%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT143+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 : n003.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 05:06:06 PM UTC 2026
% Result : Theorem 252.30s 180.89s
% Output : CNFRefutation 292.62s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_623)
% Comments :
%------------------------------------------------------------------------------
fof(fact_converse__rtranclE2,axiom,
! [X17,X86,X87,X88,X64,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X64),X88) != hAPP(hAPP(c_Product__Type_OPair(X6,X14),X87),X86)
=> ~ ! [X29,X30] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30))),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_mem__splitE,axiom,
! [X78,X5,X47,X14,X9,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X47,tc_fun(X6,tc_HOL_Obool)),X5),X78)))
=> ~ ! [X3,X65] :
( X78 = hAPP(hAPP(c_Product__Type_OPair(X14,X47),X3),X65)
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(X5,X3),X65))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitE) ).
fof(fact_Cons__listrel1E2,axiom,
! [X17,X52,X11,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_List_Olistrel1(X6,X17)))
=> ( ! [X3] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X52)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X11)),X17)) )
=> ~ ! [X75] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X75),X52)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1E2) ).
fof(conj_0,conjecture,
! [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),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X4)),v_c____),v_b____)),v_b____),v_a____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X4)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_lexord__append__leftD,axiom,
! [X17,X63,X53,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X12),X53)),hAPP(hAPP(c_List_Oappend(X6),X12),X63))),c_List_Olexord(X6,X17)))
=> ( ! [X29] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X29)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X53),X63)),c_List_Olexord(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_Cons__listrel1E1,axiom,
! [X17,X52,X51,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),X52)),c_List_Olistrel1(X6,X17)))
=> ( ! [X65] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X6),X65),X51)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X65)),X17)) )
=> ~ ! [X75] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X75)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1E1) ).
fof(fact_listrel__Cons2,axiom,
! [X17,X52,X11,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_List_Olistrel(X6,X17)))
=> ~ ! [X3,X67] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X67)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X11)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X67),X52)),c_List_Olistrel(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_listrel__Cons1,axiom,
! [X17,X51,X52,X11,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52)),X51)),c_List_Olistrel(X6,X17)))
=> ~ ! [X65,X66] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X65),X66)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X65)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X52),X66)),c_List_Olistrel(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_compose__assoc,axiom,
! [X48,X49,X50,X46,X1,X47,X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X14,X47)),X1),c_FuncSet_OPi(X14,X47,X7,c_COMBK(tc_fun(X47,tc_HOL_Obool),X14,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(X6,X47,X50,X8,X49,c_FuncSet_Ocompose(X6,X14,X47,X8,X1,X2)) = c_FuncSet_Ocompose(X6,X14,X50,X8,c_FuncSet_Ocompose(X14,X47,X50,X7,X49,X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__assoc) ).
fof(fact_compose__def,axiom,
! [X2,X1,X8,X14,X47,X6] : c_FuncSet_Ocompose(X6,X47,X14,X8,X1,X2) = c_FuncSet_Orestrict(X6,X14,hAPP(hAPP(c_COMBB(X47,X14,X6),X1),X2),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__def) ).
fof(fact_funcset__compose,axiom,
! [X46,X1,X47,X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X14,X47)),X1),c_FuncSet_OPi(X14,X47,X7,c_COMBK(tc_fun(X47,tc_HOL_Obool),X14,X46))))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X47)),c_FuncSet_Ocompose(X6,X14,X47,X8,X1,X2)),c_FuncSet_OPi(X6,X47,X8,c_COMBK(tc_fun(X47,tc_HOL_Obool),X6,X46)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__compose) ).
fof(fact_RangeE,axiom,
! [X17,X14,X18,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X18),c_Relation_ORange(X14,X6,X17)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X6)),hAPP(hAPP(c_Product__Type_OPair(X14,X6),X3),X18)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).
fof(fact_Id__compose,axiom,
! [X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional(X6,X14,X8)))
=> c_FuncSet_Ocompose(X6,X14,X14,X8,c_FuncSet_Orestrict(X14,X14,c_COMBI(X14),X7),X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__compose) ).
fof(fact_compose__extensional,axiom,
! [X1,X2,X8,X47,X14,X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),c_FuncSet_Ocompose(X6,X47,X14,X8,X2,X1)),c_FuncSet_Oextensional(X6,X14,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__extensional) ).
fof(fact_lexord__irreflexive,axiom,
! [X11,X17,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X11),X11)),c_List_Olexord(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_override__on__def,axiom,
! [X1,X2,X14,X8,X19,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X19) = hAPP(X1,X19) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X19) = hAPP(X2,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__def) ).
fof(fact_override__on__apply__notin,axiom,
! [X1,X2,X14,X8,X19,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X19) = hAPP(X2,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).
fof(fact_compose__Id,axiom,
! [X7,X8,X1,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X1),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X1),c_FuncSet_Oextensional(X6,X14,X8)))
=> c_FuncSet_Ocompose(X6,X6,X14,X8,X1,c_FuncSet_Orestrict(X6,X6,c_COMBI(X6),X8)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__Id) ).
fof(fact_DomainE,axiom,
! [X17,X14,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Relation_ODomain(X6,X14,X17)))
=> ~ ! [X65] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X65)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).
fof(fact_compose__id__inv__into,axiom,
! [X7,X8,X2,X6,X14] :
( c_Set_Oimage(X14,X6,X2,X8) = X7
=> c_FuncSet_Ocompose(X6,X14,X6,X7,X2,c_FuncSet_Orestrict(X6,X14,c_Hilbert__Choice_Oinv__into(X14,X6,X8,X2),X7)) = c_FuncSet_Orestrict(X6,X6,c_COMBI(X6),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__id__inv__into) ).
fof(fact_notin__Lin__iff,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( X12 != X11
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X11)),X10))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X12)),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X18,X19,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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),X19),X18)),X10))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X19)),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_not__acc__down,axiom,
! [X13,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X13)))
=> ~ ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X69),X12)),X13))
=> hBOOL(hAPP(hAPP(c_member(X6),X69),c_Wellfounded_Oacc(X6,X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(fact_not__Nil__listrel1,axiom,
! [X17,X51,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),X51)),c_List_Olistrel1(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_Nil__notin__lex,axiom,
! [X17,X52,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),X52)),c_List_Olex(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_not__listrel1__Nil,axiom,
! [X17,X51,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),c_List_Olist_ONil(X6))),c_List_Olistrel1(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_Nil2__notin__lex,axiom,
! [X17,X51,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),c_List_Olist_ONil(X6))),c_List_Olex(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_lexord__Nil__right,axiom,
! [X17,X12,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),c_List_Olist_ONil(X6))),c_List_Olexord(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_surj__compose,axiom,
! [X46,X1,X47,X7,X8,X2,X6,X14] :
( c_Set_Oimage(X14,X6,X2,X8) = X7
=> ( c_Set_Oimage(X6,X47,X1,X7) = X46
=> c_Set_Oimage(X14,X47,c_FuncSet_Ocompose(X14,X6,X47,X8,X1,X2),X8) = X46 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__compose) ).
fof(fact_PiE,axiom,
! [X12,X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X12)),hAPP(X7,X12)))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_extensional__funcset__arb,axiom,
! [X12,X97,X24,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional__funcset(X6,X14,X24,X97)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X24))
=> hAPP(X2,X12) = c_HOL_Oundefined(X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
fof(fact_cut__def,axiom,
! [X2,X14,X17,X12,X11,X6] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X17))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X2),X17),X12),X11) = hAPP(X2,X11) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X17))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X2),X17),X12),X11) = c_HOL_Oundefined(X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__def) ).
fof(fact_in__measures_I1_J,axiom,
! [X11,X12,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_List_Omeasures(X6,c_List_Olist_ONil(tc_fun(X6,tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [X11,X13,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Relation_ODomain(X6,X6,X13)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X13)))
<=> X12 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_inf2E,axiom,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X8,X7),X12),X11))
=> ~ ( hBOOL(hAPP(hAPP(X8,X12),X11))
=> ~ hBOOL(hAPP(hAPP(X7,X12),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).
fof(fact_compose__eq,axiom,
! [X2,X1,X14,X47,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Ocompose(X6,X47,X14,X8,X1,X2),X12) = hAPP(X1,hAPP(X2,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__eq) ).
fof(fact_irrefl__def,axiom,
! [X17,X6] :
( c_Relation_Oirrefl(X6,X17)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_extensional__arb,axiom,
! [X12,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional(X6,X14,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(X2,X12) = c_HOL_Oundefined(X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__arb) ).
fof(fact_IntE,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).
fof(fact_dropWhile__eq__Cons__conv,axiom,
! [X52,X11,X51,X16,X6] :
( c_List_OdropWhile(X6,X16,X51) = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52)
<=> ( X51 = hAPP(hAPP(c_List_Oappend(X6),c_List_OtakeWhile(X6,X16,X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))
& ~ hBOOL(hAPP(X16,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
fof(fact_restrict__def,axiom,
! [X2,X14,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = c_HOL_Oundefined(X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__def) ).
fof(fact_restrict__apply,axiom,
! [X2,X14,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = c_HOL_Oundefined(X14) ) ),
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,
~ ! [X20] : ~ 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),X20),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,X7,X8,X6] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X12))
=> ~ ( hBOOL(hAPP(X8,X12))
=> ~ hBOOL(hAPP(X7,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
fof(fact_internal__split__conv,axiom,
! [X18,X19,X5,X6,X47,X14] : hAPP(hAPP(c_Product__Type_Ointernal__split(X14,X47,X6),X5),hAPP(hAPP(c_Product__Type_OPair(X14,X47),X19),X18)) = hAPP(hAPP(X5,X19),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).
fof(fact_internal__split__def,axiom,
! [X47,X14,X6] : c_Product__Type_Ointernal__split(X6,X14,X47) = c_Product__Type_Oprod_Oprod__case(X6,X14,X47),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(fact_takeWhile__tail,axiom,
! [X89,X51,X6,X12,X16] :
( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Oappend(X6),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X89))) = c_List_OtakeWhile(X6,X16,X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__tail) ).
fof(fact_takeWhile_Osimps_I2_J,axiom,
! [X51,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_OtakeWhile(X6,X16,X51)) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = c_List_Olist_ONil(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
fof(fact_le__infE,axiom,
! [X37,X38,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X35,X38)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X35,X37) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X6,X14] :
( class_Orderings_Oord(X14)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,X14),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X14),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X14),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_dropWhile_Osimps_I2_J,axiom,
! [X51,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = c_List_OdropWhile(X6,X16,X51) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
fof(fact_less__le__not__le,axiom,
! [X11,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X11,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> X12 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X38,X37,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X37,X38)
=> ~ c_Orderings_Oord__class_Oless(X6,X38,X37) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> ( c_Orderings_Oord__class_Oless(X6,X11,X12)
| X12 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__not__less,axiom,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> c_Orderings_Oord__class_Oless__eq(X6,X11,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_leD,axiom,
! [X35,X44,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> ~ c_Orderings_Oord__class_Oless(X6,X35,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__le,axiom,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> c_Orderings_Oord__class_Oless(X6,X11,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_order__less__not__sym,axiom,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ~ c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ~ c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__asym_H,axiom,
! [X37,X38,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X38,X37)
=> ~ c_Orderings_Oord__class_Oless(X6,X37,X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__asym,axiom,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ~ c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> X12 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(help_c__fconj__2,axiom,
! [X104,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X104))
| hBOOL(X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X104,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X104))
| hBOOL(X104) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(help_c__fequal__1,axiom,
! [X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X11))
| X12 = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X12,X11,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X11,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> X12 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE,axiom,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( X35 != X44
=> ( ~ c_Orderings_Oord__class_Oless(X6,X35,X44)
=> c_Orderings_Oord__class_Oless(X6,X44,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__cases,axiom,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ( X35 != X44
=> c_Orderings_Oord__class_Oless(X6,X44,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_not__leE,axiom,
! [X35,X44,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> c_Orderings_Oord__class_Oless(X6,X35,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X35,X44)
=> c_Orderings_Oord__class_Oless__eq(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> c_Orderings_Oord__class_Oless__eq(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_order__less__irrefl,axiom,
! [X35,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X35,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(help_c__fconj__1,axiom,
! [X104,X16] :
( ~ hBOOL(X16)
| ~ hBOOL(X104)
| hBOOL(hAPP(hAPP(c_fconj,X16),X104)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_equalityE,axiom,
! [X6,X7,X8] :
( X8 = X7
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
fof(help_c__fNot__1,axiom,
! [X16] :
( ~ hBOOL(hAPP(c_fNot,X16))
| ~ hBOOL(X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [X16] :
( ~ ~ hBOOL(X16)
| hBOOL(hAPP(c_fNot,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_rtrancl__induct2,axiom,
! [X16,X17,X80,X81,X82,X83,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X83),X82)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X81),X80))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hBOOL(hAPP(hAPP(X16,X83),X82))
=> ( ! [X29,X30] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X83),X82)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ! [X84,X85] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X85))),X17))
=> ( hBOOL(hAPP(hAPP(X16,X29),X30))
=> hBOOL(hAPP(hAPP(X16,X84),X85)) ) ) )
=> hBOOL(hAPP(hAPP(X16,X81),X80)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [X16,X17,X80,X81,X82,X83,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X83),X82)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X81),X80))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hBOOL(hAPP(hAPP(X16,X81),X80))
=> ( ! [X29,X30,X84,X85] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X85))),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X85)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X81),X80))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hBOOL(hAPP(hAPP(X16,X84),X85))
=> hBOOL(hAPP(hAPP(X16,X29),X30)) ) ) )
=> hBOOL(hAPP(hAPP(X16,X83),X82)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_ac,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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____))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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),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____))),v_b____)),v_a____)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ac) ).
