,plain,
! [X4234,X4235,X4236] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4236,tc_HOL_Obool),X4235,X4234)
| c_Orderings_Oord__class_Oless(tc_fun(X4236,tc_HOL_Obool),X4235,X4234)
| X4235 = X4234 )
& ( ~ c_Orderings_Oord__class_Oless(tc_fun(X4236,tc_HOL_Obool),X4235,X4234)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4236,tc_HOL_Obool),X4235,X4234) )
& ( X4235 != X4234
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4236,tc_HOL_Obool),X4235,X4234) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_936,plain,
! [X3784,X3785,X3786] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3786,tc_HOL_Obool),X3785,X3784)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3786,tc_HOL_Obool),X3785,X3784) = X3785 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).
fof(i_0_937,plain,
! [X3781,X3782,X3783] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3783,tc_HOL_Obool),X3782,X3781)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3783,tc_HOL_Obool),X3781,X3782) = X3782 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).
fof(i_0_938,plain,
! [X3865,X3866,X3867,X3868] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3868,tc_HOL_Obool),X3867,X3866)
| ~ hBOOL(hAPP(X3867,X3865))
| hBOOL(hAPP(X3866,X3865)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_939,plain,
! [X3875,X3876,X3877,X3878] :
( ~ hBOOL(hAPP(X3878,X3877))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3876,tc_HOL_Obool),X3878,X3875)
| hBOOL(hAPP(X3875,X3877)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_940,plain,
! [X4231,X4232,X4233] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X4233,tc_HOL_Obool),X4232,X4231)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4233,tc_HOL_Obool),X4232,X4231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_941,plain,
! [X3505,X3506,X3507] :
( ( X3507 != c_List_Olist_ONil(X3506)
| c_List_Obutlast(X3506,hAPP(hAPP(c_List_Oappend(X3506),X3505),X3507)) = c_List_Obutlast(X3506,X3505) )
& ( X3507 = c_List_Olist_ONil(X3506)
| c_List_Obutlast(X3506,hAPP(hAPP(c_List_Oappend(X3506),X3505),X3507)) = hAPP(hAPP(c_List_Oappend(X3506),X3505),c_List_Obutlast(X3506,X3507)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).
fof(i_0_942,plain,
! [X3502,X3503,X3504] :
( ( X3504 != c_List_Olist_ONil(X3503)
| c_List_Obutlast(X3503,hAPP(hAPP(c_List_Olist_OCons(X3503),X3502),X3504)) = c_List_Olist_ONil(X3503) )
& ( X3504 = c_List_Olist_ONil(X3503)
| c_List_Obutlast(X3503,hAPP(hAPP(c_List_Olist_OCons(X3503),X3502),X3504)) = hAPP(hAPP(c_List_Olist_OCons(X3503),X3502),c_List_Obutlast(X3503,X3504)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).
fof(i_0_943,plain,
! [X2163,X2164,X2165] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2165),X2164),X2163))
| hBOOL(hAPP(X2163,X2164)) )
& ( ~ hBOOL(hAPP(X2163,X2164))
| hBOOL(hAPP(hAPP(c_member(X2165),X2164),X2163)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_944,plain,
! [X4254,X4255,X4256] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4255,X4256)
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| X4256 = X4255
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4256,X4255) )
& ( ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| X4256 = X4255
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4256,X4255) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4255,X4256)
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4256,X4255) )
& ( ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4256,X4255) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4255,X4256)
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| X4256 = X4255
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256)) )
& ( ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| X4256 = X4255
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4255,X4256)
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256)) )
& ( ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256))
| ~ hBOOL(hAPP(hAPP(X4254,X4255),X4256)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_945,plain,
! [X4104,X4105,X4106] :
( ( c_Orderings_Oord__class_Oless(X4106,X4105,X4104)
| X4105 = X4104
| ~ c_Orderings_Oord__class_Oless__eq(X4106,X4105,X4104)
| ~ class_Orderings_Olinorder(X4106) )
& ( X4105 != X4104
| ~ c_Orderings_Oord__class_Oless(X4106,X4105,X4104)
| ~ c_Orderings_Oord__class_Oless__eq(X4106,X4105,X4104)
| ~ class_Orderings_Olinorder(X4106) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])])]) ).
fof(i_0_946,plain,
! [X4010,X4011,X4012] :
( ( c_Orderings_Oord__class_Oless__eq(X4012,X4011,X4010)
| X4011 != X4010
| ~ class_Orderings_Oorder(X4012) )
& ( c_Orderings_Oord__class_Oless__eq(X4012,X4010,X4011)
| X4011 != X4010
| ~ class_Orderings_Oorder(X4012) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4012,X4011,X4010)
| ~ c_Orderings_Oord__class_Oless__eq(X4012,X4010,X4011)
| X4011 = X4010
| ~ class_Orderings_Oorder(X4012) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_947,plain,
! [X4004,X4005,X4006] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4006,X4004,X4005)
| X4004 = X4005
| ~ c_Orderings_Oord__class_Oless__eq(X4006,X4005,X4004)
| ~ class_Orderings_Oorder(X4006) )
& ( X4004 != X4005
| c_Orderings_Oord__class_Oless__eq(X4006,X4004,X4005)
| ~ c_Orderings_Oord__class_Oless__eq(X4006,X4005,X4004)
| ~ class_Orderings_Oorder(X4006) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_948,plain,
! [X3985,X3986,X3987] :
( ~ class_Orderings_Oorder(X3987)
| ~ c_Orderings_Oord__class_Oless__eq(X3987,X3986,X3985)
| ~ c_Orderings_Oord__class_Oless__eq(X3987,X3985,X3986)
| X3986 = X3985 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_949,plain,
! [X3978,X3979,X3980] :
( ~ class_Orderings_Oorder(X3980)
| ~ c_Orderings_Oord__class_Oless__eq(X3980,X3979,X3978)
| ~ c_Orderings_Oord__class_Oless__eq(X3980,X3978,X3979)
| X3978 = X3979 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_950,plain,
! [X4175,X4176,X4177] :
( ~ class_Orderings_Oorder(X4177)
| ~ c_Orderings_Oord__class_Oless(X4177,X4176,X4175)
| ~ c_Orderings_Oord__class_Oless(X4177,X4175,X4176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])]) ).
fof(i_0_951,plain,
! [X4145,X4146,X4147] :
( ( c_Orderings_Oord__class_Oless(X4147,X4146,X4145)
| c_Orderings_Oord__class_Oless(X4147,X4145,X4146)
| X4146 = X4145
| ~ class_Orderings_Olinorder(X4147) )
& ( ~ c_Orderings_Oord__class_Oless(X4147,X4145,X4146)
| ~ c_Orderings_Oord__class_Oless(X4147,X4146,X4145)
| ~ class_Orderings_Olinorder(X4147) )
& ( X4146 != X4145
| ~ c_Orderings_Oord__class_Oless(X4147,X4146,X4145)
| ~ class_Orderings_Olinorder(X4147) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])])]) ).
fof(i_0_952,plain,
! [X4098,X4099,X4100] :
( ~ class_Orderings_Olinorder(X4100)
| ~ c_Orderings_Oord__class_Oless__eq(X4100,X4099,X4098)
| ~ c_Orderings_Oord__class_Oless(X4100,X4098,X4099) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_953,plain,
! [X4065,X4066,X4067] :
( ( c_Orderings_Oord__class_Oless(X4067,X4066,X4065)
| c_Orderings_Oord__class_Oless__eq(X4067,X4065,X4066)
| ~ class_Orderings_Olinorder(X4067) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4067,X4065,X4066)
| ~ c_Orderings_Oord__class_Oless(X4067,X4066,X4065)
| ~ class_Orderings_Olinorder(X4067) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])])]) ).
fof(i_0_954,plain,
! [X4068,X4069,X4070] :
( ( c_Orderings_Oord__class_Oless__eq(X4070,X4069,X4068)
| c_Orderings_Oord__class_Oless(X4070,X4068,X4069)
| ~ class_Orderings_Olinorder(X4070) )
& ( ~ c_Orderings_Oord__class_Oless(X4070,X4068,X4069)
| ~ c_Orderings_Oord__class_Oless__eq(X4070,X4069,X4068)
| ~ class_Orderings_Olinorder(X4070) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])])]) ).
fof(i_0_955,plain,
! [X4202,X4203,X4204] :
( ~ class_Orderings_Opreorder(X4204)
| ~ c_Orderings_Oord__class_Oless(X4204,X4203,X4202)
| ~ c_Orderings_Oord__class_Oless(X4204,X4202,X4203) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).
fof(i_0_956,plain,
! [X4172,X4173,X4174] :
( ~ class_Orderings_Opreorder(X4174)
| ~ c_Orderings_Oord__class_Oless(X4174,X4173,X4172)
| ~ c_Orderings_Oord__class_Oless(X4174,X4172,X4173) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_957,plain,
! [X4163,X4164,X4165] :
( ~ class_Orderings_Opreorder(X4165)
| ~ c_Orderings_Oord__class_Oless(X4165,X4164,X4163)
| ~ c_Orderings_Oord__class_Oless(X4165,X4163,X4164) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_958,plain,
! [X4160,X4161,X4162] :
( ~ class_Orderings_Opreorder(X4162)
| ~ c_Orderings_Oord__class_Oless(X4162,X4161,X4160)
| ~ c_Orderings_Oord__class_Oless(X4162,X4160,X4161) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_959,plain,
! [X3725,X3726,X3727] :
( ~ class_Lattices_Osemilattice__inf(X3727)
| c_Orderings_Oord__class_Oless__eq(X3727,c_Lattices_Osemilattice__inf__class_Oinf(X3727,X3726,X3725),X3726) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).
fof(i_0_960,plain,
! [X3722,X3723,X3724] :
( ~ class_Lattices_Olattice(X3724)
| c_Orderings_Oord__class_Oless__eq(X3724,c_Lattices_Osemilattice__inf__class_Oinf(X3724,X3723,X3722),X3723) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).
fof(i_0_961,plain,
! [X3731,X3732,X3733] :
( ~ class_Lattices_Osemilattice__inf(X3733)
| c_Orderings_Oord__class_Oless__eq(X3733,c_Lattices_Osemilattice__inf__class_Oinf(X3733,X3732,X3731),X3731) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).
fof(i_0_962,plain,
! [X3728,X3729,X3730] :
( ~ class_Lattices_Olattice(X3730)
| c_Orderings_Oord__class_Oless__eq(X3730,c_Lattices_Osemilattice__inf__class_Oinf(X3730,X3729,X3728),X3728) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).
fof(i_0_963,plain,
! [X2232,X2233,X2234,X2235,X2236] :
( ( X2235 = X2233
| hAPP(hAPP(c_List_Olist_OCons(X2236),X2235),X2234) != hAPP(hAPP(c_List_Olist_OCons(X2236),X2233),X2232) )
& ( X2234 = X2232
| hAPP(hAPP(c_List_Olist_OCons(X2236),X2235),X2234) != hAPP(hAPP(c_List_Olist_OCons(X2236),X2233),X2232) )
& ( X2235 != X2233
| X2234 != X2232
| hAPP(hAPP(c_List_Olist_OCons(X2236),X2235),X2234) = hAPP(hAPP(c_List_Olist_OCons(X2236),X2233),X2232) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).
fof(i_0_964,plain,
! [X2502,X2503,X2504,X2505] :
( ( hAPP(hAPP(c_List_Oappend(X2505),X2504),X2503) != hAPP(hAPP(c_List_Oappend(X2505),X2502),X2503)
| X2504 = X2502 )
& ( X2504 != X2502
| hAPP(hAPP(c_List_Oappend(X2505),X2504),X2503) = hAPP(hAPP(c_List_Oappend(X2505),X2502),X2503) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).
fof(i_0_965,plain,
! [X2498,X2499,X2500,X2501] :
( ( hAPP(hAPP(c_List_Oappend(X2501),X2500),X2499) != hAPP(hAPP(c_List_Oappend(X2501),X2500),X2498)
| X2499 = X2498 )
& ( X2499 != X2498
| hAPP(hAPP(c_List_Oappend(X2501),X2500),X2499) = hAPP(hAPP(c_List_Oappend(X2501),X2500),X2498) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).
fof(i_0_966,plain,
! [X3105,X3106,X3107] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3107,tc_HOL_Obool),X3106,X3105) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3107,tc_HOL_Obool),X3105,X3106),
inference(variable_rename,[status(thm)],[fact_Int__commute]) ).
fof(i_0_967,plain,
! [X4113,X4114,X4115] :
( ~ class_Orderings_Oorder(X4115)
| ~ c_Orderings_Oord__class_Oless__eq(X4115,X4114,X4113)
| X4113 = X4114
| c_Orderings_Oord__class_Oless(X4115,X4114,X4113) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_968,plain,
! [X4110,X4111,X4112] :
( ~ class_Orderings_Oorder(X4112)
| ~ c_Orderings_Oord__class_Oless__eq(X4112,X4111,X4110)
| X4111 = X4110
| c_Orderings_Oord__class_Oless(X4112,X4111,X4110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_969,plain,
! [X4107,X4108,X4109] :
( ~ class_Orderings_Oorder(X4109)
| ~ c_Orderings_Oord__class_Oless__eq(X4109,X4108,X4107)
| c_Orderings_Oord__class_Oless(X4109,X4108,X4107)
| X4108 = X4107 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_970,plain,
! [X4092,X4093,X4094] :
( ~ class_Orderings_Oorder(X4094)
| X4093 = X4092
| ~ c_Orderings_Oord__class_Oless__eq(X4094,X4093,X4092)
| c_Orderings_Oord__class_Oless(X4094,X4093,X4092) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_971,plain,
! [X4080,X4081,X4082] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4082,X4081,X4080)
| c_Orderings_Oord__class_Oless(X4082,X4081,X4080)
| X4081 = X4080
| ~ class_Orderings_Oorder(X4082) )
& ( ~ c_Orderings_Oord__class_Oless(X4082,X4081,X4080)
| c_Orderings_Oord__class_Oless__eq(X4082,X4081,X4080)
| ~ class_Orderings_Oorder(X4082) )
& ( X4081 != X4080
| c_Orderings_Oord__class_Oless__eq(X4082,X4081,X4080)
| ~ class_Orderings_Oorder(X4082) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_972,plain,
! [X4074,X4075,X4076] :
( ( c_Orderings_Oord__class_Oless__eq(X4076,X4075,X4074)
| ~ c_Orderings_Oord__class_Oless(X4076,X4075,X4074)
| ~ class_Orderings_Oorder(X4076) )
& ( X4075 != X4074
| ~ c_Orderings_Oord__class_Oless(X4076,X4075,X4074)
| ~ class_Orderings_Oorder(X4076) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4076,X4075,X4074)
| X4075 = X4074
| c_Orderings_Oord__class_Oless(X4076,X4075,X4074)
| ~ class_Orderings_Oorder(X4076) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_973,plain,
! [X4089,X4090,X4091] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4091,X4090,X4089)
| X4090 = X4089
| c_Orderings_Oord__class_Oless(X4091,X4090,X4089)
| ~ class_Orderings_Olinorder(X4091) )
& ( X4090 != X4089
| c_Orderings_Oord__class_Oless__eq(X4091,X4090,X4089)
| c_Orderings_Oord__class_Oless(X4091,X4090,X4089)
| ~ class_Orderings_Olinorder(X4091) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])])]) ).