fof(fact_inf__Int__eq2,axiom,
! [X11,X12,X24,X13,X14,X6] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X13),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X24)),X12),X11))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X11)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X13,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_adm__wf__def,axiom,
! [X27,X13,X14,X6] :
( c_Recdef_Oadm__wf(X6,X14,X13,X27)
<=> ! [X98,X100,X3] :
( ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X69),X3)),X13))
=> hAPP(X98,X69) = hAPP(X100,X69) )
=> hAPP(hAPP(X27,X98),X3) = hAPP(hAPP(X27,X100),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__wf__def) ).
fof(fact_accp__acc__eq,axiom,
! [X12,X17,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),X6),c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X6,X6)),tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X6),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool),X6),c_member(tc_prod(X6,X6)))),c_Product__Type_OPair(X6,X6)))),X17)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [X51,X12,X16,X6] : c_List_Opartition(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X6),tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_COMBS(tc_List_Olist(X6),tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X6),tc_fun(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)))),tc_fun(tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)))),tc_List_Olist(X6)),c_COMBS(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),tc_fun(tc_List_Olist(X6),tc_fun(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)))),tc_List_Olist(X6)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_fun(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),tc_List_Olist(X6)),c_If(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(X16,X12)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X6),tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),tc_List_Olist(X6)),c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(c_List_Olist_OCons(X6),X12))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X6),tc_fun(tc_List_Olist(X6),tc_List_Olist(X6)),tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),tc_fun(tc_fun(tc_List_Olist(X6),tc_List_Olist(X6)),tc_fun(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)))),tc_List_Olist(X6)),c_COMBB(tc_List_Olist(X6),tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_List_Olist(X6))),c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)))),hAPP(c_List_Olist_OCons(X6),X12)))),c_List_Opartition(X6,X16,X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(fact_ab,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_F,v_P____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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____)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab) ).
fof(fact_pred__subset__eq2,axiom,
! [X24,X13,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X13),hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X13,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_mem__splitI2,axiom,
! [X5,X9,X47,X14,X6,X78] :
( ! [X29,X30] :
( X78 = hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30)
=> hBOOL(hAPP(hAPP(c_member(X47),X9),hAPP(hAPP(X5,X29),X30))) )
=> hBOOL(hAPP(hAPP(c_member(X47),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_fun(X47,tc_HOL_Obool)),X5),X78))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI2) ).
fof(fact_cuts__eq,axiom,
! [X1,X12,X17,X2,X14,X6] :
( hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X2),X17),X12) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X1),X17),X12)
<=> ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X65),X12)),X17))
=> hAPP(X2,X65) = hAPP(X1,X65) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cuts__eq) ).
fof(fact__C2_C,axiom,
! [X21,X16,X22,X23,X18,X19] :
( X19 != X18
=> ( X23 != X22
=> ( X19 != X22
=> ( X18 != X23
=> ( 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))),X16),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))),X21),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [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),X19),X18)),hAPP(X16,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),X23),X22)),hAPP(X21,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),X19),X18)),hAPP(v_F,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),X23),X22)),hAPP(v_F,X21))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__C1_C,axiom,
! [X21,X16,X22,X23,X18,X19] :
( X19 != X18
=> ( X23 != X22
=> ( X19 != X22
=> ( X18 != X23
=> ( 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))),X16),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))),X21),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [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),X19),X18)),hAPP(X16,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),X23),X22)),hAPP(X21,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),X19),X18)),hAPP(v_F,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),X23),X22)),hAPP(v_F,X21))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_listrelp__listrel__eq,axiom,
! [X64,X12,X17,X6] :
( c_List_Olistrelp(X6,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_HOL_Obool)),X6),c_COMBC(X6,tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_prod(X6,X6)),tc_fun(X6,tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X6),tc_fun(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_HOL_Obool),X6),c_member(tc_prod(X6,X6)))),c_Product__Type_OPair(X6,X6)))),X17),X12,X64)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X64)),c_List_Olistrel(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_DomainP__Domain__eq,axiom,
! [X12,X17,X14,X6] :
( c_Predicate_ODomainP(X6,X14,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X17),X12)
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Relation_ODomain(X6,X14,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_RangeP__Range__eq,axiom,
! [X12,X17,X14,X6] :
( c_Predicate_ORangeP(X6,X14,hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X17),X12)
<=> hBOOL(hAPP(hAPP(c_member(X14),X12),c_Relation_ORange(X6,X14,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X24,X13,X14,X6] :
( hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X13) = hAPP(hAPP(c_COMBC(X6,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBC(X14,tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_fun(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),tc_HOL_Obool),X14),c_member(tc_prod(X6,X14)))),c_Product__Type_OPair(X6,X14)))),X24)
<=> X13 = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_adm__lemma,axiom,
! [X27,X13,X14,X6] : c_Recdef_Oadm__wf(X6,X14,X13,hAPP(hAPP(c_COMBC(tc_fun(X6,X14),tc_fun(X6,X6),tc_fun(X6,X14)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X14)),tc_fun(tc_fun(X6,X6),tc_fun(X6,X14)),tc_fun(X6,X14)),c_COMBS(X6,X6,X14)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_fun(X6,X14)),tc_fun(X6,tc_fun(X6,X14)),tc_fun(X6,X14)),hAPP(c_COMBB(tc_fun(X6,X14),tc_fun(X6,X14),X6),X27)),hAPP(hAPP(c_COMBC(tc_fun(X6,X14),tc_fun(tc_prod(X6,X6),tc_HOL_Obool),tc_fun(X6,tc_fun(X6,X14))),c_Recdef_Ocut(X6,X14)),X13)))),c_COMBI(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__lemma) ).
fof(fact_Pi__cong,axiom,
! [X7,X14,X1,X2,X8,X6] :
( ! [X45] :
( hBOOL(hAPP(hAPP(c_member(X6),X45),X8))
=> hAPP(X2,X45) = hAPP(X1,X45) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,X7)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X1),c_FuncSet_OPi(X6,X14,X8,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__cong) ).
fof(fact_restrictI,axiom,
! [X7,X2,X14,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X3)),hAPP(X7,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),c_FuncSet_Orestrict(X6,X14,X2,X8)),c_FuncSet_OPi(X6,X14,X8,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrictI) ).
fof(fact_Pi__I_H,axiom,
! [X7,X2,X14,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X3)),hAPP(X7,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I_H) ).
fof(fact_Pi__I,axiom,
! [X7,X2,X14,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X3)),hAPP(X7,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X27] :
( c_Arrow__Order__Mirabelle_OIIA(X27)
<=> ! [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))
=> ! [X28] :
( 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))),X28),c_Arrow__Order__Mirabelle_OProf))
=> ! [X29,X30] :
( ! [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),X29),X30)),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),X29),X30)),hAPP(X28,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),X29),X30)),hAPP(X27,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),X29),X30)),hAPP(X27,X28))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact_restrict__in__funcset,axiom,
! [X7,X2,X14,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X3)),X7)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),c_FuncSet_Orestrict(X6,X14,X2,X8)),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
fof(fact_funcsetI,axiom,
! [X7,X2,X14,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X3)),X7)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(fact_Eps__split__eq,axiom,
! [X11,X12,X14,X6] : c_Hilbert__Choice_OEps(tc_prod(X6,X14),hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6,tc_fun(X14,tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X14,tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X14)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6),c_fconj),hAPP(c_fequal,X12)))),hAPP(c_fequal,X11)))) = hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_Id__on__def_H,axiom,
! [X8,X6] : c_Relation_OId__on(X6,X8) = hAPP(c_Product__Type_Oprod_Oprod__case(X6,X6,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X6,tc_HOL_Obool,tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X6,tc_HOL_Obool)),X6),c_COMBC(X6,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X6,tc_HOL_Obool),tc_fun(X6,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X6),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6),c_fconj)),c_fequal))),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_lexord__linear,axiom,
! [X11,X12,X17,X6] :
( ! [X29,X30] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X30)),X17))
| X29 = X30
| hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X30),X29)),X17)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X11)),c_List_Olexord(X6,X17)))
| X12 = X11
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X11),X12)),c_List_Olexord(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__linear) ).
fof(fact_listsp__conj__eq,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,hAPP(hAPP(c_COMBS(X6,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6),c_fconj),X8)),X7)),X12))
<=> ( hBOOL(hAPP(c_List_Olistsp(X6,X8),X12))
& hBOOL(hAPP(c_List_Olistsp(X6,X7),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [X17,X11,X52,X12,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_Olist_ONil(X6)))),hAPP(hAPP(c_List_Oappend(X6),X52),hAPP(hAPP(c_List_Olist_OCons(X6),X11),c_List_Olist_ONil(X6))))),c_List_Olistrel1(X6,X17)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17)))
& X12 = X11 )
| ( X51 = X52
& hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_Pi__mono,axiom,
! [X46,X7,X14,X8,X6] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),hAPP(X7,X3),hAPP(X46,X3)) )
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X6,X14),tc_HOL_Obool),c_FuncSet_OPi(X6,X14,X8,X7),c_FuncSet_OPi(X6,X14,X8,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_in__lex__prod,axiom,
! [X31,X17,X22,X23,X18,X19,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X23),X22))),c_Wellfounded_Olex__prod(X6,X14,X17,X31)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X23)),X17))
| ( X19 = X23
& hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X14)),hAPP(hAPP(c_Product__Type_OPair(X14,X14),X18),X22)),X31)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact_dictatorI,axiom,
! [X36,X27] :
( 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))),X27),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))
=> ! [X29,X30] :
( X29 != X30
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X29),X30)),hAPP(X3,X36)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X29),X30)),hAPP(X27,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X27,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_inv__into__def,axiom,
! [X12,X2,X8,X14,X6] : hAPP(c_Hilbert__Choice_Oinv__into(X6,X14,X8,X2),X12) = c_Hilbert__Choice_OEps(X6,hAPP(hAPP(c_COMBS(X6,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X6),c_fconj),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8))),hAPP(hAPP(c_COMBC(X6,X14,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X14,tc_fun(X14,tc_HOL_Obool),X6),c_fequal),X2)),X12))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__def) ).
fof(fact_listrel1E,axiom,
! [X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17)))
=> ~ ! [X3,X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X65)),X17))
=> ! [X59,X68] :
( X51 = hAPP(hAPP(c_List_Oappend(X6),X59),hAPP(hAPP(c_List_Olist_OCons(X6),X3),X68))
=> X52 != hAPP(hAPP(c_List_Oappend(X6),X59),hAPP(hAPP(c_List_Olist_OCons(X6),X65),X68)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1E) ).
fof(fact_lists__IntI,axiom,
! [X7,X8,X89,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X89),c_List_Olists(X6,X8)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X89),c_List_Olists(X6,X7)))
=> hBOOL(hAPP(c_List_Olistsp(X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X7))),X89)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__IntI) ).
fof(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096,axiom,
! [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),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X4)),v_c____),v_b____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X4)),v_c____),v_b____)),v_b____),v_a____))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) ).
fof(fact_extensionalityI,axiom,
! [X1,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional(X6,X14,X8)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X1),c_FuncSet_Oextensional(X6,X14,X8)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hAPP(X2,X3) = hAPP(X1,X3) )
=> X2 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensionalityI) ).
fof(fact_lexord__append__left__rightI,axiom,
! [X11,X12,X53,X17,X18,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X53),hAPP(hAPP(c_List_Olist_OCons(X6),X19),X12))),hAPP(hAPP(c_List_Oappend(X6),X53),hAPP(hAPP(c_List_Olist_OCons(X6),X18),X11)))),c_List_Olexord(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
fof(fact_same__fstI,axiom,
! [X6,X13,X11,X15,X14,X12,X16] :
( hBOOL(hAPP(X16,X12))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X14)),hAPP(hAPP(c_Product__Type_OPair(X14,X14),X15),X11)),hAPP(X13,X12)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X15)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X11))),c_Recdef_Osame__fst(X6,X14,X16,X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_split__twice,axiom,
! [X78,X1,X90,X50,X2,X6,X47,X14] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X47,X6),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X50,X90,tc_prod(X14,X47)),X1),X78)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X50,X90,X6),hAPP(hAPP(c_COMBB(tc_fun(X90,tc_prod(X14,X47)),tc_fun(X90,X6),X50),hAPP(c_COMBB(tc_prod(X14,X47),X6,X90),hAPP(c_Product__Type_Oprod_Oprod__case(X14,X47,X6),X2))),X1)),X78),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__twice) ).
fof(fact_append__eq__append__conv2,axiom,
! [X58,X57,X52,X51,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X51),X52) = hAPP(hAPP(c_List_Oappend(X6),X57),X58)
<=> ? [X59] :
( ( X51 = hAPP(hAPP(c_List_Oappend(X6),X57),X59)
& hAPP(hAPP(c_List_Oappend(X6),X59),X52) = X58 )
| ( hAPP(hAPP(c_List_Oappend(X6),X51),X59) = X57
& X52 = hAPP(hAPP(c_List_Oappend(X6),X59),X58) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_inf__Int__eq,axiom,
! [X12,X24,X13,X6] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X13),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X24)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X13,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_Range__iff,axiom,
! [X17,X14,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Relation_ORange(X14,X6,X17)))
<=> ? [X65] : hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X6)),hAPP(hAPP(c_Product__Type_OPair(X14,X6),X65),X19)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [X17,X52,X11,X51,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_List_Olistrel1(X6,X17)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17))
& X51 = X52 )
| ( X12 = X11
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_Cons__in__lex,axiom,
! [X17,X52,X11,X51,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_List_Olex(X6,X17)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17))
& c_Nat_Osize__class_Osize(tc_List_Olist(X6),X51) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X52) )
| ( X12 = X11
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olex(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_lexord__cons__cons,axiom,
! [X17,X11,X18,X12,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X19),X12)),hAPP(hAPP(c_List_Olist_OCons(X6),X18),X11))),c_List_Olexord(X6,X17)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),X17))
| ( X19 = X18
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X11)),c_List_Olexord(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [X52,X51,X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_listrel_OCons,axiom,
! [X52,X51,X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_List_Olistrel(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_OCons) ).
fof(fact_inv__into__funcset,axiom,
! [X7,X8,X2,X6,X14] :
( c_Set_Oimage(X14,X6,X2,X8) = X7
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),c_FuncSet_Orestrict(X6,X14,c_Hilbert__Choice_Oinv__into(X14,X6,X8,X2),X7)),c_FuncSet_OPi(X6,X14,X7,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X8)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__funcset) ).
fof(fact_unanimity__def,axiom,
! [X27] :
( c_Arrow__Order__Mirabelle_Ounanimity(X27)
<=> ! [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))
=> ! [X29,X30] :
( ! [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),X29),X30)),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),X29),X30)),hAPP(X27,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [X57,X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X52),X57)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X57)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [X12,X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X52))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
fof(fact_lexord__trans,axiom,
! [X9,X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X11)),c_List_Olexord(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X11),X9)),c_List_Olexord(X6,X17)))
=> ( c_Relation_Otrans(X6,X17)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X9)),c_List_Olexord(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__trans) ).
fof(fact_append__listrel1I,axiom,
! [X60,X61,X17,X52,X51,X6] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17)))
& X61 = X60 )
| ( X51 = X52
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X61),X60)),c_List_Olistrel1(X6,X17))) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X51),X61)),hAPP(hAPP(c_List_Oappend(X6),X52),X60))),c_List_Olistrel1(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__listrel1I) ).
fof(fact_lexord__append__leftI,axiom,
! [X12,X17,X63,X53,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X53),X63)),c_List_Olexord(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X12),X53)),hAPP(hAPP(c_List_Oappend(X6),X12),X63))),c_List_Olexord(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_listrel1I2,axiom,
! [X12,X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X52))),c_List_Olistrel1(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I2) ).
fof(fact_in__below,axiom,
! [X11,X12,X10,X18,X19] :
( X19 != X18
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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),X11)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X10),X19),X18)))
<=> ( X12 != X11
& ( X11 = X19
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X18)),X10)) )
& ( X11 != X19
=> ( ( X12 = X19
=> ( X11 = X18
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X11)),X10)) ) )
& ( X12 != X19
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X11)),X10)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_in__above,axiom,
! [X11,X12,X10,X18,X19] :
( X19 != X18
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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),X11)),c_Arrow__Order__Mirabelle_Oabove(X10,X19,X18)))
<=> ( X12 != X11
& ( X12 = X18
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X11)),X10)) )
& ( X12 != X18
=> ( ( X11 = X18
=> ( X12 = X19
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X19)),X10)) ) )
& ( X11 != X18
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X11)),X10)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_override__on__apply__in,axiom,
! [X1,X2,X14,X8,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X19) = hAPP(X1,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
fof(fact_inv__into__into,axiom,
! [X8,X2,X14,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),c_Set_Oimage(X14,X6,X2,X8)))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(c_Hilbert__Choice_Oinv__into(X14,X6,X8,X2),X12)),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).
fof(fact_listrel1I1,axiom,
! [X51,X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X51))),c_List_Olistrel1(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I1) ).
fof(fact_split__paired__Eps,axiom,
! [X16,X14,X6] : c_Hilbert__Choice_OEps(tc_prod(X6,X14),X16) = c_Hilbert__Choice_OEps(tc_prod(X6,X14),hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,tc_HOL_Obool),X6),hAPP(c_COMBB(tc_prod(X6,X14),tc_HOL_Obool,X14),X16)),c_Product__Type_OPair(X6,X14)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_single__valued__confluent,axiom,
! [X9,X11,X12,X17,X6] :
( c_Relation_Osingle__valued(X6,X6,X17)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X9)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X9)),c_Transitive__Closure_Ortrancl(X6,X17)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X9),X11)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Domain__iff,axiom,
! [X17,X14,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Relation_ODomain(X6,X14,X17)))
<=> ? [X65] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X65)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(fact_Cons__eq__append__conv,axiom,
! [X57,X52,X51,X12,X6] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51) = hAPP(hAPP(c_List_Oappend(X6),X52),X57)
<=> ( ( X52 = c_List_Olist_ONil(X6)
& hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51) = X57 )
| ? [X62] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X12),X62) = X52
& X51 = hAPP(hAPP(c_List_Oappend(X6),X62),X57) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append__eq__Cons__conv,axiom,
! [X51,X12,X57,X52,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X52),X57) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)
<=> ( ( X52 = c_List_Olist_ONil(X6)
& X57 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51) )
| ? [X62] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X62)
& hAPP(hAPP(c_List_Oappend(X6),X62),X57) = X51 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_inv__into__injective,axiom,
! [X11,X12,X2,X8,X14,X6] :
( hAPP(c_Hilbert__Choice_Oinv__into(X6,X14,X8,X2),X12) = hAPP(c_Hilbert__Choice_Oinv__into(X6,X14,X8,X2),X11)
=> ( hBOOL(hAPP(hAPP(c_member(X14),X12),c_Set_Oimage(X6,X14,X2,X8)))
=> ( hBOOL(hAPP(hAPP(c_member(X14),X11),c_Set_Oimage(X6,X14,X2,X8)))
=> X12 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_lists__Int__eq,axiom,
! [X7,X8,X6] : c_List_Olistsp(X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X7))) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X6),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X6),tc_fun(tc_List_Olist(X6),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X6))),c_List_Olists(X6,X8)),hAPP(hAPP(c_COMBC(tc_List_Olist(X6),tc_fun(tc_List_Olist(X6),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X6))),c_List_Olists(X6,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__Int__eq) ).
fof(fact_rotate1__def,axiom,
! [X51,X6] : c_List_Orotate1(X6,X51) = c_List_Olist_Olist__case(tc_List_Olist(X6),X6,c_List_Olist_ONil(X6),hAPP(hAPP(c_COMBB(tc_List_Olist(X6),tc_fun(tc_List_Olist(X6),tc_List_Olist(X6)),X6),hAPP(c_COMBC(tc_List_Olist(X6),tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Oappend(X6))),hAPP(hAPP(c_COMBC(X6,tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_OCons(X6)),c_List_Olist_ONil(X6))),X51),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__def) ).
fof(fact_listsp__lists__eq,axiom,
! [X12,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),X12))
<=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X12),c_List_Olists(X6,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).
fof(fact_in__measures_I2_J,axiom,
! [X107,X2,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_List_Omeasures(X6,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6,tc_Nat_Onat)),X2),X107))))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X11))
| ( hAPP(X2,X12) = hAPP(X2,X11)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_List_Omeasures(X6,X107))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_rtrancl__trans,axiom,
! [X5,X17,X18,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X18),X5)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [X5,X17,X18,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X18),X5)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [X5,X17,X18,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X18),X5)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_listrel__reflcl__if__listrel1,axiom,
! [X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
fof(fact_lexord__lex,axiom,
! [X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X11)),c_List_Olex(X6,X17)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X11)),c_List_Olexord(X6,X17)))
& c_Nat_Osize__class_Osize(tc_List_Olist(X6),X12) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__lex) ).
fof(fact_trans__def,axiom,
! [X17,X6] :
( c_Relation_Otrans(X6,X17)
<=> ! [X3,X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X65)),X17))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X65),X69)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X69)),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).
fof(fact_transD,axiom,
! [X5,X18,X19,X17,X6] :
( c_Relation_Otrans(X6,X17)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X18),X5)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X5)),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transD) ).
fof(fact_measures__lesseq,axiom,
! [X107,X6,X11,X12,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X11))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_List_Omeasures(X6,X107)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_List_Omeasures(X6,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6,tc_Nat_Onat)),X2),X107)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).
fof(fact_pair__imageI,axiom,
! [X2,X47,X8,X18,X19,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18)),X8))
=> hBOOL(hAPP(hAPP(c_member(X47),hAPP(hAPP(X2,X19),X18)),c_Set_Oimage(tc_prod(X6,X14),X47,hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X47),X2),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__imageI) ).
fof(fact_listrel1I,axiom,
! [X52,X60,X61,X51,X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17))
=> ( X51 = hAPP(hAPP(c_List_Oappend(X6),X61),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X60))
=> ( X52 = hAPP(hAPP(c_List_Oappend(X6),X61),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X60))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I) ).
fof(fact_image__iff,axiom,
! [X8,X2,X14,X9,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X9),c_Set_Oimage(X14,X6,X2,X8)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X14),X3),X8))
& X9 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_single__valuedI,axiom,
! [X17,X14,X6] :
( ! [X3,X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X65)),X17))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X69)),X17))
=> X65 = X69 ) )
=> c_Relation_Osingle__valued(X6,X14,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedI) ).
fof(fact_single__valued__def,axiom,
! [X17,X14,X6] :
( c_Relation_Osingle__valued(X6,X14,X17)
<=> ! [X3,X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X65)),X17))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X69)),X17))
=> X65 = X69 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(fact_curryD,axiom,
! [X18,X19,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X6,X14,tc_HOL_Obool,X2),X19),X18))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryD) ).
fof(fact_curryE,axiom,
! [X18,X19,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X6,X14,tc_HOL_Obool,X2),X19),X18))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryE) ).
fof(fact_funcset__image,axiom,
! [X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7))))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),c_Set_Oimage(X6,X14,X2,X8),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_subset__image__iff,axiom,
! [X8,X2,X14,X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,c_Set_Oimage(X14,X6,X2,X8))
<=> ? [X105] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),X105,X8)
& X7 = c_Set_Oimage(X14,X6,X2,X105) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_splitD_H,axiom,
! [X5,X18,X19,X13,X47,X14,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_fun(X47,tc_HOL_Obool)),X13),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18)),X5))
=> hBOOL(hAPP(hAPP(hAPP(X13,X19),X18),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD_H) ).
fof(fact_funcset__mem,axiom,
! [X12,X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X7))))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X12)),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_single__valuedD,axiom,
! [X9,X11,X12,X17,X14,X6] :
( c_Relation_Osingle__valued(X6,X14,X17)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X11)),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X9)),X17))
=> X11 = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X6,X14] :
( class_Orderings_Oord(X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X14),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X14,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096,axiom,
! [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),v_a____),v_b____)),hAPP(v_P____,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),v_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X4)),v_c____),v_b____))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) ).
fof(fact_lexord__Nil__left,axiom,
! [X17,X11,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),X11)),c_List_Olexord(X6,X17)))
<=> ? [X29,X3] : X11 = hAPP(hAPP(c_List_Olist_OCons(X6),X29),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_const__Lin__Prof,axiom,
! [X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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,X10)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_mlex__leq,axiom,
! [X13,X6,X11,X12,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X11))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X13))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Wellfounded_Omlex__prod(X6,X2,X13))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_image__Int__subset,axiom,
! [X7,X8,X2,X14,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Set_Oimage(X14,X6,X2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14,tc_HOL_Obool),X8,X7)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),c_Set_Oimage(X14,X6,X2,X8),c_Set_Oimage(X14,X6,X2,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int__subset) ).
fof(fact_in__rel__def,axiom,
! [X11,X12,X13,X14,X6] :
( c_FunDef_Oin__rel(X6,X14,X13,X12,X11)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X11)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_lexn__length,axiom,
! [X74,X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olexn(X6,X17,X74)))
=> ( c_Nat_Osize__class_Osize(tc_List_Olist(X6),X51) = X74
& c_Nat_Osize__class_Osize(tc_List_Olist(X6),X52) = X74 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn__length) ).
fof(fact_acc_OaccI,axiom,
! [X17,X12,X6] :
( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X65),X12)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X65),c_Wellfounded_Oacc(X6,X17))) )
=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(fact_acc_Osimps,axiom,
! [X17,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Wellfounded_Oacc(X6,X17)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X19)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X3),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(fact_split__eta,axiom,
! [X2,X47,X14,X6] : hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X47),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,X47),X6),hAPP(c_COMBB(tc_prod(X6,X14),X47,X14),X2)),c_Product__Type_OPair(X6,X14))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__eta) ).
fof(fact_rtrancl__listrel1__eq__len,axiom,
! [X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),X11)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X6),X12) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_listrel__Nil1,axiom,
! [X17,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),X51)),c_List_Olistrel(X6,X17)))
=> X51 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_f__inv__into__f,axiom,
! [X8,X2,X14,X11,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X11),c_Set_Oimage(X14,X6,X2,X8)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X14,X6,X8,X2),X11)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_listrel__Nil2,axiom,
! [X17,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),c_List_Olist_ONil(X6))),c_List_Olistrel(X6,X17)))
=> X51 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_listrel1__eq__len,axiom,
! [X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel1(X6,X17)))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X6),X51) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_listrel__eq__len,axiom,
! [X17,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X52)),c_List_Olistrel(X6,X17)))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X6),X51) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_split__paired__All,axiom,
! [X14,X6,X16] :
( ! [X91] : hBOOL(hAPP(X16,X91))
<=> ! [X29,X30] : hBOOL(hAPP(X16,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(fact_curryI,axiom,
! [X18,X19,X14,X6,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X6,X14,tc_HOL_Obool,X2),X19),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryI) ).