fof(i_0_974,plain,
! [X4095,X4096,X4097] :
( ~ class_Orderings_Oorder(X4097)
| X4096 = X4095
| ~ c_Orderings_Oord__class_Oless__eq(X4097,X4095,X4096)
| c_Orderings_Oord__class_Oless(X4097,X4095,X4096) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_975,plain,
! [X3734,X3735,X3736] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3736,X3735,X3734)
| c_Lattices_Osemilattice__inf__class_Oinf(X3736,X3735,X3734) = X3735
| ~ class_Lattices_Osemilattice__inf(X3736) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(X3736,X3735,X3734) != X3735
| c_Orderings_Oord__class_Oless__eq(X3736,X3735,X3734)
| ~ class_Lattices_Osemilattice__inf(X3736) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).
fof(i_0_976,plain,
! [X3749,X3750,X3751] :
( ~ class_Lattices_Osemilattice__inf(X3751)
| ~ c_Orderings_Oord__class_Oless__eq(X3751,X3750,X3749)
| c_Lattices_Osemilattice__inf__class_Oinf(X3751,X3750,X3749) = X3750 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).
fof(i_0_977,plain,
! [X3752,X3753,X3754] :
( ~ class_Lattices_Osemilattice__inf(X3754)
| ~ c_Orderings_Oord__class_Oless__eq(X3754,X3753,X3752)
| c_Lattices_Osemilattice__inf__class_Oinf(X3754,X3752,X3753) = X3753 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).
fof(i_0_978,plain,
! [X4101,X4102,X4103] :
( ~ class_Orderings_Opreorder(X4103)
| ~ c_Orderings_Oord__class_Oless(X4103,X4102,X4101)
| c_Orderings_Oord__class_Oless__eq(X4103,X4102,X4101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_979,plain,
! [X3574,X3575,X3576] :
( ~ c_List_Odistinct(X3576,X3575)
| c_List_Odistinct(X3576,c_List_OdropWhile(X3576,X3574,X3575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile])]) ).
fof(i_0_980,plain,
! [X3541,X3542,X3543] :
( ~ c_List_Odistinct(X3543,X3542)
| c_List_Odistinct(X3543,c_List_OtakeWhile(X3543,X3541,X3542)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).
fof(i_0_981,plain,
! [X2421,X2422,X2423] :
( ~ c_List_Odistinct(X2423,X2422)
| c_List_Odistinct(X2423,c_List_Oinsert(X2423,X2421,X2422)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])]) ).
fof(i_0_982,plain,
! [X4217,X4218] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4218,X4217)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4218,X4217) )
& ( X4218 != X4217
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4218,X4217) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4218,X4217)
| X4218 = X4217
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4218,X4217) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_983,plain,
! [X3476,X3477,X3478] :
( X3478 != c_List_Olist_ONil(X3477)
| c_List_Olast(X3477,hAPP(hAPP(c_List_Oappend(X3477),X3476),X3478)) = c_List_Olast(X3477,X3476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).
fof(i_0_984,plain,
! [X3470,X3471,X3472] :
( ( X3472 != c_List_Olist_ONil(X3471)
| c_List_Olast(X3471,hAPP(hAPP(c_List_Oappend(X3471),X3470),X3472)) = c_List_Olast(X3471,X3470) )
& ( X3472 = c_List_Olist_ONil(X3471)
| c_List_Olast(X3471,hAPP(hAPP(c_List_Oappend(X3471),X3470),X3472)) = c_List_Olast(X3471,X3472) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).
fof(i_0_985,plain,
! [X4063,X4064] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4064,X4063)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4064,X4063) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_986,plain,
! [X3473,X3474,X3475] :
( X3475 = c_List_Olist_ONil(X3474)
| c_List_Olast(X3474,hAPP(hAPP(c_List_Oappend(X3474),X3473),X3475)) = c_List_Olast(X3474,X3475) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).
fof(i_0_987,plain,
! [X3467,X3468,X3469] :
( ( X3469 != c_List_Olist_ONil(X3468)
| c_List_Olast(X3468,hAPP(hAPP(c_List_Olist_OCons(X3468),X3467),X3469)) = X3467 )
& ( X3469 = c_List_Olist_ONil(X3468)
| c_List_Olast(X3468,hAPP(hAPP(c_List_Olist_OCons(X3468),X3467),X3469)) = c_List_Olast(X3468,X3469) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).
fof(i_0_988,plain,
! [X3464,X3465,X3466] :
( X3466 = c_List_Olist_ONil(X3465)
| c_List_Olast(X3465,hAPP(hAPP(c_List_Olist_OCons(X3465),X3464),X3466)) = c_List_Olast(X3465,X3466) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).
fof(i_0_989,plain,
! [X3809,X3810,X3811] :
( ~ hBOOL(hAPP(X3810,X3811))
| hBOOL(hAPP(X3810,c_Hilbert__Choice_OEps(X3809,X3810))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).
fof(i_0_990,plain,
! [X3796,X3797,X3798] :
( ~ hBOOL(hAPP(X3797,X3798))
| hBOOL(hAPP(X3797,c_Hilbert__Choice_OEps(X3796,X3797))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).
fof(i_0_991,plain,
! [X3793,X3794,X3795] :
( ~ hBOOL(hAPP(X3795,X3794))
| hBOOL(hAPP(X3795,c_Hilbert__Choice_OEps(X3793,X3795))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).
fof(i_0_992,plain,
! [X2147,X2148] :
( hAPP(X2148,esk1_2(X2147,X2148)) != hAPP(X2147,esk1_2(X2147,X2148))
| X2148 = X2147 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_993,plain,
! [X3461,X3462,X3463] :
( X3463 != c_List_Olist_ONil(X3462)
| c_List_Olast(X3462,hAPP(hAPP(c_List_Olist_OCons(X3462),X3461),X3463)) = X3461 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).
fof(i_0_994,plain,
! [X4304,X4305] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4305),X4304))
| hBOOL(X4305) ),
inference(variable_rename,[status(thm)],[i_0_571]) ).
fof(i_0_995,plain,
! [X4306,X4307] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4307),X4306))
| hBOOL(X4306) ),
inference(variable_rename,[status(thm)],[i_0_572]) ).
fof(i_0_996,plain,
! [X4296,X4297] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4297),X4296))
| X4297 = X4296 ),
inference(variable_rename,[status(thm)],[i_0_573]) ).
fof(i_0_997,plain,
! [X4274,X4275,X4276,X4277] : hAPP(c_COMBK(X4277,X4276,X4275),X4274) = X4275,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_998,plain,
! [X4142,X4143,X4144] :
( ( X4143 = X4142
| c_Orderings_Oord__class_Oless(X4144,X4143,X4142)
| c_Orderings_Oord__class_Oless(X4144,X4142,X4143)
| ~ class_Orderings_Olinorder(X4144) )
& ( ~ c_Orderings_Oord__class_Oless(X4144,X4143,X4142)
| X4143 != X4142
| ~ class_Orderings_Olinorder(X4144) )
& ( ~ c_Orderings_Oord__class_Oless(X4144,X4142,X4143)
| X4143 != X4142
| ~ class_Orderings_Olinorder(X4144) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_999,plain,
! [X4205,X4206,X4207] :
( ~ class_Orderings_Olinorder(X4207)
| c_Orderings_Oord__class_Oless(X4207,X4206,X4205)
| X4206 = X4205
| c_Orderings_Oord__class_Oless(X4207,X4205,X4206) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).
fof(i_0_1000,plain,
! [X4154,X4155,X4156] :
( ~ class_Orderings_Olinorder(X4156)
| X4155 = X4154
| c_Orderings_Oord__class_Oless(X4156,X4155,X4154)
| c_Orderings_Oord__class_Oless(X4156,X4154,X4155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])]) ).
fof(i_0_1001,plain,
! [X4151,X4152,X4153] :
( ( c_Orderings_Oord__class_Oless(X4153,X4151,X4152)
| X4151 = X4152
| c_Orderings_Oord__class_Oless(X4153,X4152,X4151)
| ~ class_Orderings_Olinorder(X4153) )
& ( X4151 != X4152
| ~ c_Orderings_Oord__class_Oless(X4153,X4151,X4152)
| c_Orderings_Oord__class_Oless(X4153,X4152,X4151)
| ~ class_Orderings_Olinorder(X4153) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])])]) ).
fof(i_0_1002,plain,
! [X4148,X4149,X4150] :
( ~ class_Orderings_Olinorder(X4150)
| c_Orderings_Oord__class_Oless(X4150,X4149,X4148)
| X4149 = X4148
| c_Orderings_Oord__class_Oless(X4150,X4148,X4149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_1003,plain,
! [X2368,X2369] : c_List_Oinsert(X2369,X2368,c_List_Olist_ONil(X2369)) = hAPP(hAPP(c_List_Olist_OCons(X2369),X2368),c_List_Olist_ONil(X2369)),
inference(variable_rename,[status(thm)],[fact_insert__Nil]) ).
fof(i_0_1004,plain,
! [X4086,X4087,X4088] :
( ~ class_Orderings_Olinorder(X4088)
| c_Orderings_Oord__class_Oless__eq(X4088,X4087,X4086)
| c_Orderings_Oord__class_Oless(X4088,X4086,X4087) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_577])]) ).
fof(i_0_1005,plain,
! [X4071,X4072,X4073] :
( ~ class_Orderings_Olinorder(X4073)
| c_Orderings_Oord__class_Oless__eq(X4073,X4072,X4071)
| c_Orderings_Oord__class_Oless(X4073,X4071,X4072) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_1006,plain,
! [X4083,X4084,X4085] :
( ~ class_Orderings_Olinorder(X4085)
| c_Orderings_Oord__class_Oless(X4085,X4084,X4083)
| c_Orderings_Oord__class_Oless__eq(X4085,X4083,X4084) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_578])]) ).
fof(i_0_1007,plain,
! [X4013,X4014,X4015] :
( ~ class_Orderings_Olinorder(X4015)
| c_Orderings_Oord__class_Oless__eq(X4015,X4014,X4013)
| c_Orderings_Oord__class_Oless__eq(X4015,X4013,X4014) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_1008,plain,
! [X3971,X3972,X3973] :
( ~ class_Orderings_Olinorder(X3973)
| c_Orderings_Oord__class_Oless__eq(X3973,X3972,X3971)
| c_Orderings_Oord__class_Oless__eq(X3973,X3971,X3972) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])]) ).
fof(i_0_1009,plain,
! [X3253,X3254,X3255] :
( ~ class_Lattices_Osemilattice__inf(X3255)
| c_Lattices_Osemilattice__inf__class_Oinf(X3255,X3254,X3253) = c_Lattices_Osemilattice__inf__class_Oinf(X3255,X3253,X3254) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).
fof(i_0_1010,plain,
! [X3247,X3248,X3249] :
( ~ class_Lattices_Osemilattice__inf(X3249)
| c_Lattices_Osemilattice__inf__class_Oinf(X3249,X3248,X3247) = c_Lattices_Osemilattice__inf__class_Oinf(X3249,X3247,X3248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).
fof(i_0_1011,plain,
! [X3250,X3251,X3252] :
( ~ class_Lattices_Olattice(X3252)
| c_Lattices_Osemilattice__inf__class_Oinf(X3252,X3251,X3250) = c_Lattices_Osemilattice__inf__class_Oinf(X3252,X3250,X3251) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).
fof(i_0_1012,plain,
! [X4247,X4248] :
( X4248 = X4247
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4248,X4247)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4247,X4248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])]) ).
fof(i_0_1013,plain,
! [X4245,X4246] :
( ( X4246 = X4245
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4246,X4245)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4245,X4246) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4246,X4245)
| X4246 != X4245 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4245,X4246)
| X4246 != X4245 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_1014,plain,
! [X4258,X4259] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4259,X4258)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4258,X4259) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_1015,plain,
! [X4169,X4170,X4171] :
( ~ class_Orderings_Oorder(X4171)
| ~ c_Orderings_Oord__class_Oless(X4171,X4170,X4169)
| X4169 != X4170 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_1016,plain,
! [X4166,X4167,X4168] :
( ~ class_Orderings_Oorder(X4168)
| ~ c_Orderings_Oord__class_Oless(X4168,X4167,X4166)
| X4167 != X4166 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_1017,plain,
! [X4157,X4158,X4159] :
( ~ class_Orderings_Oorder(X4159)
| ~ c_Orderings_Oord__class_Oless(X4159,X4158,X4157)
| X4158 != X4157 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_1018,plain,
! [X3048,X3049] : hBOOL(hAPP(c_List_Olistsp(X3049,X3048),c_List_Olist_ONil(X3049))),
inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J]) ).
fof(i_0_1019,plain,
! [X3038,X3039] : hBOOL(hAPP(c_List_Olistsp(X3039,X3038),c_List_Olist_ONil(X3039))),
inference(variable_rename,[status(thm)],[fact_listsp_ONil]) ).
fof(i_0_1020,plain,
! [X2531,X2532,X2533] :
( ( X2532 = c_List_Olist_ONil(X2533)
| hAPP(hAPP(c_List_Oappend(X2533),X2532),X2531) != c_List_Olist_ONil(X2533) )
& ( X2531 = c_List_Olist_ONil(X2533)
| hAPP(hAPP(c_List_Oappend(X2533),X2532),X2531) != c_List_Olist_ONil(X2533) )
& ( X2532 != c_List_Olist_ONil(X2533)
| X2531 != c_List_Olist_ONil(X2533)
| hAPP(hAPP(c_List_Oappend(X2533),X2532),X2531) = c_List_Olist_ONil(X2533) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).
fof(i_0_1021,plain,
! [X2542,X2543,X2544] :
( ( X2543 = c_List_Olist_ONil(X2544)
| c_List_Olist_ONil(X2544) != hAPP(hAPP(c_List_Oappend(X2544),X2543),X2542) )
& ( X2542 = c_List_Olist_ONil(X2544)
| c_List_Olist_ONil(X2544) != hAPP(hAPP(c_List_Oappend(X2544),X2543),X2542) )
& ( X2543 != c_List_Olist_ONil(X2544)
| X2542 != c_List_Olist_ONil(X2544)
| c_List_Olist_ONil(X2544) = hAPP(hAPP(c_List_Oappend(X2544),X2543),X2542) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).
fof(i_0_1022,plain,
! [X4140,X4141] :
( ~ class_Orderings_Opreorder(X4141)
| ~ c_Orderings_Oord__class_Oless(X4141,X4140,X4140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_581])]) ).