fof(fact_transI,axiom,
! [X17,X6] :
( ! [X3,X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X65)),X17))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X65),X69)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X69)),X17)) ) )
=> c_Relation_Otrans(X6,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transI) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X17,X6] :
( c_Nitpick_Orefl_H(X6,X17)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_mem__splitI,axiom,
! [X47,X14,X18,X19,X5,X9,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(X5,X19),X18)))
=> hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X47,tc_fun(X6,tc_HOL_Obool)),X5),hAPP(hAPP(c_Product__Type_OPair(X14,X47),X19),X18)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI) ).
fof(fact_lexord__append__rightI,axiom,
! [X17,X12,X6,X11] :
( ? [X30,X69] : X11 = hAPP(hAPP(c_List_Olist_OCons(X6),X30),X69)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),hAPP(hAPP(c_List_Oappend(X6),X12),X11))),c_List_Olexord(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_restrict__extensional,axiom,
! [X8,X2,X14,X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),c_FuncSet_Orestrict(X6,X14,X2,X8)),c_FuncSet_Oextensional(X6,X14,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__extensional) ).
fof(fact_Pi__mem,axiom,
! [X12,X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X12)),hAPP(X7,X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_extensional__funcset__mem,axiom,
! [X12,X97,X24,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional__funcset(X6,X14,X24,X97)))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X24))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X12)),X97)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
fof(fact_pred__subset__eq,axiom,
! [X24,X13,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X13),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X13,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_measures__less,axiom,
! [X107,X6,X11,X12,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X11))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_List_Omeasures(X6,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X6,tc_Nat_Onat)),X2),X107)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__less) ).
fof(fact_in__mkbot,axiom,
! [X9,X10,X11,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),X11)),c_Arrow__Order__Mirabelle_Omkbot(X10,X9)))
<=> ( X11 != X9
& ( X12 = X9
=> X12 != X11 )
& ( X12 != X9
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X11)),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X9,X10,X11,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),X11)),c_Arrow__Order__Mirabelle_Omktop(X10,X9)))
<=> ( X12 != X9
& ( X11 = X9
=> X12 != X11 )
& ( X11 != X9
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X11)),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(fact_iff,axiom,
! [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),v_a____),v_b____)),hAPP(v_P____,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),v_b____),v_a____)),hAPP(v_P_H____,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iff) ).
fof(fact_image__inv__into__cancel,axiom,
! [X106,X103,X8,X2,X6,X14] :
( c_Set_Oimage(X14,X6,X2,X8) = X103
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X106,X103)
=> c_Set_Oimage(X14,X6,X2,c_Set_Oimage(X6,X14,c_Hilbert__Choice_Oinv__into(X14,X6,X8,X2),X106)) = X106 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_below__Lin,axiom,
! [X10,X11,X12] :
( X12 != X11
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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,X10),X12),X11)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_acc__downwards__aux,axiom,
! [X17,X19,X18,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X18),X19)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Wellfounded_Oacc(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(X6),X18),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [X18,X17,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Wellfounded_Oacc(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X18),X19)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(X6),X18),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(fact_dictator__def,axiom,
! [X36,X27] :
( c_Arrow__Order__Mirabelle_Odictator(X27,X36)
<=> ! [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(X27,X3) = hAPP(X3,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_cut__apply,axiom,
! [X2,X14,X17,X19,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X19)),X17))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X2),X17),X19),X12) = hAPP(X2,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__apply) ).
fof(fact_tfl__cut__apply,axiom,
! [X14,X19,X12,X6,X98,X99] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X19)),X99))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X98),X99),X19),X12) = hAPP(X98,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
fof(fact_acc__downward,axiom,
! [X19,X17,X18,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X18),c_Wellfounded_Oacc(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X19),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
fof(fact_above__Lin,axiom,
! [X10,X11,X12] :
( X12 != X11
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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(X10,X12,X11)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_DomainI,axiom,
! [X17,X18,X19,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X19),c_Relation_ODomain(X6,X14,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).
fof(fact_RangeI,axiom,
! [X17,X18,X19,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18)),X17))
=> hBOOL(hAPP(hAPP(c_member(X14),X18),c_Relation_ORange(X6,X14,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).
fof(fact_funcset__id,axiom,
! [X8,X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X6)),c_COMBI(X6)),c_FuncSet_OPi(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_listrel_ONil,axiom,
! [X17,X6] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),c_List_Olist_ONil(X6))),c_List_Olistrel(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_ONil) ).
fof(fact_Id__on__iff,axiom,
! [X8,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Relation_OId__on(X6,X8)))
<=> ( X12 = X11
& hBOOL(hAPP(hAPP(c_member(X6),X12),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(fact_in__measure,axiom,
! [X2,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Wellfounded_Omeasure(X6,X2)))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_inf2D1,axiom,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X8,X7),X12),X11))
=> hBOOL(hAPP(hAPP(X8,X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X8,X7),X12),X11))
=> hBOOL(hAPP(hAPP(X7,X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [X17,X51,X6] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X51)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_mktop__Lin,axiom,
! [X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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(X10,X12)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mkbot__Lin,axiom,
! [X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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(X10,X12)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_takeWhile__not__last,axiom,
! [X6,X51] :
( X51 != c_List_Olist_ONil(X6)
=> ( c_List_Odistinct(X6,X51)
=> c_List_OtakeWhile(X6,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6),c_fNot),hAPP(hAPP(c_COMBC(X6,X6,tc_HOL_Obool),c_fequal),c_List_Olast(X6,X51))),X51) = c_List_Obutlast(X6,X51) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [X51,X17,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X51),c_Wellfounded_Oacc(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),c_Wellfounded_Oacc(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_image__image,axiom,
! [X8,X1,X47,X2,X6,X14] : c_Set_Oimage(X14,X6,X2,c_Set_Oimage(X47,X14,X1,X8)) = c_Set_Oimage(X47,X6,hAPP(hAPP(c_COMBB(X14,X6,X47),X2),X1),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_extensional__subset,axiom,
! [X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional(X6,X14,X8)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional(X6,X14,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__subset) ).
fof(fact_splitD,axiom,
! [X18,X19,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18)))
=> hBOOL(hAPP(hAPP(X2,X19),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD) ).
fof(fact_prod_Orecs,axiom,
! [X18,X19,X42,X6,X47,X14] : c_Product__Type_Oprod_Oprod__rec(X14,X47,X6,X42,hAPP(hAPP(c_Product__Type_OPair(X14,X47),X19),X18)) = hAPP(hAPP(X42,X19),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
fof(fact_mlex__less,axiom,
! [X13,X6,X11,X12,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X2,X12),hAPP(X2,X11))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Wellfounded_Omlex__prod(X6,X2,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_imageI,axiom,
! [X2,X14,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X12)),c_Set_Oimage(X6,X14,X2,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_list_Osimps_I5_J,axiom,
! [X33,X19,X41,X42,X14,X6] : c_List_Olist_Olist__case(X6,X14,X42,X41,hAPP(hAPP(c_List_Olist_OCons(X14),X19),X33)) = hAPP(hAPP(X41,X19),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_inf2I,axiom,
! [X14,X6,X7,X11,X12,X8] :
( hBOOL(hAPP(hAPP(X8,X12),X11))
=> ( hBOOL(hAPP(hAPP(X7,X12),X11))
=> hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X8,X7),X12),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).
fof(fact_image__eqI,axiom,
! [X6,X8,X14,X12,X2,X18] :
( X18 = hAPP(X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X14),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X18),c_Set_Oimage(X14,X6,X2,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X14,X2,X18,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( X18 = hAPP(X2,X12)
=> hBOOL(hAPP(hAPP(c_member(X14),X18),c_Set_Oimage(X6,X14,X2,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_extensional__funcset__def,axiom,
! [X97,X24,X14,X6] : c_FuncSet_Oextensional__funcset(X6,X14,X24,X97) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X6,X14),tc_HOL_Obool),c_FuncSet_OPi(X6,X14,X24,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X97)),c_FuncSet_Oextensional(X6,X14,X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
fof(fact_Range__Int__subset,axiom,
! [X7,X8,X14,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Relation_ORange(X14,X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X14,X6),tc_HOL_Obool),X8,X7)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),c_Relation_ORange(X14,X6,X8),c_Relation_ORange(X14,X6,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_Domain__Int__subset,axiom,
! [X7,X8,X14,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Relation_ODomain(X6,X14,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X8,X7)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),c_Relation_ODomain(X6,X14,X8),c_Relation_ODomain(X6,X14,X7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_append__in__lists__conv,axiom,
! [X8,X52,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X51),X52)),c_List_Olists(X6,X8)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X51),c_List_Olists(X6,X8)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X52),c_List_Olists(X6,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_Id__on__eqI,axiom,
! [X8,X6,X18,X19] :
( X19 = X18
=> ( hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X18)),c_Relation_OId__on(X6,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Pi__anti__mono,axiom,
! [X7,X14,X8,X103,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X103,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X6,X14),tc_HOL_Obool),c_FuncSet_OPi(X6,X14,X8,X7),c_FuncSet_OPi(X6,X14,X103,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_curry__conv,axiom,
! [X18,X19,X2,X6,X47,X14] : hAPP(hAPP(c_Product__Type_Ocurry(X14,X47,X6,X2),X19),X18) = hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X14,X47),X19),X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__conv) ).
fof(fact_curry__def,axiom,
! [X11,X12,X5,X6,X47,X14] : hAPP(hAPP(c_Product__Type_Ocurry(X14,X47,X6,X5),X12),X11) = hAPP(X5,hAPP(hAPP(c_Product__Type_OPair(X14,X47),X12),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__def) ).
fof(fact_list_Osimps_I4_J,axiom,
! [X41,X42,X14,X6] : c_List_Olist_Olist__case(X6,X14,X42,X41,c_List_Olist_ONil(X14)) = X42,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_image__mono,axiom,
! [X2,X14,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),c_Set_Oimage(X6,X14,X2,X8),c_Set_Oimage(X6,X14,X2,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_Cons__in__lists__iff,axiom,
! [X8,X51,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),c_List_Olists(X6,X8)))
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X51),c_List_Olists(X6,X8))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_Id__onE,axiom,
! [X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X5),c_Relation_OId__on(X6,X8)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> X5 != hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(fact_pred__equals__eq,axiom,
! [X24,X13,X6] :
( hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X13) = hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X24)
<=> X13 = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X17,X19,X6] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X19)),c_Transitive__Closure_Ortrancl(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_third__alt,axiom,
! [X37,X38] :
( X38 != X37
=> ? [X20] : c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X38),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X37),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X20),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_third__alt) ).
fof(fact_extensional__restrict,axiom,
! [X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional(X6,X14,X8)))
=> c_FuncSet_Orestrict(X6,X14,X2,X8) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__restrict) ).
fof(fact_prod__caseI,axiom,
! [X14,X6,X18,X19,X42] :
( hBOOL(hAPP(hAPP(X42,X19),X18))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_HOL_Obool),X42),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__caseI) ).
fof(fact_splitI,axiom,
! [X14,X6,X18,X19,X2] :
( hBOOL(hAPP(hAPP(X2,X19),X18))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitI) ).
fof(fact_image__restrict__eq,axiom,
! [X8,X2,X6,X14] : c_Set_Oimage(X14,X6,c_FuncSet_Orestrict(X14,X6,X2,X8),X8) = c_Set_Oimage(X14,X6,X2,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__restrict__eq) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [X70,X71,X72,X73,X17,X6] :
( c_List_Olistrelp(X6,X17,hAPP(hAPP(c_List_Olist_OCons(X6),X73),X72),hAPP(hAPP(c_List_Olist_OCons(X6),X71),X70))
<=> ( hBOOL(hAPP(hAPP(X17,X73),X71))
& c_List_Olistrelp(X6,X17,X72,X70) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_listrelp_OCons,axiom,
! [X52,X51,X6,X11,X12,X17] :
( hBOOL(hAPP(hAPP(X17,X12),X11))
=> ( c_List_Olistrelp(X6,X17,X51,X52)
=> c_List_Olistrelp(X6,X17,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_lists_Osimps,axiom,
! [X8,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X19),c_List_Olists(X6,X8)))
<=> ( X19 = c_List_Olist_ONil(X6)
| ? [X29,X79] :
( X19 = hAPP(hAPP(c_List_Olist_OCons(X6),X29),X79)
& hBOOL(hAPP(hAPP(c_member(X6),X29),X8))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X79),c_List_Olists(X6,X8))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_Osimps) ).
fof(fact_listsp__infI,axiom,
! [X7,X89,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),X89))
=> ( hBOOL(hAPP(c_List_Olistsp(X6,X7),X89))
=> hBOOL(hAPP(c_List_Olistsp(X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)),X89)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__infI) ).
fof(fact_complete__Lin,axiom,
! [X18,X19] :
( X19 != X18
=> ? [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),X19),X18)),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(fact_maps__simps_I1_J,axiom,
! [X51,X12,X2,X6,X14] : c_List_Omaps(X14,X6,X2,hAPP(hAPP(c_List_Olist_OCons(X14),X12),X51)) = hAPP(hAPP(c_List_Oappend(X6),hAPP(X2,X12)),c_List_Omaps(X14,X6,X2,X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).