fof(i_0_1023,plain,
! [X4302,X4303] :
( ~ hBOOL(X4303)
| ~ hBOOL(X4302)
| hBOOL(hAPP(hAPP(c_fconj,X4303),X4302)) ),
inference(variable_rename,[status(thm)],[i_0_582]) ).
fof(i_0_1024,plain,
! [X2525,X2526,X2527] :
( ( hAPP(hAPP(c_List_Oappend(X2527),X2526),X2525) != X2525
| X2526 = c_List_Olist_ONil(X2527) )
& ( X2526 != c_List_Olist_ONil(X2527)
| hAPP(hAPP(c_List_Oappend(X2527),X2526),X2525) = X2525 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).
fof(i_0_1025,plain,
! [X2528,X2529,X2530] :
( ( hAPP(hAPP(c_List_Oappend(X2530),X2529),X2528) != X2529
| X2528 = c_List_Olist_ONil(X2530) )
& ( X2528 != c_List_Olist_ONil(X2530)
| hAPP(hAPP(c_List_Oappend(X2530),X2529),X2528) = X2529 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).
fof(i_0_1026,plain,
! [X2537,X2538,X2539] :
( ( X2539 != hAPP(hAPP(c_List_Oappend(X2538),X2539),X2537)
| X2537 = c_List_Olist_ONil(X2538) )
& ( X2537 != c_List_Olist_ONil(X2538)
| X2539 = hAPP(hAPP(c_List_Oappend(X2538),X2539),X2537) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).
fof(i_0_1027,plain,
! [X2534,X2535,X2536] :
( ( X2536 != hAPP(hAPP(c_List_Oappend(X2535),X2534),X2536)
| X2534 = c_List_Olist_ONil(X2535) )
& ( X2534 != c_List_Olist_ONil(X2535)
| X2536 = hAPP(hAPP(c_List_Oappend(X2535),X2534),X2536) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).
fof(i_0_1028,plain,
! [X2187,X2188,X2189] : hAPP(hAPP(c_List_Olist_OCons(X2189),X2188),X2187) != c_List_Olist_ONil(X2189),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).
fof(i_0_1029,plain,
! [X2184,X2185,X2186] : c_List_Olist_ONil(X2186) != hAPP(hAPP(c_List_Olist_OCons(X2186),X2185),X2184),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
fof(i_0_1030,plain,
! [X4252,X4253] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4253,X4252)
| X4253 != X4252 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_1031,plain,
! [X4250,X4251] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4251,X4250)
| X4250 != X4251 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_1032,plain,
! [X2744,X2745] : c_List_Olistrel(X2745,c_Transitive__Closure_Ortrancl(X2745,X2744)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X2745),c_List_Olistrel1(X2745,X2744)),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).
fof(i_0_1033,plain,
! [X2211,X2212,X2213] : hAPP(hAPP(c_List_Olist_OCons(X2213),X2212),X2211) != X2211,
inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).
fof(i_0_1034,plain,
! [X2208,X2209,X2210] : X2210 != hAPP(hAPP(c_List_Olist_OCons(X2209),X2208),X2210),
inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).
fof(i_0_1035,plain,
! [X4249] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4249,X4249),
inference(variable_rename,[status(thm)],[i_0_583]) ).
fof(i_0_1036,plain,
! [X4244] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4244,X4244),
inference(variable_rename,[status(thm)],[i_0_584]) ).
fof(i_0_1037,plain,
! [X2985,X2986] : c_Relation_ORange(X2986,X2986,c_Relation_OId__on(X2986,X2985)) = X2985,
inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).
fof(i_0_1038,plain,
! [X2981,X2982] : c_Relation_ODomain(X2982,X2982,c_Relation_OId__on(X2982,X2981)) = X2981,
inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).
fof(i_0_1039,plain,
! [X3858,X3859,X3860] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3858,tc_HOL_Obool),X3860,X3859)
| X3860 != X3859 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3858,tc_HOL_Obool),X3859,X3860)
| X3860 != X3859 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_585])])]) ).
fof(i_0_1040,plain,
! [X3872,X3873,X3874] :
( X3874 != X3873
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3872,tc_HOL_Obool),X3874,X3873) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_1041,plain,
! [X3869,X3870,X3871] :
( X3871 != X3870
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3869,tc_HOL_Obool),X3870,X3871) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_1042,plain,
! [X2987,X2988] : c_Relation_Osingle__valued(X2988,X2988,c_Relation_OId__on(X2988,X2987)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).
fof(i_0_1043,plain,
! [X4298,X4299] :
( X4299 != X4298
| hBOOL(hAPP(hAPP(c_fequal,X4299),X4298)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1044,plain,
! [X3103,X3104] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3104,tc_HOL_Obool),X3103,X3103) = X3103,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
fof(i_0_1045,plain,
! [X2667,X2668] :
( ( ~ c_List_Odistinct(X2668,c_List_Orotate1(X2668,X2667))
| c_List_Odistinct(X2668,X2667) )
& ( ~ c_List_Odistinct(X2668,X2667)
| c_List_Odistinct(X2668,c_List_Orotate1(X2668,X2667)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).
fof(i_0_1046,plain,
! [X3882,X3883] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3883,tc_HOL_Obool),X3882,X3882),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_1047,plain,
! [X2740,X2741] :
( ~ c_Relation_Otrans(X2741,X2740)
| c_Relation_Otrans(tc_List_Olist(X2741),c_List_Olistrel(X2741,X2740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__trans])]) ).
fof(i_0_1048,plain,
! [X2742,X2743] :
( ~ c_Relation_Otrans(X2743,X2742)
| c_Relation_Otrans(tc_List_Olist(X2743),c_List_Olexord(X2743,X2742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__transI])]) ).
fof(i_0_1049,plain,
! [X2522,X2523,X2524] :
( X2524 != X2523
| X2524 = hAPP(hAPP(c_List_Oappend(X2522),c_List_Olist_ONil(X2522)),X2523) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).
fof(i_0_1050,plain,
! [X3508,X3509] :
( X3509 = c_List_Olist_ONil(X3508)
| ~ c_List_Odistinct(X3508,X3509)
| c_List_Odistinct(X3508,c_List_Obutlast(X3508,X3509)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).
fof(i_0_1051,plain,
! [X2663,X2664] : c_Nat_Osize__class_Osize(tc_List_Olist(X2664),c_List_Orotate1(X2664,X2663)) = c_Nat_Osize__class_Osize(tc_List_Olist(X2664),X2663),
inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).
fof(i_0_1052,plain,
! [X4007,X4008,X4009] :
( ~ class_Orderings_Opreorder(X4009)
| X4008 != X4007
| c_Orderings_Oord__class_Oless__eq(X4009,X4008,X4007) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1053,plain,
! [X2545,X2546] : hAPP(hAPP(c_List_Oappend(X2546),c_List_Olist_ONil(X2546)),X2545) = X2545,
inference(variable_rename,[status(thm)],[fact_append__Nil]) ).
fof(i_0_1054,plain,
! [X3572,X3573] : c_List_OdropWhile(X3573,X3572,c_List_Olist_ONil(X3573)) = c_List_Olist_ONil(X3573),
inference(variable_rename,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).
fof(i_0_1055,plain,
! [X3539,X3540] : c_List_OtakeWhile(X3540,X3539,c_List_Olist_ONil(X3540)) = c_List_Olist_ONil(X3540),
inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).
fof(i_0_1056,plain,
! [X3245,X3246] :
( ~ class_Lattices_Osemilattice__inf(X3246)
| c_Lattices_Osemilattice__inf__class_Oinf(X3246,X3245,X3245) = X3245 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).
fof(i_0_1057,plain,
! [X3243,X3244] :
( ~ class_Lattices_Osemilattice__inf(X3244)
| c_Lattices_Osemilattice__inf__class_Oinf(X3244,X3243,X3243) = X3243 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).
fof(i_0_1058,plain,
! [X3945,X3946] :
( ~ class_Orderings_Opreorder(X3946)
| c_Orderings_Oord__class_Oless__eq(X3946,X3945,X3945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1059,plain,
! [X2352,X2353] : c_List_Osplice(X2353,c_List_Olist_ONil(X2353),X2352) = X2352,
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).
fof(i_0_1060,plain,
! [X2350,X2351] : c_List_Osplice(X2351,X2350,c_List_Olist_ONil(X2351)) = X2350,
inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).
fof(i_0_1061,plain,
! [X2540,X2541] : hAPP(hAPP(c_List_Oappend(X2541),X2540),c_List_Olist_ONil(X2541)) = X2540,
inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).
fof(i_0_1062,plain,
! [X4260,X4261] :
( X4261 != X4260
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4261,X4260) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1063,plain,
! [X2800,X2801] : c_Transitive__Closure_Ortrancl(X2801,c_Transitive__Closure_Ortrancl(X2801,X2800)) = c_Transitive__Closure_Ortrancl(X2801,X2800),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).
fof(i_0_1064,plain,
! [X4257] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4257,X4257),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1065,plain,
! [X4300] :
( ~ hBOOL(hAPP(c_fNot,X4300))
| ~ hBOOL(X4300) ),
inference(variable_rename,[status(thm)],[i_0_586]) ).
fof(i_0_1066,plain,
! [X2983,X2984] : c_Relation_Otrans(X2984,c_Relation_OId__on(X2984,X2983)),
inference(variable_rename,[status(thm)],[fact_trans__Id__on]) ).
fof(i_0_1067,plain,
! [X2802,X2803] : c_Relation_Otrans(X2803,c_Transitive__Closure_Ortrancl(X2803,X2802)),
inference(variable_rename,[status(thm)],[fact_trans__rtrancl]) ).
fof(i_0_1068,plain,
! [X3799,X3800] : c_Hilbert__Choice_OEps(X3800,hAPP(c_fequal,X3799)) = X3799,
inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).
fof(i_0_1069,plain,
! [X4268,X4269] :
( ~ class_Orderings_Oorder(X4269)
| class_Orderings_Oorder(tc_fun(X4268,X4269)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1070,plain,
! [X4270,X4271] :
( ~ class_Orderings_Oord(X4271)
| class_Orderings_Oord(tc_fun(X4270,X4271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1071,plain,
! [X4264,X4265] :
( ~ class_Orderings_Opreorder(X4265)
| class_Orderings_Opreorder(tc_fun(X4264,X4265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1072,plain,
! [X4262,X4263] :
( ~ class_Lattices_Olattice(X4263)
| class_Lattices_Osemilattice__inf(tc_fun(X4262,X4263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).
fof(i_0_1073,plain,
! [X4266,X4267] :
( ~ class_Lattices_Olattice(X4267)
| class_Lattices_Olattice(tc_fun(X4266,X4267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).
fof(i_0_1074,plain,
! [X2665,X2666] :
( ( c_List_Orotate1(X2666,X2665) != c_List_Olist_ONil(X2666)
| X2665 = c_List_Olist_ONil(X2666) )
& ( X2665 != c_List_Olist_ONil(X2666)
| c_List_Orotate1(X2666,X2665) = c_List_Olist_ONil(X2666) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).
fof(i_0_1075,plain,
! [X4301] :
( hBOOL(X4301)
| hBOOL(hAPP(c_fNot,X4301)) ),
inference(variable_rename,[status(thm)],[i_0_587]) ).
fof(i_0_1076,plain,
! [X3491] : c_List_Obutlast(X3491,c_List_Olist_ONil(X3491)) = c_List_Olist_ONil(X3491),
inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).
fof(i_0_1077,plain,
! [X4272,X4273] : hAPP(c_COMBI(X4273),X4272) = X4272,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1078,plain,
! [X2183] : c_List_Odistinct(X2183,c_List_Olist_ONil(X2183)),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
cnf(i_0_1079,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk65_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk66_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk67_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk68_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
| hBOOL(hAPP(hAPP(X3,X6),X5))
| ~ hBOOL(hAPP(hAPP(X3,X8),X7))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1080,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk69_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk70_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk71_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk72_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
| hBOOL(hAPP(hAPP(X3,X8),X7))
| ~ hBOOL(hAPP(hAPP(X3,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1081,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk71_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk72_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))
| hBOOL(hAPP(hAPP(X3,X8),X7))
| ~ hBOOL(hAPP(hAPP(X3,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1082,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk65_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk66_8(X5,X6,X7,X8,X4,X3,X2,X1)))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))
| hBOOL(hAPP(hAPP(X5,X8),X7))
| ~ hBOOL(hAPP(hAPP(X5,X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1083,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk73_7(X3,X4,X5,X6,X7,X2,X1)),esk74_7(X3,X4,X5,X6,X7,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3)))
| hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1084,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk73_7(X5,X6,X7,X4,X3,X2,X1)),esk74_7(X5,X6,X7,X4,X3,X2,X1)))),X5))
| hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1085,plain,
( hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(X1,esk67_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk68_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| ~ hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1086,plain,
( hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(X1,esk69_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk70_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| ~ hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1087,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1088,plain,
( hBOOL(hAPP(hAPP(X1,esk65_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk66_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1089,plain,
( hBOOL(hAPP(hAPP(X1,esk71_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk72_8(X1,X2,X3,X4,X5,X6,X7,X8)))
| hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1090,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X6)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1091,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk97_7(X2,X3,X4,X1,X5,X6,X7)),X7)),X3))
| hAPP(hAPP(X2,X5),X7) = hAPP(hAPP(X2,X6),X7)
| ~ c_Recdef_Oadm__wf(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1092,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1093,plain,
c_List_Opartition(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X1),tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_fun(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBS(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_List_Olist(X1),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),c_If(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(X2,X3)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_List_Olist(X1)),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(c_List_Olist_OCons(X1),X3))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),tc_fun(tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),tc_fun(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))),tc_List_Olist(X1)),c_COMBB(tc_List_Olist(X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))),c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)))),hAPP(c_List_Olist_OCons(X1),X3)))),c_List_Opartition(X1,X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1094,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_Obelow),v_P____)),v_c____)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1095,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1096,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1097,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X4,tc_fun(X1,tc_HOL_Obool)),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk86_6(X3,X2,X1,X4,X5,X6)),esk87_6(X3,X2,X1,X4,X5,X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1098,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1099,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk93_6(X2,X3,X4,X5,X6,X1)),X3)),X4))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X6),X5),X4),X3) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X6),X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1100,plain,
( hAPP(hAPP(X2,X1),X7) = hAPP(hAPP(X2,X6),X7)
| hAPP(X1,esk97_7(X2,X3,X4,X5,X1,X6,X7)) != hAPP(X6,esk97_7(X2,X3,X4,X5,X1,X6,X7))
| ~ c_Recdef_Oadm__wf(X5,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1101,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| X5 = X1
| X4 = X2
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1102,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| X2 = X4
| X1 = X5
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1103,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(v_F,X4)))
| X2 = X6
| X1 = X5
| X6 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk5_6(X4,X3,X5,X6,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(X4,esk5_6(X4,X3,X5,X6,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1104,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olistrel(X1,X2)))
| ~ c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1105,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Relation_ODomain(X1,X2,X3)))
| ~ c_Predicate_ODomainP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1106,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),c_Relation_ORange(X1,X2,X3)))
| ~ c_Predicate_ORangeP(X1,X2,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1107,plain,
( X3 = X4
| hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3) != hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2),c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1108,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk84_6(X4,X3,X5,X6,X2,X1)),esk85_6(X4,X3,X5,X6,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1109,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X3,X6,X2,X1,X5,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X3,X6,X2,X1,X5,X4))))
| X5 = X1
| X4 = X2
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1110,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X6,X3,X5,X4,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X6,X3,X5,X4,X2,X1))))
| X2 = X4
| X1 = X5
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1111,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk5_6(X4,X3,X5,X6,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(X4,esk5_6(X4,X3,X5,X6,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(v_F,X4)))
| X2 = X6
| X1 = X5
| X6 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1112,plain,
( c_List_Olistrelp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1113,plain,
( c_Predicate_ODomainP(X1,X3,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1),c_COMBC(X3,tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X1,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_prod(X1,X3),tc_fun(tc_fun(tc_prod(X1,X3),tc_HOL_Obool),tc_HOL_Obool),X3),c_member(tc_prod(X1,X3)))),c_Product__Type_OPair(X1,X3)))),X4),X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ODomain(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1114,plain,
( c_Predicate_ORangeP(X3,X1,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3),hAPP(c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1),c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X4),X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ORange(X3,X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1115,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),esk76_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel1(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk75_5(X2,X3,X4,X5,X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel1(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1116,plain,
c_Recdef_Oadm__wf(X1,X2,X3,hAPP(hAPP(c_COMBC(tc_fun(X1,X2),tc_fun(X1,X1),tc_fun(X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X2)),tc_fun(tc_fun(X1,X1),tc_fun(X1,X2)),tc_fun(X1,X2)),c_COMBS(X1,X1,X2)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(X1,X2)),tc_fun(X1,tc_fun(X1,X2)),tc_fun(X1,X2)),hAPP(c_COMBB(tc_fun(X1,X2),tc_fun(X1,X2),X1),X4)),hAPP(hAPP(c_COMBC(tc_fun(X1,X2),tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_fun(X1,X2))),c_Recdef_Ocut(X1,X2)),X3)))),c_COMBI(X1))),
inference(split_conjunct,[status(thm)],[i_0_607]),
[final] ).
cnf(i_0_1117,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk42_5(X5,X4,X3,X2,X1)),esk42_5(X5,X4,X3,X2,X1))),X5))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X4)),c_List_Olexord(X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),hAPP(hAPP(c_List_Oappend(X1),X2),X4))),c_List_Olexord(X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1118,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),esk24_6(X5,X2,X3,X6,X4,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1119,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),esk24_6(X5,X2,X6,X3,X4,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1120,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),c_FuncSet_Orestrict(X5,X1,X2,X4)),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk90_5(X3,X2,X1,X4,X5))),hAPP(X3,esk90_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1121,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),esk76_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel1(X1,X2)))
| X5 = hAPP(hAPP(c_List_Olist_OCons(X1),esk75_5(X2,X3,X4,X5,X1)),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel1(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1122,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk23_5(X3,X2,X1,X4,X5))),hAPP(X3,esk23_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1123,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk19_5(X3,X2,X1,X4,X5))),hAPP(X3,esk19_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1124,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),esk44_5(X3,X4,X2,X5,X1))),c_List_Olistrel1(X1,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),esk43_5(X3,X4,X2,X5,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel1(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1125,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk76_5(X4,X5,X3,X1,X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk75_5(X4,X5,X3,X1,X2)),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5))),c_List_Olistrel1(X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1126,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),esk35_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1127,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk34_5(X2,X3,X4,X5,X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))),c_List_Olistrel(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1128,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
| hAPP(X6,esk24_6(X5,X2,X3,X6,X4,X1)) != hAPP(X3,esk24_6(X5,X2,X3,X6,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1129,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
| hAPP(X3,esk24_6(X5,X2,X6,X3,X4,X1)) != hAPP(X6,esk24_6(X5,X2,X6,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1130,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk14_5(X3,X4,X5,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk14_5(X3,X4,X5,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1131,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk14_5(X3,X5,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk14_5(X3,X5,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1132,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk84_6(X1,X4,X3,X2,X5,X6)),esk85_6(X1,X4,X3,X2,X5,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1133,plain,
( hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X5),X1),X4),X3) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X5),X2),X4),X3)
| hAPP(X1,esk93_6(X2,X3,X4,X1,X5,X6)) != hAPP(X2,esk93_6(X2,X3,X4,X1,X5,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1134,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk86_6(X4,X5,X6,X3,X2,X1)),esk87_6(X4,X5,X6,X3,X2,X1))
| hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1135,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),c_FuncSet_Orestrict(X5,X1,X2,X4)),c_FuncSet_OPi(X5,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X5,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk91_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1136,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X5,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk21_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_617]),
[final] ).
cnf(i_0_1137,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),esk44_5(X3,X4,X2,X5,X1))),c_List_Olistrel1(X1,X3)))
| X4 = hAPP(hAPP(c_List_Olist_OCons(X1),esk43_5(X3,X4,X2,X5,X1)),X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel1(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1138,plain,
c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(c_fequal,X3)))),hAPP(c_fequal,X4)))) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1139,plain,
c_Relation_OId__on(X1,X2) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),X1),c_COMBC(X1,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj)),c_fequal))),X2)),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1140,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk44_5(X4,X1,X5,X3,X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),esk43_5(X4,X1,X5,X3,X2))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5)),X1)),c_List_Olistrel1(X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1141,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk14_5(X3,X4,X5,X1,X2))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk14_5(X3,X4,X5,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1142,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk14_5(X3,X5,X4,X1,X2))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk14_5(X3,X5,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1143,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),esk37_5(X3,X4,X2,X5,X1))),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),X4)),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1144,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk36_5(X3,X4,X5,X2,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),X4)),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1145,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk29_4(X2,X3,X4,X1)),esk28_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1146,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olexord(X1,X4)))
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk28_4(X2,X3,X4,X1)),esk29_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1147,plain,
( c_FuncSet_Orestrict(X1,X9,hAPP(hAPP(c_COMBB(X6,X9,X1),X10),c_FuncSet_Orestrict(X1,X6,hAPP(hAPP(c_COMBB(X2,X6,X1),X7),X3),X4)),X4) = c_FuncSet_Orestrict(X1,X9,hAPP(hAPP(c_COMBB(X2,X9,X1),c_FuncSet_Orestrict(X2,X9,hAPP(hAPP(c_COMBB(X6,X9,X2),X10),X7),X5)),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X9)),X10),c_FuncSet_OPi(X6,X9,X8,c_COMBK(tc_fun(X9,tc_HOL_Obool),X6,X11))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X6)),X7),c_FuncSet_OPi(X2,X6,X5,c_COMBK(tc_fun(X6,tc_HOL_Obool),X2,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_622,c_0_623]),c_0_623]),c_0_623]),c_0_623]),
[final] ).
cnf(i_0_1148,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X4)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1149,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X4)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1150,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1151,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X1),X2)),c_List_Olistrel1(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X6),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1152,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X1),tc_HOL_Obool),c_FuncSet_OPi(X5,X1,X4,X2),c_FuncSet_OPi(X5,X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(X2,esk104_5(X3,X2,X1,X4,X5)),hAPP(X3,esk104_5(X3,X2,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1153,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1154,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X7)),X8))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X1),tc_prod(X5,X1))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X1),tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X6),X2)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X7),X3))),c_Wellfounded_Olex__prod(X5,X1,X8,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1155,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk8_2(X1,X2)),esk9_2(X1,X2))),hAPP(X2,esk7_2(X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1156,plain,
hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) = c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X2,tc_fun(X2,tc_HOL_Obool),X1),c_fequal),X4)),X5))),
inference(split_conjunct,[status(thm)],[i_0_629]),
[final] ).
cnf(i_0_1157,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk38_4(X2,X3,X4,X1)),esk39_4(X2,X3,X4,X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X3)),c_List_Olistrel1(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1158,plain,
( X1 = X2
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X1),hAPP(hAPP(c_List_Olist_OCons(X5),X3),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X2),hAPP(hAPP(c_List_Olist_OCons(X5),X4),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1159,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3,X5),tc_prod(X3,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3,X5),tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X6)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X2),X7))),c_Wellfounded_Olex__prod(X3,X5,X4,X8))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1160,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk8_2(X1,X2)),esk9_2(X1,X2))),hAPP(esk7_2(X1,X2),X1)))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1161,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk7_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1162,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X6)),c_FuncSet_Orestrict(X1,X6,hAPP(hAPP(c_COMBB(X2,X6,X1),X7),X3),X4)),c_FuncSet_OPi(X1,X6,X4,c_COMBK(tc_fun(X6,tc_HOL_Obool),X1,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X6)),X7),c_FuncSet_OPi(X2,X6,X5,c_COMBK(tc_fun(X6,tc_HOL_Obool),X2,X8))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[i_0_631,c_0_623]),
[final] ).
cnf(i_0_1163,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk91_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),c_FuncSet_Orestrict(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1164,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk8_2(X1,X2) != esk9_2(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_628]),
[final] ).
cnf(i_0_1165,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk90_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),c_FuncSet_Orestrict(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1166,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),X2)),X4)),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1167,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4))),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1168,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk44_5(X4,X1,X5,X3,X2))
| X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk43_5(X4,X1,X5,X3,X2)),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5)),X1)),c_List_Olistrel1(X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1169,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk36_5(X3,X1,X4,X5,X2)),esk37_5(X3,X1,X4,X5,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4)),X1)),c_List_Olistrel(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1170,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X5),c_List_Olist_ONil(X1)))),hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),c_List_Olist_ONil(X1))))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| X5 != X6 ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1171,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk21_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_617]),
[final] ).
cnf(i_0_1172,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk92_5(X2,X3,X4,X5,X1)),X3))
| X4 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X5)),X2),c_FuncSet_Oextensional(X1,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X5)),X4),c_FuncSet_Oextensional(X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1173,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3)))),hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))))),c_List_Olistrel1(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1174,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk76_5(X4,X5,X3,X1,X2))
| X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk75_5(X4,X5,X3,X1,X2)),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X5))),c_List_Olistrel1(X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1175,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk34_5(X3,X4,X5,X1,X2)),esk35_5(X3,X4,X5,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X5),X4))),c_List_Olistrel(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1176,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk23_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1177,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk19_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1178,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk104_5(X2,X3,X4,X5,X1)),X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X5,X3),c_FuncSet_OPi(X1,X4,X5,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1179,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X6))),hAPP(hAPP(c_List_Oappend(X1),X5),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7)))),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1180,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Recdef_Osame__fst(X7,X3,X1,X6)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_635]),
[final] ).
cnf(i_0_1181,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Wellfounded_Olex__prod(X7,X3,X8,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1182,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X5),tc_prod(X1,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X5),tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X7))),c_Wellfounded_Olex__prod(X1,X5,X4,X8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1183,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,tc_prod(X1,X2)),X7),X8)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X6,X3),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X1,X2)),tc_fun(X6,X3),X5),hAPP(c_COMBB(tc_prod(X1,X2),X3,X6),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4))),X7)),X8),
inference(split_conjunct,[status(thm)],[i_0_636]),
[final] ).
cnf(i_0_1184,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk31_5(X3,X4,X1,X5,X2)),X3)
| hAPP(hAPP(c_List_Oappend(X2),esk30_5(X3,X4,X1,X5,X2)),X1) = X3
| hAPP(hAPP(c_List_Oappend(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1185,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3)))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_638]),
[final] ).
cnf(i_0_1186,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk55_4(X4,X3,X2,X1)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ORange(X3,X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_639]),
[final] ).
cnf(i_0_1187,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk53_4(X4,X3,X2,X1)),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ORange(X3,X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_640]),
[final] ).
cnf(i_0_1188,plain,
( X1 = X2
| hAPP(X1,esk92_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk92_5(X2,X3,X1,X4,X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X2),c_FuncSet_Oextensional(X5,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X4)),X1),c_FuncSet_Oextensional(X5,X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1189,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1190,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1191,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X6)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olexord(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1192,plain,
( hAPP(esk98_4(X3,X4,X5,X1),X2) = hAPP(esk99_4(X3,X4,X5,X1),X2)
| c_Recdef_Oadm__wf(X1,X5,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk100_4(X3,X4,X5,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1193,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1194,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X6)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1195,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(split_conjunct,[status(thm)],[fact_assms_I1_J]),
[final] ).
cnf(i_0_1196,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),c_FuncSet_Orestrict(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5)),c_FuncSet_OPi(X2,X1,X5,c_COMBK(tc_fun(X1,tc_HOL_Obool),X2,X4))))
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1197,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) = c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1198,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X3))),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1199,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X1,X2)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X2,esk10_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1200,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olistrel1(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1201,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olex(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1202,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X5)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X6))),c_List_Olexord(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1203,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk31_5(X3,X4,X5,X2,X1)) = X4
| hAPP(hAPP(c_List_Oappend(X1),esk30_5(X3,X4,X5,X2,X1)),X5) = X3
| hAPP(hAPP(c_List_Oappend(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1204,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk31_5(X3,X4,X1,X5,X2)),X3)
| X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk30_5(X3,X4,X1,X5,X2))
| hAPP(hAPP(c_List_Oappend(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1205,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X5)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1206,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1207,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X5)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olexord(X1,X4)))
| ~ c_Relation_Otrans(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1208,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X5)),hAPP(hAPP(c_List_Oappend(X1),X3),X6))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4)))
| X5 != X6 ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1209,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Oappend(X3),X1),X4)),hAPP(hAPP(c_List_Oappend(X3),X2),X5))),c_List_Olistrel1(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1210,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olistrel1(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1211,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olex(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olex(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1212,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olexord(X3,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olexord(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1213,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X5),X2)),hAPP(hAPP(c_List_Oappend(X1),X5),X3))),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1214,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X2)),hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1215,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk40_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk39_4(X3,X1,X4,X2)),esk41_4(X3,X1,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X4),X1)),c_List_Olistrel1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1216,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk40_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk38_4(X3,X4,X1,X2)),esk41_4(X3,X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X1),X4)),c_List_Olistrel1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_630]),
[final] ).
cnf(i_0_1217,plain,
( c_FuncSet_Orestrict(X1,X2,hAPP(hAPP(c_COMBB(X2,X2,X1),c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5)),X3),X4) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[i_0_654,c_0_623]),
[final] ).
cnf(i_0_1218,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_638]),
[final] ).
cnf(i_0_1219,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_FuncSet_Orestrict(X1,X2,hAPP(hAPP(c_COMBB(X3,X2,X1),X5),X6),X4)),c_FuncSet_Oextensional(X1,X2,X4))),
inference(rw,[status(thm)],[i_0_655,c_0_623]),
[final] ).