fof(fact_r__into__rtrancl,axiom,
! [X17,X78,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X78),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X78),c_Transitive__Closure_Ortrancl(X6,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_lists__accI,axiom,
! [X17,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X51),c_Wellfounded_Oacc(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X51),c_List_Olists(X6,c_Wellfounded_Oacc(X6,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accI) ).
fof(fact_lists__accD,axiom,
! [X17,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X51),c_List_Olists(X6,c_Wellfounded_Oacc(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X51),c_Wellfounded_Oacc(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accD) ).
fof(fact_IntD1,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).
fof(fact_Int__iff,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)))
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
& hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD2,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).
fof(fact_IntI,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X7))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
fof(fact_Int__mono,axiom,
! [X48,X7,X46,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X46)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X48)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X46,X48)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [X43,X44,X34,X35,X6] : c_List_Osplice(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34),hAPP(hAPP(c_List_Olist_OCons(X6),X44),X43)) = hAPP(hAPP(c_List_Olist_OCons(X6),X35),hAPP(hAPP(c_List_Olist_OCons(X6),X44),c_List_Osplice(X6,X34,X43))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_split__curry,axiom,
! [X2,X47,X14,X6] : hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X47),c_Product__Type_Ocurry(X6,X14,X47,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__curry) ).
fof(fact_accp_Oequations,axiom,
! [X19,X17,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X19))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X17,X3),X19))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp_Osimps,axiom,
! [X19,X17,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X19))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X17,X3),X19))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(help_c__COMBS__1,axiom,
! [X13,X104,X16,X6,X47,X14] : hAPP(hAPP(hAPP(c_COMBS(X14,X47,X6),X16),X104),X13) = hAPP(hAPP(X16,X13),hAPP(X104,X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_trans__lex__prod,axiom,
! [X76,X14,X77,X6] :
( c_Relation_Otrans(X6,X77)
=> ( c_Relation_Otrans(X14,X76)
=> c_Relation_Otrans(tc_prod(X6,X14),c_Wellfounded_Olex__prod(X6,X14,X77,X76)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
fof(fact_RangeP_Oequations,axiom,
! [X71,X17,X14,X6] :
( c_Predicate_ORangeP(X6,X14,X17,X71)
<=> ? [X29] : hBOOL(hAPP(hAPP(X17,X29),X71)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(help_c__COMBC__1,axiom,
! [X13,X104,X16,X6,X47,X14] : hAPP(hAPP(hAPP(c_COMBC(X14,X47,X6),X16),X104),X13) = hAPP(hAPP(X16,X13),X104),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBB__1,axiom,
! [X13,X104,X16,X47,X6,X14] : hAPP(hAPP(hAPP(c_COMBB(X14,X6,X47),X16),X104),X13) = hAPP(X16,hAPP(X104,X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_inf1D1,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X12))
=> hBOOL(hAPP(X8,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(fact_inf1D2,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X12))
=> hBOOL(hAPP(X7,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).
fof(fact_append__in__listsp__conv,axiom,
! [X52,X51,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),hAPP(hAPP(c_List_Oappend(X6),X51),X52)))
<=> ( hBOOL(hAPP(c_List_Olistsp(X6,X8),X51))
& hBOOL(hAPP(c_List_Olistsp(X6,X8),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).
fof(fact_listsp_Oequations_I2_J,axiom,
! [X71,X73,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),hAPP(hAPP(c_List_Olist_OCons(X6),X73),X71)))
<=> ( hBOOL(hAPP(X8,X73))
& hBOOL(hAPP(c_List_Olistsp(X6,X8),X71)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).
fof(fact_append1__eq__conv,axiom,
! [X11,X52,X12,X51,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_Olist_ONil(X6))) = hAPP(hAPP(c_List_Oappend(X6),X52),hAPP(hAPP(c_List_Olist_OCons(X6),X11),c_List_Olist_ONil(X6)))
<=> ( X51 = X52
& X12 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_listsp_Osimps,axiom,
! [X19,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),X19))
<=> ( X19 = c_List_Olist_ONil(X6)
| ? [X29,X79] :
( X19 = hAPP(hAPP(c_List_Olist_OCons(X6),X29),X79)
& hBOOL(hAPP(X8,X29))
& hBOOL(hAPP(c_List_Olistsp(X6,X8),X79)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Osimps) ).
fof(fact_some__eq__trivial,axiom,
! [X12,X6] : c_Hilbert__Choice_OEps(X6,hAPP(hAPP(c_COMBC(X6,X6,tc_HOL_Obool),c_fequal),X12)) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_Domain__mono,axiom,
! [X31,X17,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X17,X31)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Relation_ODomain(X6,X14,X17),c_Relation_ODomain(X6,X14,X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(fact_curry__split,axiom,
! [X2,X47,X14,X6] : c_Product__Type_Ocurry(X6,X14,X47,hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X47),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__split) ).
fof(fact_rtrancl__subset,axiom,
! [X24,X13,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X13,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X24,c_Transitive__Closure_Ortrancl(X6,X13))
=> c_Transitive__Closure_Ortrancl(X6,X24) = c_Transitive__Closure_Ortrancl(X6,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [X18,X19,X42,X6,X47,X14] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X47,X6),X42),hAPP(hAPP(c_Product__Type_OPair(X14,X47),X19),X18)) = hAPP(hAPP(X42,X19),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_split__conv,axiom,
! [X18,X19,X2,X6,X47,X14] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X47,X6),X2),hAPP(hAPP(c_Product__Type_OPair(X14,X47),X19),X18)) = hAPP(hAPP(X2,X19),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).
fof(fact_Int__greatest,axiom,
! [X7,X8,X46,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X46,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X46,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X46,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).
fof(fact_Int__assoc,axiom,
! [X46,X7,X8,X6] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X46) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X7,X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).
fof(fact_Int__left__commute,axiom,
! [X46,X7,X8,X6] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X7,X46)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X7,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).
fof(fact_inf__mono,axiom,
! [X101,X37,X94,X38,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X38,X94)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X37,X101)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37),c_Lattices_Osemilattice__inf__class_Oinf(X6,X94,X101)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).
fof(fact_listrel1__mono,axiom,
! [X31,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,X31)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_HOL_Obool),c_List_Olistrel1(X6,X17),c_List_Olistrel1(X6,X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel__mono,axiom,
! [X31,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,X31)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_HOL_Obool),c_List_Olistrel(X6,X17),c_List_Olistrel(X6,X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__mono) ).
fof(fact_inf1I,axiom,
! [X6,X7,X12,X8] :
( hBOOL(hAPP(X8,X12))
=> ( hBOOL(hAPP(X7,X12))
=> hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [X31,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,c_Transitive__Closure_Ortrancl(X6,X31))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X6,X17),c_Transitive__Closure_Ortrancl(X6,X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_append__assoc,axiom,
! [X55,X43,X34,X6] : hAPP(hAPP(c_List_Oappend(X6),hAPP(hAPP(c_List_Oappend(X6),X34),X43)),X55) = hAPP(hAPP(c_List_Oappend(X6),X34),hAPP(hAPP(c_List_Oappend(X6),X43),X55)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).
fof(fact_append__Cons,axiom,
! [X43,X34,X35,X6] : hAPP(hAPP(c_List_Oappend(X6),hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34)),X43) = hAPP(hAPP(c_List_Olist_OCons(X6),X35),hAPP(hAPP(c_List_Oappend(X6),X34),X43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).
fof(fact_predicate2D,axiom,
! [X11,X12,X104,X16,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X16,X104)
=> ( hBOOL(hAPP(hAPP(X16,X12),X11))
=> hBOOL(hAPP(hAPP(X104,X12),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X104,X14,X6,X11,X12,X16] :
( hBOOL(hAPP(hAPP(X16,X12),X11))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X16,X104)
=> hBOOL(hAPP(hAPP(X104,X12),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_set__rev__mp,axiom,
! [X7,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> hBOOL(hAPP(hAPP(c_member(X6),X12),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_psubsetD,axiom,
! [X5,X7,X8,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_in__mono,axiom,
! [X12,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X12),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_set__mp,axiom,
! [X12,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X12),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_subsetD,axiom,
! [X5,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_rtrancl__mono,axiom,
! [X31,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,X31)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X6,X17),c_Transitive__Closure_Ortrancl(X6,X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_DomainP_Ointros,axiom,
! [X14,X6,X18,X19,X17] :
( hBOOL(hAPP(hAPP(X17,X19),X18))
=> c_Predicate_ODomainP(X6,X14,X17,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_RangeP_Ointros,axiom,
! [X14,X6,X18,X19,X17] :
( hBOOL(hAPP(hAPP(X17,X19),X18))
=> c_Predicate_ORangeP(X6,X14,X17,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_takeWhile__dropWhile__id,axiom,
! [X51,X16,X6] : hAPP(hAPP(c_List_Oappend(X6),c_List_OtakeWhile(X6,X16,X51)),c_List_OdropWhile(X6,X16,X51)) = X51,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [X17,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_HOL_Obool),c_List_Olistrel1(X6,c_Transitive__Closure_Ortrancl(X6,X17)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_butlast__snoc,axiom,
! [X35,X34,X6] : c_List_Obutlast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),hAPP(hAPP(c_List_Olist_OCons(X6),X35),c_List_Olist_ONil(X6)))) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__snoc) ).
fof(fact_last__snoc,axiom,
! [X35,X34,X6] : c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),hAPP(hAPP(c_List_Olist_OCons(X6),X35),c_List_Olist_ONil(X6)))) = X35,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__snoc) ).
fof(fact_single__valued__subset,axiom,
! [X31,X17,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X17,X31)
=> ( c_Relation_Osingle__valued(X6,X14,X31)
=> c_Relation_Osingle__valued(X6,X14,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(fact_length__dropWhile__le,axiom,
! [X51,X16,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OdropWhile(X6,X16,X51)),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).
fof(fact_length__takeWhile__le,axiom,
! [X51,X16,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X51)),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_le__inf__iff,axiom,
! [X9,X11,X12,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,c_Lattices_Osemilattice__inf__class_Oinf(X6,X11,X9))
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
& c_Orderings_Oord__class_Oless__eq(X6,X12,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).
fof(fact_le__infI,axiom,
! [X37,X38,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X38)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X37)
=> c_Orderings_Oord__class_Oless__eq(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).
fof(fact_inf__greatest,axiom,
! [X93,X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X93)
=> c_Orderings_Oord__class_Oless__eq(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,X93)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).
fof(fact_accp__downward,axiom,
! [X19,X18,X17,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X18))
=> ( hBOOL(hAPP(hAPP(X17,X19),X18))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
fof(fact_acc__subset,axiom,
! [X76,X77,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X77,X76)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Wellfounded_Oacc(X6,X76),c_Wellfounded_Oacc(X6,X77)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(fact_inf_Oassoc,axiom,
! [X94,X37,X38,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37),X94) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,c_Lattices_Osemilattice__inf__class_Oinf(X6,X37,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__assoc,axiom,
! [X93,X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44),X93) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [X93,X44,X35,X6] :
( class_Lattices_Olattice(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44),X93) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_inf_Oleft__commute,axiom,
! [X94,X38,X37,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X37,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X94)) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,c_Lattices_Osemilattice__inf__class_Oinf(X6,X37,X94)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__left__commute,axiom,
! [X93,X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,X93)) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [X93,X44,X35,X6] :
( class_Lattices_Olattice(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,X93)) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_append__butlast__last__id,axiom,
! [X6,X34] :
( X34 != c_List_Olist_ONil(X6)
=> hAPP(hAPP(c_List_Oappend(X6),c_List_Obutlast(X6,X34)),hAPP(hAPP(c_List_Olist_OCons(X6),c_List_Olast(X6,X34)),c_List_Olist_ONil(X6))) = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
fof(fact_accp__subset,axiom,
! [X76,X77,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X6,tc_HOL_Obool)),X77,X76)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Wellfounded_Oaccp(X6,X76),c_Wellfounded_Oaccp(X6,X77)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__subset) ).
fof(fact_subset__psubset__trans,axiom,
! [X46,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X7,X46)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X46,X7,X8,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X46)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_subset__trans,axiom,
! [X46,X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X46)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X46) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_trans__Int,axiom,
! [X31,X17,X6] :
( c_Relation_Otrans(X6,X17)
=> ( c_Relation_Otrans(X6,X31)
=> c_Relation_Otrans(X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Int) ).
fof(fact_listsp__inf__eq,axiom,
! [X7,X8,X6] : c_List_Olistsp(X6,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X6),tc_HOL_Obool),c_List_Olistsp(X6,X8),c_List_Olistsp(X6,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).
fof(fact_Int__left__absorb,axiom,
! [X7,X8,X6] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [X17,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6)),tc_HOL_Obool),c_List_Olistrel(X6,X17),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_Pair__inject,axiom,
! [X92,X26,X37,X38,X14,X6] :
( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X38),X37) = hAPP(hAPP(c_Product__Type_OPair(X6,X14),X26),X92)
=> ~ ( X38 = X26
=> X37 != X92 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(fact_Pair__eq,axiom,
! [X22,X23,X18,X19,X14,X6] :
( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X18) = hAPP(hAPP(c_Product__Type_OPair(X6,X14),X23),X22)
<=> ( X19 = X23
& X18 = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
fof(fact_impossible__Cons,axiom,
! [X35,X43,X34,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X34),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X43))
=> X34 != hAPP(hAPP(c_List_Olist_OCons(X6),X35),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_impossible__Cons) ).