cnf(i_0_1220,plain,
( X1 = X2
| c_Nat_Osize__class_Osize(tc_List_Olist(X3),X4) = c_Nat_Osize__class_Osize(tc_List_Olist(X3),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4)),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))),c_List_Olex(X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1221,plain,
( X1 = X2
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X1),X3)),hAPP(hAPP(c_List_Olist_OCons(X5),X2),X4))),c_List_Olistrel1(X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1222,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X5),X4)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1223,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5)))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1224,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk27_3(X2,X3,X1)),esk27_3(X2,X3,X1))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1225,plain,
( c_Fun_Ooverride__on(X1,X4,X5,X6,X3,X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_659]),
[final] ).
cnf(i_0_1226,plain,
( c_Fun_Ooverride__on(X1,X4,X5,X6,X3,X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_660]),
[final] ).
cnf(i_0_1227,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Fun_Ooverride__on(X1,X4,X5,X6,X3,X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_661]),
[final] ).
cnf(i_0_1228,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Fun_Ooverride__on(X1,X4,X5,X6,X3,X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_660]),
[final] ).
cnf(i_0_1229,plain,
( hBOOL(hAPP(hAPP(c_member(X3),hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_662]),
[final] ).
cnf(i_0_1230,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olex(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| c_Nat_Osize__class_Osize(tc_List_Olist(X1),X5) != c_Nat_Osize__class_Osize(tc_List_Olist(X1),X6) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1231,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| X5 != X6 ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1232,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X5))),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_663]),
[final] ).
cnf(i_0_1233,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1234,plain,
c_Hilbert__Choice_OEps(tc_prod(X1,X2),X3) = c_Hilbert__Choice_OEps(tc_prod(X1,X2),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBB(tc_prod(X1,X2),tc_HOL_Obool,X2),X3)),c_Product__Type_OPair(X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1235,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),c_Transitive__Closure_Ortrancl(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ c_Relation_Osingle__valued(X1,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),c_Transitive__Closure_Ortrancl(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_665]),
[final] ).
cnf(i_0_1236,plain,
( c_FuncSet_Orestrict(X1,X2,hAPP(hAPP(c_COMBB(X1,X2,X1),X3),c_FuncSet_Orestrict(X1,X1,c_COMBI(X1),X4)),X4) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(rw,[status(thm)],[i_0_666,c_0_623]),
[final] ).
cnf(i_0_1237,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk56_4(X4,X3,X2,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ODomain(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_667]),
[final] ).
cnf(i_0_1238,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk52_4(X4,X3,X2,X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ODomain(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1239,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk31_5(X3,X4,X5,X2,X1)) = X4
| X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk30_5(X3,X4,X5,X2,X1))
| hAPP(hAPP(c_List_Oappend(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1240,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk32_5(X3,X4,X1,X5,X2)),X3)
| hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) = X3
| hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1241,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk33_5(X2,X3,X4,X5,X1)),X4) = X2
| X4 = hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)
| hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1242,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk33_5(X2,X3,X4,X5,X1)),X4) = X2
| X5 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1243,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk32_5(X3,X4,X1,X5,X2)),X3)
| X4 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Olist_OCons(X2),X5),X1) != hAPP(hAPP(c_List_Oappend(X2),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1244,plain,
( X5 = X6
| hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),c_Set_Oimage(X1,X2,X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1245,plain,
( c_Recdef_Oadm__wf(X4,X3,X2,X1)
| hAPP(hAPP(X1,esk98_4(X1,X2,X3,X4)),esk100_4(X1,X2,X3,X4)) != hAPP(hAPP(X1,esk99_4(X1,X2,X3,X4)),esk100_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1246,plain,
( X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X5),X2),X3)))
| X2 = X3
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1247,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X5),X4)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| X2 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1248,plain,
( X1 = X4
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X4),X5)))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1249,plain,
( X2 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X5),X4)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1250,plain,
c_List_Olistsp(X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),c_List_Olists(X1,X2)),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X1))),c_List_Olists(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_672]),
[final] ).
cnf(i_0_1251,plain,
( X3 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Oabove(X5,X4,X2)))
| X4 = X2
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1252,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5)))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| X1 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1253,plain,
( X1 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5)))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1254,plain,
( X2 = X4
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Oabove(X3,X5,X4)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1255,plain,
c_List_Orotate1(X1,X2) = c_List_Olist_Olist__case(tc_List_Olist(X1),X1,c_List_Olist_ONil(X1),hAPP(hAPP(c_COMBB(tc_List_Olist(X1),tc_fun(tc_List_Olist(X1),tc_List_Olist(X1)),X1),hAPP(c_COMBC(tc_List_Olist(X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Oappend(X1))),hAPP(hAPP(c_COMBC(X1,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_OCons(X1)),c_List_Olist_ONil(X1))),X2),
inference(split_conjunct,[status(thm)],[i_0_673]),
[final] ).
cnf(i_0_1256,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_674]),
[final] ).
cnf(i_0_1257,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X4)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X5,X2),hAPP(X5,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat)),X5),X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1258,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_676]),
[final] ).
cnf(i_0_1259,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_677]),
[final] ).
cnf(i_0_1260,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_678]),
[final] ).
cnf(i_0_1261,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_1262,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_680]),
[final] ).
cnf(i_0_1263,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) != c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_681]),
[final] ).
cnf(i_0_1264,plain,
( c_FuncSet_Orestrict(X2,X2,hAPP(hAPP(c_COMBB(X1,X2,X2),X3),c_FuncSet_Orestrict(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5)),X5) = c_FuncSet_Orestrict(X2,X2,c_COMBI(X2),X5)
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(rw,[status(thm)],[i_0_682,c_0_623]),
[final] ).
cnf(i_0_1265,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_683]),
[final] ).
cnf(i_0_1266,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_1267,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_681]),
[final] ).
cnf(i_0_1268,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X2),X1)),c_List_Olexord(X4,X3)))
| X2 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X1),X2)),c_List_Olexord(X4,X3)))
| esk28_4(X1,X2,X3,X4) != esk29_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1269,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_1270,plain,
( hBOOL(hAPP(hAPP(c_member(X6),hAPP(hAPP(X7,X3),X4)),c_Set_Oimage(tc_prod(X1,X2),X6,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X6),X7),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_686]),
[final] ).
cnf(i_0_1271,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1272,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X5),X8)),c_List_Olistrel1(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| X5 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X7))
| X8 != hAPP(hAPP(c_List_Oappend(X1),X6),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_687]),
[final] ).
cnf(i_0_1273,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk83_4(X2,X3,X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),c_Set_Oimage(X1,X5,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1274,plain,
( X3 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X5))
| X3 = X2
| X2 = X4
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X5),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1275,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| X3 = X2
| X2 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X4),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1276,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| X2 = X4
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X5),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1277,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1278,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_690]),
[final] ).
cnf(i_0_1279,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk77_3(X3,X2,X1)),esk79_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_1280,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk77_3(X3,X2,X1)),esk78_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_1281,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk49_3(X3,X2,X1)),esk51_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_692]),
[final] ).
cnf(i_0_1282,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk49_3(X3,X2,X1)),esk50_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_692]),
[final] ).
cnf(i_0_1283,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1284,plain,
( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_693]),
[final] ).
cnf(i_0_1285,plain,
( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1286,plain,
( X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X5),X2),X4)))
| X2 = X4
| X1 != X2
| X3 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1287,plain,
( X4 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X5),X2),X3)))
| X2 = X3
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1288,plain,
( X2 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X5),X4)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| X2 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1289,plain,
( X1 = X4
| X2 = X4
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X4),X5)))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1290,plain,
( X3 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X5),X2),X4)))
| X2 = X4
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1291,plain,
( X3 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| X3 = X2
| X4 = X2
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Oabove(X5,X4,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1292,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
| X3 = X2
| X5 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Oabove(X4,X5,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1293,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| X3 = X2
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),c_Arrow__Order__Mirabelle_Oabove(X5,X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1294,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1295,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk102_5(X5,X4,X2,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,c_Set_Oimage(X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1296,plain,
( hBOOL(hAPP(hAPP(hAPP(X4,X5),X6),X7))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_697]),
[final] ).
cnf(i_0_1297,plain,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(X1,esk15_1(X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(X1,esk16_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1298,plain,
( X3 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Oabove(X5,X4,X2)))
| X4 = X2
| X1 != X2
| X3 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1299,plain,
( X3 = X2
| X3 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Oabove(X5,X4,X2)))
| X4 = X2
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1300,plain,
( X1 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5)))
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| X1 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1301,plain,
( X2 = X4
| X1 = X4
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Oabove(X3,X5,X4)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1302,plain,
( X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),c_Arrow__Order__Mirabelle_Oabove(X5,X3,X2)))
| X3 = X2
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1303,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_698]),
[final] ).
cnf(i_0_1304,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk102_5(X2,X3,X1,X4,X5),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4,c_Set_Oimage(X1,X5,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1305,plain,
( X5 = X6
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_699]),
[final] ).
cnf(i_0_1306,plain,
( X5 = X6
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X6)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_692]),
[final] ).
cnf(i_0_1307,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk103_4(X3,X2,X4,X1)),hAPP(X3,esk103_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_700]),
[final] ).
cnf(i_0_1308,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_674]),
[final] ).
cnf(i_0_1309,plain,
( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk25_3(X3,X2,X1)),esk26_3(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olexord(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_1310,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,X1)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_1311,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_1312,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool),X4,X5)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4),c_Set_Oimage(X2,X1,X3,X5))),
inference(split_conjunct,[status(thm)],[i_0_704]),
[final] ).
cnf(i_0_1313,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1314,plain,
( c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X4)),c_List_Olexn(X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_706]),
[final] ).
cnf(i_0_1315,plain,
( c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X4),X2)),c_List_Olexn(X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_706]),
[final] ).
cnf(i_0_1316,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk61_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1317,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk57_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_708]),
[final] ).
cnf(i_0_1318,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk54_3(X2,X3,X1)),X3)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1319,plain,
( X4 = X5
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1320,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,X3),X1),hAPP(c_COMBB(tc_prod(X1,X2),X3,X2),X4)),c_Product__Type_OPair(X1,X2))) = X4,
inference(split_conjunct,[status(thm)],[i_0_710]),
[final] ).
cnf(i_0_1321,plain,
( c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) = c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_1322,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(esk16_1(X1),X2)))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(esk15_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1323,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(esk15_1(X1),X2)))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(esk16_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1324,plain,
( c_FunDef_Oin__rel(X1,X2,X5,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1325,plain,
( X2 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_712]),
[final] ).
cnf(i_0_1326,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_713]),
[final] ).
cnf(i_0_1327,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X2)),c_List_Olex(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_714]),
[final] ).
cnf(i_0_1328,plain,
( hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1329,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X3))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1330,plain,
( X2 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_716]),
[final] ).
cnf(i_0_1331,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olistrel1(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_717]),
[final] ).
cnf(i_0_1332,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olex(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_718]),
[final] ).
cnf(i_0_1333,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),c_List_Olist_ONil(X1))),c_List_Olexord(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_719]),
[final] ).
cnf(i_0_1334,plain,
( X4 = X5
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1335,plain,
( c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) = c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel1(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_720]),
[final] ).
cnf(i_0_1336,plain,
( c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) = c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olistrel(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_721]),
[final] ).
cnf(i_0_1337,plain,
( c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) = c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olex(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_681]),
[final] ).
cnf(i_0_1338,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk32_5(X3,X4,X5,X2,X1)) = X4
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = X3
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1339,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk33_5(X4,X3,X5,X1,X2))
| X5 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1340,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk81_3(X3,X2,X1)),esk82_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_722]),
[final] ).
cnf(i_0_1341,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2,X3,tc_HOL_Obool,X1),X4),X5))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_723]),
[final] ).
cnf(i_0_1342,plain,
( c_Relation_Otrans(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk94_2(X2,X1)),esk96_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_724]),
[final] ).
cnf(i_0_1343,plain,
( c_Relation_Otrans(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk45_2(X2,X1)),esk47_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_1344,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk22_2(X2,X1)),esk22_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_725]),
[final] ).
cnf(i_0_1345,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk32_5(X3,X4,X5,X2,X1)) = X4
| X4 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1346,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk33_5(X4,X3,X5,X1,X2))
| X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1347,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X7,tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Product__Type_OPair(X6,X7),X4),X5))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_1348,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),X5),hAPP(hAPP(c_List_Oappend(X2),X5),X1))),c_List_Olexord(X2,X6)))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_1349,plain,
( c_Set_Oimage(X1,X6,c_FuncSet_Orestrict(X1,X6,hAPP(hAPP(c_COMBB(X2,X6,X1),X7),X3),X4),X4) = X8
| c_Set_Oimage(X2,X6,X7,X5) != X8
| c_Set_Oimage(X1,X2,X3,X4) != X5 ),
inference(rw,[status(thm)],[i_0_728,c_0_623]),
[final] ).
cnf(i_0_1350,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),c_FuncSet_Orestrict(X1,X2,X3,X4)),c_FuncSet_Oextensional(X1,X2,X4))),
inference(split_conjunct,[status(thm)],[i_0_729]),
[final] ).
cnf(i_0_1351,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_730]),
[final] ).
cnf(i_0_1352,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1353,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional__funcset(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1354,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1355,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1356,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat)),X1),X5))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_734]),
[final] ).
cnf(i_0_1357,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1358,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1359,plain,
( X1 = X2
| X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1360,plain,
( X1 = X2
| X2 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1361,plain,
( X2 = X4
| X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1362,plain,
( X1 = X4
| X2 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1363,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_737]),
[final] ).
cnf(i_0_1364,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P_H____,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_737]),
[final] ).
cnf(i_0_1365,plain,
( hAPP(X3,X7) = hAPP(X6,X7)
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X3),X4),X5) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X6),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X5)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1366,plain,
( c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X6)) = X6
| c_Set_Oimage(X1,X2,X3,X4) != X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X6,X5) ),
inference(split_conjunct,[status(thm)],[i_0_738]),
[final] ).
cnf(i_0_1367,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(X1,esk15_1(X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk17_1(X1)),esk18_1(X1))),hAPP(X1,esk16_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1368,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X3),X1),X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_739]),
[final] ).
cnf(i_0_1369,plain,
( X1 = hAPP(X2,esk83_4(X3,X2,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X1),c_Set_Oimage(X4,X5,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1370,plain,
( X3 = X2
| X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X5),X2),X4)))
| X2 = X4
| X1 != X2
| X3 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1371,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hAPP(X3,X6) = c_HOL_Oundefined(X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional__funcset(X1,X2,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_1372,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1373,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_742]),
[final] ).
cnf(i_0_1374,plain,
( hAPP(X1,X3) = hAPP(X3,X2)
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_743]),
[final] ).
cnf(i_0_1375,plain,
( X3 = X2
| X3 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Oabove(X5,X4,X2)))
| X4 = X2
| X1 != X2
| X3 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1376,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_744]),
[final] ).
cnf(i_0_1377,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_1378,plain,
( hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = hAPP(X6,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_746]),
[final] ).
cnf(i_0_1379,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1380,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1381,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,c_List_Olist_ONil(tc_fun(X1,tc_Nat_Onat))))),
inference(split_conjunct,[status(thm)],[i_0_748]),
[final] ).