fof(fact_inf__apply,axiom,
! [X12,X1,X2,X14,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14,X6),X2,X1),X12) = c_Lattices_Osemilattice__inf__class_Oinf(X6,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,X14,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14,X6),X2,X1),X12) = c_Lattices_Osemilattice__inf__class_Oinf(X6,hAPP(X2,X12),hAPP(X1,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).
fof(fact_rotate__simps,axiom,
! [X34,X35,X14,X6] :
( c_List_Orotate1(X6,c_List_Olist_ONil(X6)) = c_List_Olist_ONil(X6)
& c_List_Orotate1(X14,hAPP(hAPP(c_List_Olist_OCons(X14),X35),X34)) = hAPP(hAPP(c_List_Oappend(X14),X34),hAPP(hAPP(c_List_Olist_OCons(X14),X35),c_List_Olist_ONil(X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__simps) ).
fof(fact_snoc__eq__iff__butlast,axiom,
! [X52,X12,X51,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_Olist_ONil(X6))) = X52
<=> ( X52 != c_List_Olist_ONil(X6)
& c_List_Obutlast(X6,X52) = X51
& c_List_Olast(X6,X52) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_append__eq__appendI,axiom,
! [X54,X43,X55,X56,X34,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X34),X56) = X55
=> ( X43 = hAPP(hAPP(c_List_Oappend(X6),X56),X54)
=> hAPP(hAPP(c_List_Oappend(X6),X34),X43) = hAPP(hAPP(c_List_Oappend(X6),X55),X54) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
fof(fact_Cons__eq__appendI,axiom,
! [X55,X34,X43,X56,X35,X6] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X35),X56) = X43
=> ( X34 = hAPP(hAPP(c_List_Oappend(X6),X56),X55)
=> hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34) = hAPP(hAPP(c_List_Oappend(X6),X43),X55) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
fof(fact_listsp__mono,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X6),tc_HOL_Obool),c_List_Olistsp(X6,X8),c_List_Olistsp(X6,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__mono) ).
fof(fact_lists__mono,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X6),tc_HOL_Obool),c_List_Olists(X6,X8),c_List_Olists(X6,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__mono) ).
fof(fact_listrelp_Oequations_I1_J,axiom,
! [X17,X6] : c_List_Olistrelp(X6,X17,c_List_Olist_ONil(X6),c_List_Olist_ONil(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(fact_listrelp_ONil,axiom,
! [X17,X6] : c_List_Olistrelp(X6,X17,c_List_Olist_ONil(X6),c_List_Olist_ONil(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
fof(fact_maps__simps_I2_J,axiom,
! [X2,X6,X14] : c_List_Omaps(X14,X6,X2,c_List_Olist_ONil(X14)) = c_List_Olist_ONil(X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).
fof(fact_less__infI1,axiom,
! [X37,X35,X38,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X38,X35)
=> c_Orderings_Oord__class_Oless(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).
fof(fact_less__infI2,axiom,
! [X38,X35,X37,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X37,X35)
=> c_Orderings_Oord__class_Oless(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).
fof(fact_le__infI1,axiom,
! [X37,X35,X38,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X38,X35)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [X38,X35,X37,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X37,X35)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37),X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).
fof(fact_image__ident,axiom,
! [X96,X6] : c_Set_Oimage(X6,X6,c_COMBI(X6),X96) = X96,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_set__eq__subset,axiom,
! [X6,X7,X8] :
( X8 = X7
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8)
=> X8 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_eq__mem,axiom,
! [X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),hAPP(c_fequal,X11)))
<=> X12 = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__funD,axiom,
! [X12,X1,X2,X6,X14] :
( class_Orderings_Oord(X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X14),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X14,hAPP(X2,X12),hAPP(X1,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X12,X1,X2,X6,X14] :
( class_Orderings_Oord(X14)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X14),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X14,hAPP(X2,X12),hAPP(X1,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_order__less__trans,axiom,
! [X93,X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ( c_Orderings_Oord__class_Oless(X6,X44,X93)
=> c_Orderings_Oord__class_Oless(X6,X35,X93) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X93,X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> ( c_Orderings_Oord__class_Oless(X6,X44,X93)
=> c_Orderings_Oord__class_Oless(X6,X35,X93) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X93,X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X93)
=> c_Orderings_Oord__class_Oless(X6,X35,X93) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X93,X35,X44,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X44,X35)
=> ( c_Orderings_Oord__class_Oless(X6,X93,X44)
=> c_Orderings_Oord__class_Oless(X6,X93,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X93,X35,X44,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> ( c_Orderings_Oord__class_Oless(X6,X93,X44)
=> c_Orderings_Oord__class_Oless(X6,X93,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X93,X35,X44,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X44,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X93,X44)
=> c_Orderings_Oord__class_Oless(X6,X93,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X93,X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X93)
=> c_Orderings_Oord__class_Oless__eq(X6,X35,X93) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X93,X35,X44,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X93,X44)
=> c_Orderings_Oord__class_Oless__eq(X6,X93,X35) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_lists_ONil,axiom,
! [X8,X6] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),c_List_Olist_ONil(X6)),c_List_Olists(X6,X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_ONil) ).
fof(fact_Int__lower1,axiom,
! [X7,X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [X7,X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).
fof(fact_inf_Oleft__idem,axiom,
! [X37,X38,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37)) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__left__idem,axiom,
! [X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44)) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [X44,X35,X6] :
( class_Lattices_Olattice(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44)) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_partition_Osimps_I1_J,axiom,
! [X16,X6] : c_List_Opartition(X6,X16,c_List_Olist_ONil(X6)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),c_List_Olist_ONil(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_splice_Osimps_I2_J,axiom,
! [X39,X40,X6] : c_List_Osplice(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39),c_List_Olist_ONil(X6)) = hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
fof(fact_some__eq__ex,axiom,
! [X6,X16] :
( hBOOL(hAPP(X16,c_Hilbert__Choice_OEps(X6,X16)))
<=> ? [X91] : hBOOL(hAPP(X16,X91)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
<=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X7)
| X8 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X7)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
& X8 != X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_Int__absorb2,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [X8,X7,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8)
=> c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).
fof(fact_predicate1D,axiom,
! [X12,X104,X16,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X16,X104)
=> ( hBOOL(hAPP(X16,X12))
=> hBOOL(hAPP(X104,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X104,X6,X12,X16] :
( hBOOL(hAPP(X16,X12))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X16,X104)
=> hBOOL(hAPP(X104,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_psubset__imp__subset,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_butlast__append,axiom,
! [X34,X6,X43] :
( ( X43 = c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),X43)) = c_List_Obutlast(X6,X34) )
& ( X43 != c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),X43)) = hAPP(hAPP(c_List_Oappend(X6),X34),c_List_Obutlast(X6,X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__append) ).
fof(fact_butlast_Osimps_I2_J,axiom,
! [X35,X6,X34] :
( ( X34 = c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34)) = c_List_Olist_ONil(X6) )
& ( X34 != c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34)) = hAPP(hAPP(c_List_Olist_OCons(X6),X35),c_List_Obutlast(X6,X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
fof(fact_mem__def,axiom,
! [X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
<=> hBOOL(hAPP(X8,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_nat__less__cases,axiom,
! [X16,X74,X110] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X110,X74)
=> hBOOL(hAPP(hAPP(X16,X74),X110)) )
=> ( ( X110 = X74
=> hBOOL(hAPP(hAPP(X16,X74),X110)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X74,X110)
=> hBOOL(hAPP(hAPP(X16,X74),X110)) )
=> hBOOL(hAPP(hAPP(X16,X74),X110)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_xt1_I5_J,axiom,
! [X35,X44,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> X35 = X44 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X44,X35,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> X35 = X44 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X12,X11,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X11,X12)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> X12 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X11,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( X12 = X11
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
& c_Orderings_Oord__class_Oless__eq(X6,X11,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_inf__le1,axiom,
! [X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44),X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [X44,X35,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44),X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le2,axiom,
! [X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [X44,X35,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_list_Oinject,axiom,
! [X32,X23,X33,X19,X6] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X19),X33) = hAPP(hAPP(c_List_Olist_OCons(X6),X23),X32)
<=> ( X19 = X23
& X33 = X32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
fof(fact_append__same__eq,axiom,
! [X57,X51,X52,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X52),X51) = hAPP(hAPP(c_List_Oappend(X6),X57),X51)
<=> X52 = X57 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).
fof(fact_same__append__eq,axiom,
! [X57,X52,X51,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X51),X52) = hAPP(hAPP(c_List_Oappend(X6),X51),X57)
<=> X52 = X57 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).
fof(fact_Int__commute,axiom,
! [X7,X8,X6] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X7,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).
fof(fact_order__less__le,axiom,
! [X11,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
& X12 != X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__le__less,axiom,
! [X11,X12,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> ( c_Orderings_Oord__class_Oless(X6,X12,X11)
| X12 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__neq__le__trans,axiom,
! [X37,X38,X6] :
( class_Orderings_Oorder(X6)
=> ( X38 != X37
=> ( c_Orderings_Oord__class_Oless__eq(X6,X38,X37)
=> c_Orderings_Oord__class_Oless(X6,X38,X37) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X44,X35,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
| X35 = X44 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [X37,X38,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X38,X37)
=> ( X38 != X37
=> c_Orderings_Oord__class_Oless(X6,X38,X37) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [X38,X37,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X37,X38)
=> ( X38 != X37
=> c_Orderings_Oord__class_Oless(X6,X37,X38) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_xt1_I12_J,axiom,
! [X37,X38,X6] :
( class_Orderings_Oorder(X6)
=> ( X38 != X37
=> ( c_Orderings_Oord__class_Oless__eq(X6,X37,X38)
=> c_Orderings_Oord__class_Oless(X6,X37,X38) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_le__iff__inf,axiom,
! [X11,X12,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X12,X11) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__absorb1,axiom,
! [X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44) = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).
fof(fact_inf__absorb2,axiom,
! [X35,X44,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44) = X44 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).
fof(fact_order__less__imp__le,axiom,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> c_Orderings_Oord__class_Oless__eq(X6,X35,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_distinct__dropWhile,axiom,
! [X16,X51,X6] :
( c_List_Odistinct(X6,X51)
=> c_List_Odistinct(X6,c_List_OdropWhile(X6,X16,X51)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).
fof(fact_distinct__takeWhile,axiom,
! [X16,X51,X6] :
( c_List_Odistinct(X6,X51)
=> c_List_Odistinct(X6,c_List_OtakeWhile(X6,X16,X51)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
fof(fact_distinct__insert,axiom,
! [X35,X34,X6] :
( c_List_Odistinct(X6,X34)
=> c_List_Odistinct(X6,c_List_Oinsert(X6,X35,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).
fof(fact_last__append,axiom,
! [X34,X6,X43] :
( ( X43 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),X43)) = c_List_Olast(X6,X34) )
& ( X43 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),X43)) = c_List_Olast(X6,X43) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__append) ).
fof(fact_last__appendL,axiom,
! [X34,X6,X43] :
( X43 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),X43)) = c_List_Olast(X6,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendL) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X108,X109] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X109,X108)
| X109 = X108 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X109,X108) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X44,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,X44)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_last__appendR,axiom,
! [X34,X6,X43] :
( X43 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X34),X43)) = c_List_Olast(X6,X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendR) ).
fof(fact_last__ConsR,axiom,
! [X35,X6,X34] :
( X34 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34)) = c_List_Olast(X6,X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsR) ).
fof(fact_last_Osimps,axiom,
! [X35,X6,X34] :
( ( X34 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34)) = X35 )
& ( X34 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34)) = c_List_Olast(X6,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last_Osimps) ).
fof(fact_someI,axiom,
! [X6,X12,X16] :
( hBOOL(hAPP(X16,X12))
=> hBOOL(hAPP(X16,c_Hilbert__Choice_OEps(X6,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
fof(fact_tfl__some,axiom,
! [X6,X102] :
( ? [X3] : hBOOL(hAPP(X102,X3))
=> hBOOL(hAPP(X102,c_Hilbert__Choice_OEps(X6,X102))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
fof(fact_someI__ex,axiom,
! [X6,X16] :
( ? [X91] : hBOOL(hAPP(X16,X91))
=> hBOOL(hAPP(X16,c_Hilbert__Choice_OEps(X6,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
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,
! [X35,X6,X34] :
( X34 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34)) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsL) ).
fof(help_c__COMBK__1,axiom,
! [X116,X115,X14,X6] : hAPP(c_COMBK(X6,X14,X115),X116) = X115,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_linorder__neq__iff,axiom,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( X12 != X11
<=> ( c_Orderings_Oord__class_Oless(X6,X12,X11)
| c_Orderings_Oord__class_Oless(X6,X11,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
| X35 = X44
| c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_insert__Nil,axiom,
! [X35,X6] : c_List_Oinsert(X6,X35,c_List_Olist_ONil(X6)) = hAPP(hAPP(c_List_Olist_OCons(X6),X35),c_List_Olist_ONil(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).
fof(fact_linorder__le__less__linear,axiom,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
| c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
| c_Orderings_Oord__class_Oless__eq(X6,X44,X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_inf_Ocommute,axiom,
! [X37,X38,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__commute,axiom,
! [X44,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [X44,X35,X6] :
( class_Lattices_Olattice(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X44) = c_Lattices_Osemilattice__inf__class_Oinf(X6,X44,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_less__imp__neq,axiom,
! [X44,X35,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> X35 != X44 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X44,X35,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> X35 != X44 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X44,X35,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> X44 != X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_listsp_Oequations_I1_J,axiom,
! [X8,X6] : hBOOL(hAPP(c_List_Olistsp(X6,X8),c_List_Olist_ONil(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).