cnf(i_0_1382,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),c_Relation_ODomain(X1,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_749]),
[final] ).
cnf(i_0_1383,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_1384,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1385,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_751]),
[final] ).
cnf(i_0_1386,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),c_Relation_ORange(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_640]),
[final] ).
cnf(i_0_1387,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),c_Relation_ORange(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1388,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))),
inference(split_conjunct,[status(thm)],[i_0_753]),
[final] ).
cnf(i_0_1389,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olist_ONil(X2)),X1)),c_List_Olexord(X2,X5)))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_1390,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_754]),
[final] ).
cnf(i_0_1391,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X4)),c_Relation_OId__on(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_755]),
[final] ).
cnf(i_0_1392,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4,X2),hAPP(X4,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omeasure(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1393,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool)),X1,X6),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_757]),
[final] ).
cnf(i_0_1394,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_fun(X5,tc_HOL_Obool)),X6,X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_757]),
[final] ).
cnf(i_0_1395,plain,
( hBOOL(hAPP(hAPP(X3,X5),X6))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X3,X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_758]),
[final] ).
cnf(i_0_1396,plain,
( hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X3,X4),X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_759]),
[final] ).
cnf(i_0_1397,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X3)))),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_1398,plain,
( c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk11_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1399,plain,
( hAPP(c_FuncSet_Orestrict(X1,X5,hAPP(hAPP(c_COMBB(X4,X5,X1),X6),X7),X3),X2) = hAPP(X6,hAPP(X7,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(rw,[status(thm)],[i_0_761,c_0_623]),
[final] ).
cnf(i_0_1400,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_755]),
[final] ).
cnf(i_0_1401,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk48_2(X2,X1)),esk48_2(X2,X1))),X2))
| c_Relation_Oirrefl(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_1402,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk95_2(X2,X1)),esk96_2(X2,X1))),X2))
| c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_724]),
[final] ).
cnf(i_0_1403,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk94_2(X2,X1)),esk95_2(X2,X1))),X2))
| c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_724]),
[final] ).
cnf(i_0_1404,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk46_2(X2,X1)),esk47_2(X2,X1))),X2))
| c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_1405,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk45_2(X2,X1)),esk46_2(X2,X1))),X2))
| c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_684]),
[final] ).
cnf(i_0_1406,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_762]),
[final] ).
cnf(i_0_1407,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_763]),
[final] ).
cnf(i_0_1408,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_764]),
[final] ).
cnf(i_0_1409,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_OtakeWhile(X2,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),hAPP(hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal),c_List_Olast(X2,X1))),X1) = c_List_Obutlast(X2,X1)
| ~ c_List_Odistinct(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_765]),
[final] ).
cnf(i_0_1410,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1411,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_766]),
[final] ).
cnf(i_0_1412,plain,
( X1 != X2
| X1 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1413,plain,
( X1 != X2
| X3 != X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1414,plain,
c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X4,X1,X5,X6)) = c_Set_Oimage(X4,X2,hAPP(hAPP(c_COMBB(X1,X2,X4),X3),X5),X6),
inference(split_conjunct,[status(thm)],[i_0_767]),
[final] ).
cnf(i_0_1415,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1416,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1417,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_768]),
[final] ).
cnf(i_0_1418,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X5),X6),X4),X3),X2) = c_HOL_Oundefined(X5) ),
inference(split_conjunct,[status(thm)],[i_0_746]),
[final] ).
cnf(i_0_1419,plain,
( hBOOL(hAPP(hAPP(X3,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5))) ),
inference(split_conjunct,[status(thm)],[i_0_769]),
[final] ).
cnf(i_0_1420,plain,
c_Product__Type_Oprod_Oprod__rec(X1,X2,X3,X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_770]),
[final] ).
cnf(i_0_1421,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_771]),
[final] ).
cnf(i_0_1422,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Transitive__Closure_Ortrancl(X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_Relation_ODomain(X3,X3,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_749]),
[final] ).
cnf(i_0_1423,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk2_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_743]),
[final] ).
cnf(i_0_1424,plain,
( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_772]),
[final] ).
cnf(i_0_1425,plain,
c_List_Olist_Olist__case(X1,X2,X3,X4,hAPP(hAPP(c_List_Olist_OCons(X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_773]),
[final] ).
cnf(i_0_1426,plain,
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X6,tc_HOL_Obool)),X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_774]),
[final] ).
cnf(i_0_1427,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk11_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1428,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk16_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1429,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk15_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1430,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X1),c_Set_Oimage(X4,X6,X2,X5)))
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_775]),
[final] ).
cnf(i_0_1431,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X4),c_Set_Oimage(X1,X6,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X4 != hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_776]),
[final] ).
cnf(i_0_1432,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X4),c_Set_Oimage(X1,X6,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X4 != hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_688]),
[final] ).
cnf(i_0_1433,plain,
c_FuncSet_Oextensional__funcset(X1,X2,X3,X4) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),c_FuncSet_OPi(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)),c_FuncSet_Oextensional(X1,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_777]),
[final] ).
cnf(i_0_1434,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096P_H_A_058_AProf_096]),
[final] ).
cnf(i_0_1435,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096P_A_058_AProf_096]),
[final] ).
cnf(i_0_1436,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ORange(X2,X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),X3,X4)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Relation_ORange(X2,X1,X3),c_Relation_ORange(X2,X1,X4))),
inference(split_conjunct,[status(thm)],[i_0_778]),
[final] ).
cnf(i_0_1437,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X1,X2,X4))),
inference(split_conjunct,[status(thm)],[i_0_779]),
[final] ).
cnf(i_0_1438,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1439,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_755]),
[final] ).
cnf(i_0_1440,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X1),X2)),c_Relation_OId__on(X3,X4)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_781]),
[final] ).
cnf(i_0_1441,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1442,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X3,X5),c_FuncSet_OPi(X1,X4,X2,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_782]),
[final] ).
cnf(i_0_1443,plain,
hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_783]),
[final] ).
cnf(i_0_1444,plain,
hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
inference(split_conjunct,[status(thm)],[i_0_784]),
[final] ).
cnf(i_0_1445,plain,
c_List_Olist_Olist__case(X1,X2,X3,X4,c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_785]),
[final] ).
cnf(i_0_1446,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2),c_Set_Oimage(X1,X4,X5,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_786]),
[final] ).
cnf(i_0_1447,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X2),X4)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1448,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Oappend(X1),X4),X2)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1449,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X2)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1450,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1)),esk13_1(X1))),hAPP(esk11_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1451,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1452,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk64_3(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X3),c_Relation_OId__on(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_1453,plain,
( X2 = X3
| hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) != hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_789]),
[final] ).
cnf(i_0_1454,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Ortrancl(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_790]),
[final] ).
cnf(i_0_1455,plain,
( X1 = X2
| c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X1),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X2),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),esk4_2(X2,X1)),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
inference(split_conjunct,[status(thm)],[i_0_791]),
[final] ).
cnf(i_0_1456,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X4,c_Set_Oimage(X1,X5,X6,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X4 != c_Set_Oimage(X1,X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1457,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk61_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1458,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk57_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_708]),
[final] ).
cnf(i_0_1459,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk54_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1460,plain,
( c_FuncSet_Orestrict(X1,X2,X3,X4) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1461,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X4)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1462,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_725]),
[final] ).
cnf(i_0_1463,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1464,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_794]),
[final] ).
cnf(i_0_1465,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk64_3(X3,X1,X2)),esk64_3(X3,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X1),c_Relation_OId__on(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_1466,plain,
c_Set_Oimage(X1,X2,c_FuncSet_Orestrict(X1,X2,X3,X4),X4) = c_Set_Oimage(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1467,plain,
( c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X4,X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_796]),
[final] ).
cnf(i_0_1468,plain,
( c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X4,X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_797]),
[final] ).
cnf(i_0_1469,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk63_3(X2,X3,X1)),c_List_Olists(X1,X2)))
| X3 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1470,plain,
( c_List_Olistrelp(X1,X2,X3,X4)
| ~ c_List_Olistrelp(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X5),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_797]),
[final] ).
cnf(i_0_1471,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| hAPP(X3,X5) = c_HOL_Oundefined(X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_Oextensional(X1,X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_799]),
[final] ).
cnf(i_0_1472,plain,
( X1 = X3
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1473,plain,
( X3 = X1
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1474,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4)),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1475,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),esk20_2(X2,X1)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_801]),
[final] ).
cnf(i_0_1476,plain,
c_List_Omaps(X1,X2,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(hAPP(c_List_Oappend(X2),hAPP(X3,X4)),c_List_Omaps(X1,X2,X3,X5)),
inference(split_conjunct,[status(thm)],[i_0_802]),
[final] ).
cnf(i_0_1477,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk62_3(X2,X3,X1)),X2))
| X3 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1478,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1479,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1480,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_Wellfounded_Oacc(tc_List_Olist(X1),c_List_Olistrel1(X1,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),c_List_Olists(X1,c_Wellfounded_Oacc(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_805]),
[final] ).
cnf(i_0_1481,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X4,X1,hAPP(hAPP(c_List_Olist_OCons(X4),X2),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_797]),
[final] ).
cnf(i_0_1482,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X5)))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1483,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
| ~ hBOOL(hAPP(X1,esk80_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_722]),
[final] ).
cnf(i_0_1484,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_806]),
[final] ).
cnf(i_0_1485,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_807]),
[final] ).
cnf(i_0_1486,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1487,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_806]),
[final] ).
cnf(i_0_1488,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X4,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1489,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1490,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_806]),
[final] ).
cnf(i_0_1491,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1492,plain,
( hBOOL(hAPP(X3,X4))
| c_List_OdropWhile(X2,X3,X1) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)
| X1 != hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1493,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk20_2(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[i_0_801]),
[final] ).
cnf(i_0_1494,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk62_3(X3,X1,X2)),esk63_3(X3,X1,X2))
| X1 = c_List_Olist_ONil(X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1495,plain,
( hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_812]),
[final] ).
cnf(i_0_1496,plain,
( hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1497,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1498,plain,
c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Osplice(X1,X3,X5))),
inference(split_conjunct,[status(thm)],[i_0_815]),
[final] ).
cnf(i_0_1499,plain,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),esk3_0),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(split_conjunct,[status(thm)],[i_0_816]),
[final] ).
cnf(i_0_1500,plain,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b____),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_c____),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(split_conjunct,[status(thm)],[fact_dist]),
[final] ).
cnf(i_0_1501,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = c_HOL_Oundefined(X4) ),
inference(split_conjunct,[status(thm)],[i_0_812]),
[final] ).
cnf(i_0_1502,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_FuncSet_Orestrict(X1,X4,X5,X3),X2) = c_HOL_Oundefined(X4) ),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1503,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),c_Product__Type_Ocurry(X1,X2,X3,X4)) = X4,
inference(split_conjunct,[status(thm)],[i_0_817]),
[final] ).
cnf(i_0_1504,plain,
( hBOOL(hAPP(hAPP(X1,esk60_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1505,plain,
( hBOOL(hAPP(hAPP(X1,esk59_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_819]),
[final] ).
cnf(i_0_1506,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_820]),
[final] ).
cnf(i_0_1507,plain,
( c_Relation_Otrans(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_821]),
[final] ).
cnf(i_0_1508,plain,
( hBOOL(hAPP(hAPP(X3,esk58_2(X4,X3)),X4))
| ~ c_Predicate_ORangeP(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_822]),
[final] ).
cnf(i_0_1509,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_823]),
[final] ).
cnf(i_0_1510,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1511,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool),X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_825]),
[final] ).
cnf(i_0_1512,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool),X4,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_825]),
[final] ).
cnf(i_0_1513,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_826]),
[final] ).
cnf(i_0_1514,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_827]),
[final] ).
cnf(i_0_1515,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk60_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1516,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk59_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_819]),
[final] ).
cnf(i_0_1517,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_1518,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_OtakeWhile(X2,X3,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5))
| c_List_OdropWhile(X2,X3,X1) != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1519,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_1520,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_828]),
[final] ).
cnf(i_0_1521,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1522,plain,
( X1 = X2
| hAPP(hAPP(c_List_Oappend(X3),X1),hAPP(hAPP(c_List_Olist_OCons(X3),X4),c_List_Olist_ONil(X3))) != hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X5),c_List_Olist_ONil(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1523,plain,
( X1 = X2
| hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) != hAPP(hAPP(c_List_Oappend(X3),X5),hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_Olist_ONil(X3))) ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1524,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk88_3(X1,X3,X2)),esk89_3(X1,X3,X2))
| X1 = c_List_Olist_ONil(X2)
| ~ hBOOL(hAPP(c_List_Olistsp(X2,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1525,plain,
c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_832]),
[final] ).
cnf(i_0_1526,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1527,plain,
c_Product__Type_Ocurry(X1,X2,X3,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)) = X4,
inference(split_conjunct,[status(thm)],[i_0_834]),
[final] ).
cnf(i_0_1528,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1529,plain,
( c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X3,c_Transitive__Closure_Ortrancl(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_835]),
[final] ).
cnf(i_0_1530,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(rw,[status(thm)],[i_0_836,c_0_837]),
[final] ).
cnf(i_0_1531,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_838]),
[final] ).
cnf(i_0_1532,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_839]),
[final] ).
cnf(i_0_1533,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_840]),
[final] ).
cnf(i_0_1534,plain,
( hBOOL(hAPP(c_List_Olistsp(X3,X1),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_List_Olistsp(X3,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1535,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1536,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X4)),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1537,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4),c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X5))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_843]),
[final] ).
cnf(i_0_1538,plain,
( hBOOL(hAPP(X1,X2))
| c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Oappend(X3),X4),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5))) = c_List_OtakeWhile(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_844]),
[final] ).
cnf(i_0_1539,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),c_List_Olistrel1(X1,X2),c_List_Olistrel1(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_845]),
[final] ).
cnf(i_0_1540,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),c_List_Olistrel(X1,X2),c_List_Olistrel(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_846]),
[final] ).
cnf(i_0_1541,plain,
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool),X1,X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_847]),
[final] ).
cnf(i_0_1542,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),esk89_3(X3,X2,X1)))
| X3 = c_List_Olist_ONil(X1)
| ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1543,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Transitive__Closure_Ortrancl(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_848]),
[final] ).
cnf(i_0_1544,plain,
hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)),X4) = hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_849]),
[final] ).
cnf(i_0_1545,plain,
hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_850]),
[final] ).
cnf(i_0_1546,plain,
( hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),X3,X4)
| ~ hBOOL(hAPP(hAPP(X3,X5),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_851]),
[final] ).
cnf(i_0_1547,plain,
( hBOOL(hAPP(hAPP(X6,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_fun(X5,tc_HOL_Obool)),X1,X6) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1548,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1549,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_854]),
[final] ).
cnf(i_0_1550,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_855]),
[final] ).
cnf(i_0_1551,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_856]),
[final] ).
cnf(i_0_1552,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_857]),
[final] ).