fof(fact_listsp_ONil,axiom,
! [X8,X6] : hBOOL(hAPP(c_List_Olistsp(X6,X8),c_List_Olist_ONil(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).
fof(fact_append__is__Nil__conv,axiom,
! [X52,X51,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X51),X52) = c_List_Olist_ONil(X6)
<=> ( X51 = c_List_Olist_ONil(X6)
& X52 = c_List_Olist_ONil(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_Nil__is__append__conv,axiom,
! [X52,X51,X6] :
( c_List_Olist_ONil(X6) = hAPP(hAPP(c_List_Oappend(X6),X51),X52)
<=> ( X51 = c_List_Olist_ONil(X6)
& X52 = c_List_Olist_ONil(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_append__self__conv2,axiom,
! [X52,X51,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X51),X52) = X52
<=> X51 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).
fof(fact_append__self__conv,axiom,
! [X52,X51,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X51),X52) = X51
<=> X52 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).
fof(fact_self__append__conv,axiom,
! [X52,X6,X51] :
( X51 = hAPP(hAPP(c_List_Oappend(X6),X51),X52)
<=> X52 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv) ).
fof(fact_self__append__conv2,axiom,
! [X51,X6,X52] :
( X52 = hAPP(hAPP(c_List_Oappend(X6),X51),X52)
<=> X51 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).
fof(fact_list_Osimps_I3_J,axiom,
! [X25,X26,X6] : hAPP(hAPP(c_List_Olist_OCons(X6),X26),X25) != c_List_Olist_ONil(X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X25,X26,X6] : c_List_Olist_ONil(X6) != hAPP(hAPP(c_List_Olist_OCons(X6),X26),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_less__not__refl2,axiom,
! [X109,X108] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X108,X109)
=> X109 != X108 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
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_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [X17,X6] : c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_not__Cons__self2,axiom,
! [X34,X35,X6] : hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34) != X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [X35,X6,X34] : X34 != hAPP(hAPP(c_List_Olist_OCons(X6),X35),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(fact_Range__Id__on,axiom,
! [X8,X6] : c_Relation_ORange(X6,X6,c_Relation_OId__on(X6,X8)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).
fof(fact_Domain__Id__on,axiom,
! [X8,X6] : c_Relation_ODomain(X6,X6,c_Relation_OId__on(X6,X8)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_equalityD1,axiom,
! [X6,X7,X8] :
( X8 = X7
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X6,X7,X8] :
( X8 = X7
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_single__valued__Id__on,axiom,
! [X8,X6] : c_Relation_Osingle__valued(X6,X6,c_Relation_OId__on(X6,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
fof(help_c__fequal__2,axiom,
! [X11,X12] :
( X12 != X11
| hBOOL(hAPP(hAPP(c_fequal,X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_Int__absorb,axiom,
! [X8,X6] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X8) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_distinct1__rotate,axiom,
! [X51,X6] :
( c_List_Odistinct(X6,c_List_Orotate1(X6,X51))
<=> c_List_Odistinct(X6,X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct1__rotate) ).
fof(fact_subset__refl,axiom,
! [X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_listrel__trans,axiom,
! [X17,X6] :
( c_Relation_Otrans(X6,X17)
=> c_Relation_Otrans(tc_List_Olist(X6),c_List_Olistrel(X6,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__trans) ).
fof(fact_lexord__transI,axiom,
! [X17,X6] :
( c_Relation_Otrans(X6,X17)
=> c_Relation_Otrans(tc_List_Olist(X6),c_List_Olexord(X6,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__transI) ).
fof(fact_eq__Nil__appendI,axiom,
! [X6,X43,X34] :
( X34 = X43
=> X34 = hAPP(hAPP(c_List_Oappend(X6),c_List_Olist_ONil(X6)),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
fof(fact_distinct__butlast,axiom,
! [X6,X34] :
( X34 != c_List_Olist_ONil(X6)
=> ( c_List_Odistinct(X6,X34)
=> c_List_Odistinct(X6,c_List_Obutlast(X6,X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__butlast) ).
fof(fact_length__rotate1,axiom,
! [X34,X6] : c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_Orotate1(X6,X34)) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate1) ).
fof(fact_order__eq__refl,axiom,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( X35 = X44
=> c_Orderings_Oord__class_Oless__eq(X6,X35,X44) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_append__Nil,axiom,
! [X43,X6] : hAPP(hAPP(c_List_Oappend(X6),c_List_Olist_ONil(X6)),X43) = X43,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).
fof(fact_dropWhile_Osimps_I1_J,axiom,
! [X16,X6] : c_List_OdropWhile(X6,X16,c_List_Olist_ONil(X6)) = c_List_Olist_ONil(X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
fof(fact_takeWhile_Osimps_I1_J,axiom,
! [X16,X6] : c_List_OtakeWhile(X6,X16,c_List_Olist_ONil(X6)) = c_List_Olist_ONil(X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(fact_inf_Oidem,axiom,
! [X38,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X38) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(fact_inf__idem,axiom,
! [X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Lattices_Osemilattice__inf__class_Oinf(X6,X35,X35) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(fact_order__refl,axiom,
! [X35,X6] :
( class_Orderings_Opreorder(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X35,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_splice_Osimps_I1_J,axiom,
! [X43,X6] : c_List_Osplice(X6,c_List_Olist_ONil(X6),X43) = X43,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(fact_splice__Nil2,axiom,
! [X34,X6] : c_List_Osplice(X6,X34,c_List_Olist_ONil(X6)) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).
fof(fact_append__Nil2,axiom,
! [X34,X6] : hAPP(hAPP(c_List_Oappend(X6),X34),c_List_Olist_ONil(X6)) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).
fof(fact_rtrancl__idemp,axiom,
! [X17,X6] : c_Transitive__Closure_Ortrancl(X6,c_Transitive__Closure_Ortrancl(X6,X17)) = c_Transitive__Closure_Ortrancl(X6,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_trans__Id__on,axiom,
! [X8,X6] : c_Relation_Otrans(X6,c_Relation_OId__on(X6,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id__on) ).
fof(fact_trans__rtrancl,axiom,
! [X17,X6] : c_Relation_Otrans(X6,c_Transitive__Closure_Ortrancl(X6,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
fof(fact_some__sym__eq__trivial,axiom,
! [X12,X6] : c_Hilbert__Choice_OEps(X6,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,X6] :
( c_List_Orotate1(X6,X51) = c_List_Olist_ONil(X6)
<=> X51 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_butlast_Osimps_I1_J,axiom,
! [X6] : c_List_Obutlast(X6,c_List_Olist_ONil(X6)) = c_List_Olist_ONil(X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
fof(help_c__COMBI__1,axiom,
! [X115,X6] : hAPP(c_COMBI(X6),X115) = X115,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [X6] : c_List_Odistinct(X6,c_List_Olist_ONil(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_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))),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),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),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____))),v_b____)),v_a____))),v_a____)),v_c____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096) ).
fof(fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_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))),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),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____))),v_b____)),v_a____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096) ).
fof(fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_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))),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',fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096) ).
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,
! [X17,X86,X87,X88,X64,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X64),X88) != hAPP(hAPP(c_Product__Type_OPair(X6,X14),X87),X86)
=> ~ ! [X29,X30] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X64),X88)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30))),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X6,X14),tc_prod(X6,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X6,X14),tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X29),X30)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X87),X86))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2]) ).
fof(i_0_510,plain,
! [X78,X5,X47,X14,X9,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X47,tc_fun(X6,tc_HOL_Obool)),X5),X78)))
=> ~ ! [X3,X65] :
( X78 = hAPP(hAPP(c_Product__Type_OPair(X14,X47),X3),X65)
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(X5,X3),X65))) ) ),
inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).
fof(i_0_511,plain,
! [X17,X52,X11,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_List_Olistrel1(X6,X17)))
=> ( ! [X3] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X52)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X11)),X17)) )
=> ~ ! [X75] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X75),X52)),c_List_Olistrel1(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Cons__listrel1E2]) ).
fof(i_0_512,negated_conjecture,
~ ! [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),v_b____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X4)),v_c____),v_b____)),v_b____),v_a____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X4)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_513,plain,
! [X17,X63,X53,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X12),X53)),hAPP(hAPP(c_List_Oappend(X6),X12),X63))),c_List_Olexord(X6,X17)))
=> ( ! [X29] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X29),X29)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X53),X63)),c_List_Olexord(X6,X17))) ) ),
inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).
fof(i_0_514,plain,
! [X17,X52,X51,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)),X52)),c_List_Olistrel1(X6,X17)))
=> ( ! [X65] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X6),X65),X51)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X65)),X17)) )
=> ~ ! [X75] :
( X52 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X75)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),X75)),c_List_Olistrel1(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Cons__listrel1E1]) ).
fof(i_0_515,plain,
! [X17,X52,X11,X51,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))),c_List_Olistrel(X6,X17)))
=> ~ ! [X3,X67] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X67)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X11)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X67),X52)),c_List_Olistrel(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).
fof(i_0_516,plain,
! [X17,X51,X52,X11,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52)),X51)),c_List_Olistrel(X6,X17)))
=> ~ ! [X65,X66] :
( X51 = hAPP(hAPP(c_List_Olist_OCons(X6),X65),X66)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X65)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X52),X66)),c_List_Olistrel(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).
fof(i_0_517,plain,
! [X2407,X2408,X2409,X2410,X2411,X2412,X2413,X2414,X2415,X2416,X2417] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2417,X2416)),X2415),c_FuncSet_OPi(X2417,X2416,X2414,c_COMBK(tc_fun(X2416,tc_HOL_Obool),X2417,X2413))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2416,X2412)),X2411),c_FuncSet_OPi(X2416,X2412,X2413,c_COMBK(tc_fun(X2412,tc_HOL_Obool),X2416,X2410))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2412,X2409)),X2408),c_FuncSet_OPi(X2412,X2409,X2410,c_COMBK(tc_fun(X2409,tc_HOL_Obool),X2412,X2407))))
| c_FuncSet_Ocompose(X2417,X2412,X2409,X2414,X2408,c_FuncSet_Ocompose(X2417,X2416,X2412,X2414,X2411,X2415)) = c_FuncSet_Ocompose(X2417,X2416,X2409,X2414,c_FuncSet_Ocompose(X2416,X2412,X2409,X2413,X2408,X2411),X2415) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__assoc])]) ).
fof(i_0_518,plain,
! [X3492,X3493,X3494,X3495,X3496,X3497] : c_FuncSet_Ocompose(X3497,X3496,X3495,X3494,X3493,X3492) = c_FuncSet_Orestrict(X3497,X3495,hAPP(hAPP(c_COMBB(X3496,X3495,X3497),X3493),X3492),X3494),
inference(variable_rename,[status(thm)],[fact_compose__def]) ).
fof(i_0_519,plain,
! [X2386,X2387,X2388,X2389,X2390,X2391,X2392,X2393] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2393,X2392)),X2391),c_FuncSet_OPi(X2393,X2392,X2390,c_COMBK(tc_fun(X2392,tc_HOL_Obool),X2393,X2389))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2392,X2388)),X2387),c_FuncSet_OPi(X2392,X2388,X2389,c_COMBK(tc_fun(X2388,tc_HOL_Obool),X2392,X2386))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2393,X2388)),c_FuncSet_Ocompose(X2393,X2392,X2388,X2390,X2387,X2391)),c_FuncSet_OPi(X2393,X2388,X2390,c_COMBK(tc_fun(X2388,tc_HOL_Obool),X2393,X2386)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__compose])]) ).
fof(i_0_520,plain,
! [X17,X14,X18,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X18),c_Relation_ORange(X14,X6,X17)))
=> ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X6)),hAPP(hAPP(c_Product__Type_OPair(X14,X6),X3),X18)),X17)) ),
inference(fof_simplification,[status(thm)],[fact_RangeE]) ).
fof(i_0_521,plain,
! [X3473,X3474,X3475,X3476,X3477] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3477,X3476)),X3475),c_FuncSet_OPi(X3477,X3476,X3474,c_COMBK(tc_fun(X3476,tc_HOL_Obool),X3477,X3473))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3477,X3476)),X3475),c_FuncSet_Oextensional(X3477,X3476,X3474)))
| c_FuncSet_Ocompose(X3477,X3476,X3476,X3474,c_FuncSet_Orestrict(X3476,X3476,c_COMBI(X3476),X3473),X3475) = X3475 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__compose])]) ).
fof(i_0_522,plain,
! [X3449,X3450,X3451,X3452,X3453,X3454] : hBOOL(hAPP(hAPP(c_member(tc_fun(X3454,X3453)),c_FuncSet_Ocompose(X3454,X3452,X3453,X3451,X3450,X3449)),c_FuncSet_Oextensional(X3454,X3453,X3451))),
inference(variable_rename,[status(thm)],[fact_compose__extensional]) ).
fof(i_0_523,plain,
! [X11,X17,X6] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X17))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X11),X11)),c_List_Olexord(X6,X17))) ),
inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).
fof(i_0_524,plain,
! [X1,X2,X14,X8,X19,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X19) = hAPP(X1,X19) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X19) = hAPP(X2,X19) ) ),
inference(fof_simplification,[status(thm)],[fact_override__on__def]) ).