cnf(i_0_1553,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_858]),
[final] ).
cnf(i_0_1554,plain,
( hBOOL(hAPP(X1,esk88_3(X2,X1,X3)))
| X2 = c_List_Olist_ONil(X3)
| ~ hBOOL(hAPP(c_List_Olistsp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1555,plain,
( c_Predicate_ODomainP(X4,X5,X1,X2)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_859]),
[final] ).
cnf(i_0_1556,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_822]),
[final] ).
cnf(i_0_1557,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_860]),
[final] ).
cnf(i_0_1558,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1559,plain,
( c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),c_List_OtakeWhile(X3,X1,X4))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1560,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),c_List_Olistrel1(X1,c_Transitive__Closure_Ortrancl(X1,X2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1561,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X2,
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1562,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1)))) = X3,
inference(split_conjunct,[status(thm)],[i_0_865]),
[final] ).
cnf(i_0_1563,plain,
( c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3,X4)
| ~ c_Relation_Osingle__valued(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_866]),
[final] ).
cnf(i_0_1564,plain,
( hBOOL(hAPP(c_List_Olistsp(X2,X5),X1))
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| ~ hBOOL(hAPP(X5,X3))
| ~ hBOOL(hAPP(c_List_Olistsp(X2,X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1565,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X1),c_List_OdropWhile(X1,X2,X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_867]),
[final] ).
cnf(i_0_1566,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X1),c_List_OtakeWhile(X1,X2,X3)),c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1567,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_869]),
[final] ).
cnf(i_0_1568,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1569,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1570,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1571,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_819]),
[final] ).
cnf(i_0_1572,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1573,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Oacc(X1,X3),c_Wellfounded_Oacc(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1574,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1575,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1576,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X4) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_876]),
[final] ).
cnf(i_0_1577,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_877]),
[final] ).
cnf(i_0_1578,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_878]),
[final] ).
cnf(i_0_1579,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_879]),
[final] ).
cnf(i_0_1580,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),c_List_Obutlast(X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X2),c_List_Olast(X2,X1)),c_List_Olist_ONil(X2))) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_880]),
[final] ).
cnf(i_0_1581,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Oaccp(X1,X3),c_Wellfounded_Oaccp(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1582,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_882]),
[final] ).
cnf(i_0_1583,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_883]),
[final] ).
cnf(i_0_1584,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1585,plain,
( c_Relation_Otrans(X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,X3))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_885]),
[final] ).
cnf(i_0_1586,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1587,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1588,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X4,X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1589,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X4,X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1590,plain,
c_List_Olistsp(X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),c_List_Olistsp(X1,X2),c_List_Olistsp(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_1591,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1592,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4,X3)
| c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1593,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)),tc_HOL_Obool),c_List_Olistrel(X1,X2),c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1594,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1595,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X1),X5) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X2),X6) ),
inference(split_conjunct,[status(thm)],[i_0_892]),
[final] ).
cnf(i_0_1596,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1597,plain,
( X1 = X2
| hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X1) != hAPP(hAPP(c_Product__Type_OPair(X3,X4),X6),X2) ),
inference(split_conjunct,[status(thm)],[i_0_892]),
[final] ).
cnf(i_0_1598,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2),c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3))
| X2 != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_893]),
[final] ).
cnf(i_0_1599,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1),X3,X4),X5) = c_Lattices_Osemilattice__inf__class_Oinf(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1600,plain,
( hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1),X3,X4),X5) = c_Lattices_Osemilattice__inf__class_Oinf(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_895]),
[final] ).
cnf(i_0_1601,plain,
c_List_Orotate1(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_896]),
[final] ).
cnf(i_0_1602,plain,
( c_List_Obutlast(X1,X2) = X3
| hAPP(hAPP(c_List_Oappend(X1),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Olist_ONil(X1))) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1603,plain,
( c_List_Olast(X1,X2) = X3
| hAPP(hAPP(c_List_Oappend(X1),X4),hAPP(hAPP(c_List_Olist_OCons(X1),X3),c_List_Olist_ONil(X1))) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1604,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1605,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1606,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1607,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5) = hAPP(hAPP(c_List_Oappend(X1),X4),X6)
| hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X4
| X5 != hAPP(hAPP(c_List_Oappend(X1),X3),X6) ),
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1608,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X5) = hAPP(hAPP(c_List_Oappend(X2),X3),X6)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X4)
| hAPP(hAPP(c_List_Oappend(X2),X4),X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1609,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X5) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)
| X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| hAPP(hAPP(c_List_Oappend(X2),X4),X5) != X6 ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1610,plain,
( X1 != c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1611,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),c_List_Olistsp(X1,X2),c_List_Olistsp(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1612,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),c_List_Olists(X1,X2),c_List_Olists(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_901]),
[final] ).
cnf(i_0_1613,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X4,X3)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1614,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_902]),
[final] ).
cnf(i_0_1615,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_903]),
[final] ).
cnf(i_0_1616,plain,
( c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = c_List_OdropWhile(X3,X1,X4)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_904]),
[final] ).
cnf(i_0_1617,plain,
c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
inference(split_conjunct,[status(thm)],[i_0_905]),
[final] ).
cnf(i_0_1618,plain,
( c_Orderings_Oord__class_Oless(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_906]),
[final] ).
cnf(i_0_1619,plain,
( c_Orderings_Oord__class_Oless(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X4,X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_907]),
[final] ).
cnf(i_0_1620,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X4),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1621,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X4,X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1622,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1623,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_911]),
[final] ).
cnf(i_0_1624,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_912]),
[final] ).
cnf(i_0_1625,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1626,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1627,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1628,plain,
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5),hAPP(X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_700]),
[final] ).
cnf(i_0_1629,plain,
( hBOOL(hAPP(X1,X2))
| c_List_OdropWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_904]),
[final] ).
cnf(i_0_1630,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_916]),
[final] ).
cnf(i_0_1631,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_917]),
[final] ).
cnf(i_0_1632,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_918]),
[final] ).
cnf(i_0_1633,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_919]),
[final] ).
cnf(i_0_1634,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_920]),
[final] ).
cnf(i_0_1635,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_921]),
[final] ).
cnf(i_0_1636,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1637,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_923]),
[final] ).
cnf(i_0_1638,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_924]),
[final] ).
cnf(i_0_1639,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1640,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3),X3),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1641,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk78_3(X1,X2,X3) != esk79_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_1642,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk50_3(X1,X2,X3) != esk51_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_692]),
[final] ).
cnf(i_0_1643,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_927]),
[final] ).
cnf(i_0_1644,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_928]),
[final] ).
cnf(i_0_1645,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_929]),
[final] ).
cnf(i_0_1646,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X3),hAPP(hAPP(c_List_Olist_OCons(X2),X4),c_List_Olist_ONil(X2))) = X1
| c_List_Obutlast(X2,X1) != X3
| c_List_Olast(X2,X1) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1647,plain,
c_List_Opartition(X1,X2,c_List_Olist_ONil(X1)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1648,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X1),c_List_Olists(X2,X3)))
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_798]),
[final] ).
cnf(i_0_1649,plain,
( ~ hBOOL(hAPP(X1,X2))
| c_List_OdropWhile(X3,X1,X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1650,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1651,plain,
c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),c_List_Olist_ONil(X1)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_931]),
[final] ).
cnf(i_0_1652,plain,
( hBOOL(hAPP(X1,esk101_2(X2,X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1653,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1654,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1655,plain,
( c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_935]),
[final] ).
cnf(i_0_1656,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_936]),
[final] ).
cnf(i_0_1657,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X2) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1658,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1659,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1660,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1661,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_935]),
[final] ).
cnf(i_0_1662,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1663,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Obutlast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = hAPP(hAPP(c_List_Oappend(X2),X3),c_List_Obutlast(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_941]),
[final] ).
cnf(i_0_1664,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = hAPP(hAPP(c_List_Olist_OCons(X2),X3),c_List_Obutlast(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_942]),
[final] ).
cnf(i_0_1665,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_943]),
[final] ).
cnf(i_0_1666,plain,
( hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = hAPP(hAPP(c_List_Oappend(X2),X1),X5)
| X1 != c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X5 ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1667,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5)
| X1 != c_List_Olist_ONil(X2)
| X3 != hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1668,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X1),X2))
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_944]),
[final] ).
cnf(i_0_1669,plain,
( hBOOL(hAPP(X1,X2))
| c_List_OtakeWhile(X3,X1,hAPP(hAPP(c_List_Olist_OCons(X3),X2),X4)) = c_List_Olist_ONil(X3) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1670,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1671,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1672,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1673,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_948]),
[final] ).
cnf(i_0_1674,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_949]),
[final] ).
cnf(i_0_1675,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_950]),
[final] ).
cnf(i_0_1676,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1677,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_952]),
[final] ).
cnf(i_0_1678,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1679,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1680,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_1681,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1682,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_1683,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_958]),
[final] ).
cnf(i_0_1684,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1685,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_959]),
[final] ).
cnf(i_0_1686,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_960]),
[final] ).
cnf(i_0_1687,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_961]),
[final] ).
cnf(i_0_1688,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1689,plain,
( X1 = X2
| hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1690,plain,
( X1 = X2
| hAPP(hAPP(c_List_Olist_OCons(X3),X4),X1) != hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1691,plain,
( X2 = X4
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_964]),
[final] ).
cnf(i_0_1692,plain,
( X3 = X4
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_965]),
[final] ).
cnf(i_0_1693,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1694,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X3,X2),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1695,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_943]),
[final] ).
cnf(i_0_1696,plain,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1697,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_968]),
[final] ).
cnf(i_0_1698,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1699,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_970]),
[final] ).
cnf(i_0_1700,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_971]),
[final] ).
cnf(i_0_1701,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_972]),
[final] ).
cnf(i_0_1702,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1703,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_973]),
[final] ).
cnf(i_0_1704,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_974]),
[final] ).
cnf(i_0_1705,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) != X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1706,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_976]),
[final] ).
cnf(i_0_1707,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1708,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_977]),
[final] ).
cnf(i_0_1709,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_971]),
[final] ).
cnf(i_0_1710,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_972]),
[final] ).
cnf(i_0_1711,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_978]),
[final] ).
cnf(i_0_1712,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1713,plain,
( c_List_Odistinct(X1,c_List_OdropWhile(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1714,plain,
( c_List_Odistinct(X1,c_List_OtakeWhile(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_980]),
[final] ).
cnf(i_0_1715,plain,
( c_List_Odistinct(X1,c_List_Oinsert(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1716,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk2_2(X2,X1)) != hAPP(esk2_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_743]),
[final] ).
cnf(i_0_1717,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1718,plain,
( c_List_Obutlast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Obutlast(X2,X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_941]),
[final] ).
cnf(i_0_1719,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1720,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1721,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1722,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_985]),
[final] ).
cnf(i_0_1723,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1724,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1725,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1726,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olast(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1727,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1728,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1729,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_1730,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_1731,plain,
( c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_942]),
[final] ).
cnf(i_0_1732,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1733,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1734,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1735,plain,
( c_List_Olast(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1)) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1736,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1737,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_995]),
[final] ).
cnf(i_0_1738,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_996]),
[final] ).
cnf(i_0_1739,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1740,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_973]),
[final] ).
cnf(i_0_1741,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1742,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1743,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1744,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1001]),
[final] ).
cnf(i_0_1745,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1746,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1747,plain,
c_List_Oinsert(X1,X2,c_List_Olist_ONil(X1)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1748,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1749,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_1750,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1751,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1752,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1753,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1007]),
[final] ).
cnf(i_0_1754,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1008]),
[final] ).
cnf(i_0_1755,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1009]),
[final] ).
cnf(i_0_1756,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1010]),
[final] ).
cnf(i_0_1757,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X3) = c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1758,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1759,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_1760,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1761,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_972]),
[final] ).
cnf(i_0_1762,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1763,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1764,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1765,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1766,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1767,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1768,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1769,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_1019]),
[final] ).
cnf(i_0_1770,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X1),X3) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1771,plain,
( X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X3),X1) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1772,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1773,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1774,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1022]),
[final] ).
cnf(i_0_1775,plain,
( hBOOL(hAPP(c_List_Olistsp(X2,X3),X1))
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1776,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1777,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1778,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1779,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1780,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1781,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1782,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1783,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1784,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1785,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_1786,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_1787,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1788,plain,
c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1789,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1790,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1791,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1792,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1793,plain,
c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1794,plain,
c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1795,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_911]),
[final] ).
cnf(i_0_1796,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_911]),
[final] ).
cnf(i_0_1797,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1798,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1799,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_935]),
[final] ).
cnf(i_0_1800,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1801,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1802,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1803,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1804,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1044]),
[final] ).
cnf(i_0_1805,plain,
( c_List_Odistinct(X1,X2)
| ~ c_List_Odistinct(X1,c_List_Orotate1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1806,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1807,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2)
| X3 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1808,plain,
( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
| X1 != c_List_Olist_ONil(X2)
| X3 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1809,plain,
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X2))
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1810,plain,
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X2))
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1811,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1812,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Odistinct(X2,c_List_Obutlast(X2,X1))
| ~ c_List_Odistinct(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1813,plain,
c_Nat_Osize__class_Osize(tc_List_Olist(X1),c_List_Orotate1(X1,X2)) = c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1814,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1815,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1816,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1817,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_971]),
[final] ).
cnf(i_0_1818,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1053]),
[final] ).
cnf(i_0_1819,plain,
c_List_OdropWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1820,plain,
c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1821,plain,
( c_List_Odistinct(X1,c_List_Orotate1(X1,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1822,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1823,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1824,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1825,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1826,plain,
( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1827,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1828,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1829,plain,
c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1059]),
[final] ).
cnf(i_0_1830,plain,
c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1060]),
[final] ).
cnf(i_0_1831,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1061]),
[final] ).
cnf(i_0_1832,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1062]),
[final] ).
cnf(i_0_1833,plain,
c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X2)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1063]),
[final] ).
cnf(i_0_1834,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1064]),
[final] ).
cnf(i_0_1835,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1065]),
[final] ).
cnf(i_0_1836,plain,
c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1066]),
[final] ).
cnf(i_0_1837,plain,
c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1067]),
[final] ).
cnf(i_0_1838,plain,
c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1068]),
[final] ).
cnf(i_0_1839,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1069]),
[final] ).
cnf(i_0_1840,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1070]),
[final] ).
cnf(i_0_1841,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1071]),
[final] ).
cnf(i_0_1842,plain,
( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1072]),
[final] ).
cnf(i_0_1843,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1073]),
[final] ).
cnf(i_0_1844,plain,
( X2 = c_List_Olist_ONil(X1)
| c_List_Orotate1(X1,X2) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1074]),
[final] ).
cnf(i_0_1845,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1075]),
[final] ).
cnf(i_0_1846,plain,
( c_List_Orotate1(X2,X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1074]),
[final] ).
cnf(i_0_1847,plain,
c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1076]),
[final] ).
cnf(i_0_1848,plain,
c_List_Orotate1(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_896]),
[final] ).
cnf(i_0_1849,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1077]),
[final] ).
cnf(i_0_1850,plain,
c_List_Odistinct(X1,c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_1078]),
[final] ).
cnf(i_0_1851,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1852,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1853,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1854,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1855,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1856,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1857,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1858,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1859,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1860,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
[final] ).
cnf(i_0_1861,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
[final] ).
cnf(i_0_1862,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1863,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1864,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1865,axiom,
X1 = X1 ).
cnf(i_0_1866,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1867,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| c_List_Orotate1(X1,X3) = c_List_Orotate1(X2,X3) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| c_List_Orotate1(X3,X1) = c_List_Orotate1(X3,X2) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X1,X3,X4,X5,X6) = c_List_Olist_Olist__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X1,X4,X5,X6) = c_List_Olist_Olist__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X4,X1,X5,X6) = c_List_Olist_Olist__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X4,X5,X1,X6) = c_List_Olist_Olist__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X4,X5,X6,X1) = c_List_Olist_Olist__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| esk79_3(X1,X3,X4) = esk79_3(X2,X3,X4) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| esk79_3(X3,X1,X4) = esk79_3(X3,X2,X4) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| esk79_3(X3,X4,X1) = esk79_3(X3,X4,X2) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| esk78_3(X1,X3,X4) = esk78_3(X2,X3,X4) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| esk78_3(X3,X1,X4) = esk78_3(X3,X2,X4) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| esk78_3(X3,X4,X1) = esk78_3(X3,X4,X2) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| esk51_3(X1,X3,X4) = esk51_3(X2,X3,X4) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| esk51_3(X3,X1,X4) = esk51_3(X3,X2,X4) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| esk51_3(X3,X4,X1) = esk51_3(X3,X4,X2) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| esk50_3(X1,X3,X4) = esk50_3(X2,X3,X4) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| esk50_3(X3,X1,X4) = esk50_3(X3,X2,X4) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| esk50_3(X3,X4,X1) = esk50_3(X3,X4,X2) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X1,X3,X4,X5) = c_FuncSet_Oextensional__funcset(X2,X3,X4,X5) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X1,X4,X5) = c_FuncSet_Oextensional__funcset(X3,X2,X4,X5) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X1,X5) = c_FuncSet_Oextensional__funcset(X3,X4,X2,X5) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X5,X1) = c_FuncSet_Oextensional__funcset(X3,X4,X5,X2) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| c_HOL_Oundefined(X1) = c_HOL_Oundefined(X2) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X1,X3,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X1,X4,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X1,X5,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X1,X6) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X1) = c_Product__Type_Oprod_Oprod__rec(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| c_List_OdropWhile(X1,X3,X4) = c_List_OdropWhile(X2,X3,X4) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| c_List_OdropWhile(X3,X1,X4) = c_List_OdropWhile(X3,X2,X4) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| c_List_OdropWhile(X3,X4,X1) = c_List_OdropWhile(X3,X4,X2) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X1,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X1) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| c_Relation_ORange(X1,X3,X4) = c_Relation_ORange(X2,X3,X4) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| c_Relation_ORange(X3,X1,X4) = c_Relation_ORange(X3,X2,X4) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| c_Relation_ORange(X3,X4,X1) = c_Relation_ORange(X3,X4,X2) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X1,X3,X4,X5) = c_FuncSet_Orestrict(X2,X3,X4,X5) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X1,X4,X5) = c_FuncSet_Orestrict(X3,X2,X4,X5) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X1,X5) = c_FuncSet_Orestrict(X3,X4,X2,X5) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X5,X1) = c_FuncSet_Orestrict(X3,X4,X5,X2) ) ).
cnf(i_0_1941,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).
cnf(i_0_1942,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| esk29_4(X1,X3,X4,X5) = esk29_4(X2,X3,X4,X5) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| esk29_4(X3,X1,X4,X5) = esk29_4(X3,X2,X4,X5) ) ).
cnf(i_0_1947,axiom,
( X1 != X2
| esk29_4(X3,X4,X1,X5) = esk29_4(X3,X4,X2,X5) ) ).
cnf(i_0_1948,axiom,
( X1 != X2
| esk29_4(X3,X4,X5,X1) = esk29_4(X3,X4,X5,X2) ) ).
cnf(i_0_1949,axiom,
( X1 != X2
| esk28_4(X1,X3,X4,X5) = esk28_4(X2,X3,X4,X5) ) ).
cnf(i_0_1950,axiom,
( X1 != X2
| esk28_4(X3,X1,X4,X5) = esk28_4(X3,X2,X4,X5) ) ).
cnf(i_0_1951,axiom,
( X1 != X2
| esk28_4(X3,X4,X1,X5) = esk28_4(X3,X4,X2,X5) ) ).
cnf(i_0_1952,axiom,
( X1 != X2
| esk28_4(X3,X4,X5,X1) = esk28_4(X3,X4,X5,X2) ) ).
cnf(i_0_1953,axiom,
( X1 != X2
| c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).
cnf(i_0_1954,axiom,
( X1 != X2
| c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).
cnf(i_0_1955,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_1956,axiom,
( X1 != X2
| esk8_2(X1,X3) = esk8_2(X2,X3) ) ).
cnf(i_0_1957,axiom,
( X1 != X2
| esk8_2(X3,X1) = esk8_2(X3,X2) ) ).
cnf(i_0_1958,axiom,
( X1 != X2
| esk9_2(X1,X3) = esk9_2(X2,X3) ) ).
cnf(i_0_1959,axiom,
( X1 != X2
| esk9_2(X3,X1) = esk9_2(X3,X2) ) ).
cnf(i_0_1960,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1961,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1962,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1963,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1964,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1965,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1966,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1967,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1968,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X1,X3,X4,X5,X6,X7) = c_Fun_Ooverride__on(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_1969,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X1,X4,X5,X6,X7) = c_Fun_Ooverride__on(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_1970,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X1,X5,X6,X7) = c_Fun_Ooverride__on(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_1971,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X1,X6,X7) = c_Fun_Ooverride__on(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_1972,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X6,X1,X7) = c_Fun_Ooverride__on(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_1973,axiom,
( X1 != X2
| c_Fun_Ooverride__on(X3,X4,X5,X6,X7,X1) = c_Fun_Ooverride__on(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_1974,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1975,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X1,X3)
| c_Relation_Otrans(X2,X3) ) ).
cnf(i_0_1976,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X3,X1)
| c_Relation_Otrans(X3,X2) ) ).
cnf(i_0_1977,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_1978,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_1979,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_1980,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1981,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1982,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1983,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1984,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1985,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1986,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1987,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1988,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1989,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1990,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1991,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_1992,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_1993,axiom,
( X1 != X2
| ~ c_List_Odistinct(X1,X3)
| c_List_Odistinct(X2,X3) ) ).
cnf(i_0_1994,axiom,
( X1 != X2
| ~ c_List_Odistinct(X3,X1)
| c_List_Odistinct(X3,X2) ) ).
cnf(i_0_1995,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_1996,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_1997,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X1,X3,X4,X5)
| c_Recdef_Oadm__wf(X2,X3,X4,X5) ) ).
cnf(i_0_1998,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X1,X4,X5)
| c_Recdef_Oadm__wf(X3,X2,X4,X5) ) ).
cnf(i_0_1999,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X1,X5)
| c_Recdef_Oadm__wf(X3,X4,X2,X5) ) ).
cnf(i_0_2000,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X5,X1)
| c_Recdef_Oadm__wf(X3,X4,X5,X2) ) ).
cnf(i_0_2001,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2002,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2003,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2004,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_2005,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_2006,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_2007,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X1,X3,X4,X5)
| c_List_Olistrelp(X2,X3,X4,X5) ) ).
cnf(i_0_2008,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X1,X4,X5)
| c_List_Olistrelp(X3,X2,X4,X5) ) ).
cnf(i_0_2009,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X1,X5)
| c_List_Olistrelp(X3,X4,X2,X5) ) ).
cnf(i_0_2010,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X5,X1)
| c_List_Olistrelp(X3,X4,X5,X2) ) ).
cnf(i_0_2011,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X1,X3,X4,X5)
| c_Predicate_ODomainP(X2,X3,X4,X5) ) ).
cnf(i_0_2012,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X1,X4,X5)
| c_Predicate_ODomainP(X3,X2,X4,X5) ) ).
cnf(i_0_2013,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X1,X5)
| c_Predicate_ODomainP(X3,X4,X2,X5) ) ).
cnf(i_0_2014,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X5,X1)
| c_Predicate_ODomainP(X3,X4,X5,X2) ) ).
cnf(i_0_2015,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X1,X3,X4,X5)
| c_Predicate_ORangeP(X2,X3,X4,X5) ) ).
cnf(i_0_2016,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X1,X4,X5)
| c_Predicate_ORangeP(X3,X2,X4,X5) ) ).
cnf(i_0_2017,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X1,X5)
| c_Predicate_ORangeP(X3,X4,X2,X5) ) ).
cnf(i_0_2018,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X5,X1)
| c_Predicate_ORangeP(X3,X4,X5,X2) ) ).
cnf(i_0_2019,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_2020,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_2021,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_2022,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_2024,plain,
X1 = X1,
inference(equality_inference,[],[1107]) ).
cnf(i_0_2025,plain,
hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X3),X4),X5) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X1,X2),X3),X4),X5),
inference(equality_inference,[],[1133]) ).
cnf(i_0_2071,plain,
X1 = X1,
inference(equality_inference,[],[1453]) ).
cnf(i_0_2076,plain,
X1 = X1,
inference(equality_inference,[],[1522]) ).
cnf(i_0_2077,plain,
X1 = X1,
inference(equality_inference,[],[1523]) ).
cnf(i_0_2079,plain,
X1 = X1,
inference(equality_inference,[],[1595]) ).
cnf(i_0_2080,plain,
X1 = X1,
inference(equality_inference,[],[1597]) ).
cnf(i_0_2084,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(equality_inference,[],[1648]) ).
cnf(i_0_2085,plain,
X1 = X1,
inference(equality_inference,[],[1689]) ).
cnf(i_0_2086,plain,
X1 = X1,
inference(equality_inference,[],[1690]) ).
cnf(i_0_2087,plain,
X1 = X1,
inference(equality_inference,[],[1691]) ).
cnf(i_0_2088,plain,
X1 = X1,
inference(equality_inference,[],[1692]) ).
cnf(i_0_2089,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1693]) ).
cnf(i_0_2090,plain,
c_List_Obutlast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))) = c_List_Obutlast(X1,X2),
inference(equality_inference,[],[1718]) ).
cnf(i_0_2091,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1))) = c_List_Olast(X1,X2),
inference(equality_inference,[],[1720]) ).
cnf(i_0_2093,plain,
X1 = X1,
inference(equality_inference,[],[1732]) ).
cnf(i_0_2094,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1733]) ).
cnf(i_0_2095,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
inference(equality_inference,[],[1735]) ).
cnf(i_0_2101,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(equality_inference,[],[1775]) ).
cnf(i_0_2102,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1786]) ).
cnf(i_0_2103,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1787]) ).
cnf(i_0_2104,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1800]) ).
cnf(i_0_2105,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1801]) ).
cnf(i_0_2106,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1803]) ).
cnf(i_0_2107,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[1811]) ).
cnf(i_0_2111,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(equality_inference,[],[1825]) ).
cnf(i_0_2112,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(equality_inference,[],[1826]) ).
cnf(i_0_2113,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[1827]) ).
cnf(i_0_2114,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
inference(equality_inference,[],[1828]) ).
cnf(i_0_2115,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1832]) ).
cnf(i_0_2116,plain,
c_List_Orotate1(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[1846]) ).
cnf(i_0_2234,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2241,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2248,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2271,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2309,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1781]) ).
cnf(i_0_2313,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(rename_variables,[],[i_0_1782]) ).
cnf(i_0_2314,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(rename_variables,[],[i_0_1831]) ).
cnf(i_0_2332,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1834]) ).
cnf(i_0_2338,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(rename_variables,[],[i_0_1831]) ).
cnf(i_0_2344,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2370,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(rename_variables,[],[i_0_1638]) ).
cnf(i_0_2373,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2376,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1781]) ).
cnf(i_0_2383,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2390,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2396,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2417,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2443,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1834]) ).
cnf(i_0_2452,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1834]) ).
cnf(i_0_2455,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1834]) ).
cnf(i_0_2458,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1792]) ).
cnf(i_0_2461,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1792]) ).
cnf(i_0_2493,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2500,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(rename_variables,[],[i_0_1638]) ).
cnf(i_0_2504,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(rename_variables,[],[i_0_1769]) ).
cnf(i_0_2512,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2515,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1792]) ).
cnf(i_0_2523,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2527,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2528,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1781]) ).
cnf(i_0_2531,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2532,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(rename_variables,[],[i_0_1782]) ).
cnf(i_0_2716,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2757,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2794,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2798,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1834]) ).
cnf(i_0_2814,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2818,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2827,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2830,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2831,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2840,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2876,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(rename_variables,[],[i_0_1638]) ).
cnf(i_0_2879,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2922,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2924,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2926,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2928,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2938,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2940,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2942,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2948,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2950,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2952,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2956,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2958,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2966,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2968,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2989,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(rename_variables,[],[i_0_1638]) ).
cnf(i_0_2990,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_2993,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(rename_variables,[],[i_0_1769]) ).
cnf(i_0_2994,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_3006,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(i_0_3019,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_OtakeWhile(X1,X2,X3)),c_List_OdropWhile(X1,X2,X3)) = X3,
inference(rename_variables,[],[i_0_1558]) ).
cnf(c_0_1853,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
i_0_1790 ).
cnf(c_0_1854,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
i_0_1506 ).
cnf(c_0_1855,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),c_List_Olist_OCons(X4)),X5),X6) != hAPP(X5,X6),
inference(spm,[status(thm)],[c_0_1853,c_0_1854]) ).
cnf(c_0_1856,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),hAPP(c_COMBS(X4,X5,X6),c_List_Olist_OCons(X7))),X8),X9) != hAPP(X9,hAPP(X8,X9)),
inference(spm,[status(thm)],[c_0_1855,c_0_1854]) ).
cnf(c_0_1857,plain,
hAPP(c_COMBI(X1),X2) = X2,
i_0_1849 ).
cnf(c_0_1858,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),hAPP(c_COMBS(X4,X5,X6),c_List_Olist_OCons(X7))),c_COMBI(X8)),X9) != hAPP(X9,X9),
inference(spm,[status(thm)],[c_0_1856,c_0_1857]) ).
cnf(c_0_1859,plain,
$false,
inference(er,[status(thm)],[c_0_1858]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT136+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n021.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 01:59:25 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 132.26/110.16 % Version : CSE_E---1.7
% 132.26/110.16 % Problem : theBenchmark.p
% 132.26/110.16 % SZS status Theorem for theBenchmark.p
% 132.26/110.16 % SZS output start CNFRefutation
% See solution above
% 206.43/184.38 % Total time : 108.918s
%------------------------------------------------------------------------------