fof(i_0_525,plain,
! [X1,X2,X14,X8,X19,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X19) = hAPP(X2,X19) ),
inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin]) ).
fof(i_0_526,plain,
! [X3478,X3479,X3480,X3481,X3482] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3482,X3481)),X3480),c_FuncSet_OPi(X3482,X3481,X3479,c_COMBK(tc_fun(X3481,tc_HOL_Obool),X3482,X3478))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3482,X3481)),X3480),c_FuncSet_Oextensional(X3482,X3481,X3479)))
| c_FuncSet_Ocompose(X3482,X3482,X3481,X3479,X3480,c_FuncSet_Orestrict(X3482,X3482,c_COMBI(X3482),X3479)) = X3480 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__Id])]) ).
fof(i_0_527,plain,
! [X17,X14,X19,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X19),c_Relation_ODomain(X6,X14,X17)))
=> ~ ! [X65] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X65)),X17)) ),
inference(fof_simplification,[status(thm)],[fact_DomainE]) ).
fof(i_0_528,plain,
! [X3584,X3585,X3586,X3587,X3588] :
( c_Set_Oimage(X3588,X3587,X3586,X3585) != X3584
| c_FuncSet_Ocompose(X3587,X3588,X3587,X3584,X3586,c_FuncSet_Orestrict(X3587,X3588,c_Hilbert__Choice_Oinv__into(X3588,X3587,X3585,X3586),X3584)) = c_FuncSet_Orestrict(X3587,X3587,c_COMBI(X3587),X3584) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__id__inv__into])]) ).
fof(i_0_529,plain,
! [X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),c_Arrow__Order__Mirabelle_OLin))
=> ( X12 != X11
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X11)),X10))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X12)),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_530,plain,
! [X18,X19,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X10),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),X19),X18)),X10))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X19)),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_531,plain,
! [X13,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X13)))
=> ~ ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X69),X12)),X13))
=> hBOOL(hAPP(hAPP(c_member(X6),X69),c_Wellfounded_Oacc(X6,X13))) ) ),
inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).
fof(i_0_532,plain,
! [X17,X51,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),X51)),c_List_Olistrel1(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).
fof(i_0_533,plain,
! [X17,X52,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),c_List_Olist_ONil(X6)),X52)),c_List_Olex(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).
fof(i_0_534,plain,
! [X17,X51,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),c_List_Olist_ONil(X6))),c_List_Olistrel1(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).
fof(i_0_535,plain,
! [X17,X51,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X51),c_List_Olist_ONil(X6))),c_List_Olex(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).
fof(i_0_536,plain,
! [X17,X12,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X6),tc_List_Olist(X6))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X6),tc_List_Olist(X6)),X12),c_List_Olist_ONil(X6))),c_List_Olexord(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).
fof(i_0_537,plain,
! [X3346,X3347,X3348,X3349,X3350,X3351,X3352,X3353] :
( c_Set_Oimage(X3353,X3352,X3351,X3350) != X3349
| c_Set_Oimage(X3352,X3348,X3347,X3349) != X3346
| c_Set_Oimage(X3353,X3348,c_FuncSet_Ocompose(X3353,X3352,X3348,X3350,X3347,X3351),X3350) = X3346 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__compose])]) ).
fof(i_0_538,plain,
! [X12,X7,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_OPi(X6,X14,X8,X7)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X12)),hAPP(X7,X12)))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_539,plain,
! [X12,X97,X24,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional__funcset(X6,X14,X24,X97)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X24))
=> hAPP(X2,X12) = c_HOL_Oundefined(X14) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__funcset__arb]) ).
fof(i_0_540,plain,
! [X2,X14,X17,X12,X11,X6] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X17))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X2),X17),X12),X11) = hAPP(X2,X11) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X12)),X17))
=> hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X6,X14),X2),X17),X12),X11) = c_HOL_Oundefined(X14) ) ),
inference(fof_simplification,[status(thm)],[fact_cut__def]) ).
fof(i_0_541,plain,
! [X11,X12,X6] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_List_Omeasures(X6,c_List_Olist_ONil(tc_fun(X6,tc_Nat_Onat))))),
inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J]) ).
fof(i_0_542,plain,
! [X11,X13,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Relation_ODomain(X6,X6,X13)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),c_Transitive__Closure_Ortrancl(X6,X13)))
<=> X12 = X11 ) ),
inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(i_0_543,plain,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X8,X7),X12),X11))
=> ~ ( hBOOL(hAPP(hAPP(X8,X12),X11))
=> ~ hBOOL(hAPP(hAPP(X7,X12),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf2E]) ).
fof(i_0_544,plain,
! [X2394,X2395,X2396,X2397,X2398,X2399,X2400] :
( ~ hBOOL(hAPP(hAPP(c_member(X2400),X2399),X2398))
| hAPP(c_FuncSet_Ocompose(X2400,X2397,X2396,X2398,X2395,X2394),X2399) = hAPP(X2395,hAPP(X2394,X2399)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__eq])]) ).
fof(i_0_545,plain,
! [X17,X6] :
( c_Relation_Oirrefl(X6,X17)
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X17)) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(i_0_546,plain,
! [X12,X8,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X14)),X2),c_FuncSet_Oextensional(X6,X14,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(X2,X12) = c_HOL_Oundefined(X14) ) ),
inference(fof_simplification,[status(thm)],[fact_extensional__arb]) ).
fof(i_0_547,plain,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X5),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X5),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_IntE]) ).
fof(i_0_548,plain,
! [X52,X11,X51,X16,X6] :
( c_List_OdropWhile(X6,X16,X51) = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52)
<=> ( X51 = hAPP(hAPP(c_List_Oappend(X6),c_List_OtakeWhile(X6,X16,X51)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X52))
& ~ hBOOL(hAPP(X16,X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).
fof(i_0_549,plain,
! [X2,X14,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = c_HOL_Oundefined(X14) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__def]) ).
fof(i_0_550,plain,
! [X2,X14,X8,X12,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = hAPP(X2,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Orestrict(X6,X14,X2,X8),X12) = c_HOL_Oundefined(X14) ) ),
inference(fof_simplification,[status(thm)],[fact_restrict__apply]) ).
fof(i_0_551,plain,
~ ! [X20] : ~ 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),X20),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_552,plain,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool),X8,X7),X12))
=> ~ ( hBOOL(hAPP(X8,X12))
=> ~ hBOOL(hAPP(X7,X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_inf1E]) ).
fof(i_0_553,plain,
! [X3310,X3311,X3312,X3313,X3314,X3315] : hAPP(hAPP(c_Product__Type_Ointernal__split(X3315,X3314,X3313),X3312),hAPP(hAPP(c_Product__Type_OPair(X3315,X3314),X3311),X3310)) = hAPP(hAPP(X3312,X3311),X3310),
inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).
fof(i_0_554,plain,
! [X3300,X3301,X3302] : c_Product__Type_Ointernal__split(X3302,X3301,X3300) = c_Product__Type_Oprod_Oprod__case(X3302,X3301,X3300),
inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).
fof(i_0_555,plain,
! [X89,X51,X6,X12,X16] :
( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Oappend(X6),X51),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X89))) = c_List_OtakeWhile(X6,X16,X51) ),
inference(fof_simplification,[status(thm)],[fact_takeWhile__tail]) ).
fof(i_0_556,plain,
! [X51,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_OtakeWhile(X6,X16,X51)) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = c_List_Olist_ONil(X6) ) ),
inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).
fof(i_0_557,plain,
! [X37,X38,X35,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X35,c_Lattices_Osemilattice__inf__class_Oinf(X6,X38,X37))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X35,X38)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X35,X37) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__infE]) ).
fof(i_0_558,plain,
! [X1,X2,X6,X14] :
( class_Orderings_Oord(X14)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,X14),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X14),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,X14),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_559,plain,
! [X51,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = c_List_OdropWhile(X6,X16,X51) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X51) ) ),
inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).
fof(i_0_560,plain,
! [X11,X12,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
& ~ c_Orderings_Oord__class_Oless__eq(X6,X11,X12) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_561,plain,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> X12 = X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_562,plain,
! [X38,X37,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X37,X38)
=> ~ c_Orderings_Oord__class_Oless(X6,X38,X37) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_563,plain,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> ( c_Orderings_Oord__class_Oless(X6,X11,X12)
| X12 = X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_564,plain,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> c_Orderings_Oord__class_Oless__eq(X6,X11,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_565,plain,
! [X35,X44,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> ~ c_Orderings_Oord__class_Oless(X6,X35,X44) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_566,plain,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> c_Orderings_Oord__class_Oless(X6,X11,X12) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_567,plain,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ~ c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_568,plain,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ~ c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_569,plain,
! [X37,X38,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X38,X37)
=> ~ c_Orderings_Oord__class_Oless(X6,X37,X38) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_570,plain,
! [X44,X35,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ~ c_Orderings_Oord__class_Oless(X6,X44,X35) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_571,plain,
! [X11,X12,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> X12 = X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_572,plain,
! [X104,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X104))
| hBOOL(X16) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_573,plain,
! [X104,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X104))
| hBOOL(X104) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_574,plain,
! [X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X11))
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_575,plain,
! [X12,X11,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X11,X12)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X12,X11)
<=> X12 = X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_576,plain,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( X35 != X44
=> ( ~ c_Orderings_Oord__class_Oless(X6,X35,X44)
=> c_Orderings_Oord__class_Oless(X6,X44,X35) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_577,plain,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X35,X44)
=> ( X35 != X44
=> c_Orderings_Oord__class_Oless(X6,X44,X35) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_578,plain,
! [X35,X44,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X44,X35)
=> c_Orderings_Oord__class_Oless(X6,X35,X44) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_579,plain,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X35,X44)
=> c_Orderings_Oord__class_Oless__eq(X6,X44,X35) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_580,plain,
! [X44,X35,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X35,X44)
=> c_Orderings_Oord__class_Oless__eq(X6,X44,X35) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_581,plain,
! [X35,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X35,X35) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_582,plain,
! [X104,X16] :
( ~ hBOOL(X16)
| ~ hBOOL(X104)
| hBOOL(hAPP(hAPP(c_fconj,X16),X104)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_583,plain,
! [X6,X7,X8] :
( X8 = X7
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_584,plain,
! [X16] :
( ~ hBOOL(hAPP(c_fNot,X16))
| ~ hBOOL(X16) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(i_0_585,plain,
! [X16] :
( hBOOL(X16)
| hBOOL(hAPP(c_fNot,X16)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(i_0_586,plain,
! [X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3015,X3014),tc_prod(X3015,X3014))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3015,X3014),tc_prod(X3015,X3014)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3013),X3012)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),esk65_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)),esk66_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)))),c_Transitive__Closure_Ortrancl(tc_prod(X3015,X3014),X3009)))
| hBOOL(hAPP(hAPP(X3008,X3011),X3010))
| ~ hBOOL(hAPP(hAPP(X3008,X3013),X3012))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3015,X3014),tc_prod(X3015,X3014))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3015,X3014),tc_prod(X3015,X3014)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3013),X3012)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3011),X3010))),c_Transitive__Closure_Ortrancl(tc_prod(X3015,X3014),X3009))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3015,X3014),tc_prod(X3015,X3014))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3015,X3014),tc_prod(X3015,X3014)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),esk65_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)),esk66_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015))),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),esk67_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)),esk68_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)))),X3009))
| hBOOL(hAPP(hAPP(X3008,X3011),X3010))
| ~ hBOOL(hAPP(hAPP(X3008,X3013),X3012))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3015,X3014),tc_prod(X3015,X3014))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3015,X3014),tc_prod(X3015,X3014)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3013),X3012)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3011),X3010))),c_Transitive__Closure_Ortrancl(tc_prod(X3015,X3014),X3009))) )
& ( hBOOL(hAPP(hAPP(X3008,esk65_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)),esk66_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)))
| hBOOL(hAPP(hAPP(X3008,X3011),X3010))
| ~ hBOOL(hAPP(hAPP(X3008,X3013),X3012))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3015,X3014),tc_prod(X3015,X3014))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3015,X3014),tc_prod(X3015,X3014)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3013),X3012)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3011),X3010))),c_Transitive__Closure_Ortrancl(tc_prod(X3015,X3014),X3009))) )
& ( ~ hBOOL(hAPP(hAPP(X3008,esk67_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)),esk68_8(X3008,X3009,X3010,X3011,X3012,X3013,X3014,X3015)))
| hBOOL(hAPP(hAPP(X3008,X3011),X3010))
| ~ hBOOL(hAPP(hAPP(X3008,X3013),X3012))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3015,X3014),tc_prod(X3015,X3014))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3015,X3014),tc_prod(X3015,X3014)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3013),X3012)),hAPP(hAPP(c_Product__Type_OPair(X3015,X3014),X3011),X3010))),c_Transitive__Closure_Ortrancl(tc_prod(X3015,X3014),X3009))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2])])])]) ).
fof(i_0_587,plain,
! [X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3027,X3026),tc_prod(X3027,X3026))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3027,X3026),tc_prod(X3027,X3026)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),esk69_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)),esk70_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027))),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),esk71_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)),esk72_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)))),X3021))
| hBOOL(hAPP(hAPP(X3020,X3025),X3024))
| ~ hBOOL(hAPP(hAPP(X3020,X3023),X3022))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3027,X3026),tc_prod(X3027,X3026))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3027,X3026),tc_prod(X3027,X3026)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3025),X3024)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3023),X3022))),c_Transitive__Closure_Ortrancl(tc_prod(X3027,X3026),X3021))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3027,X3026),tc_prod(X3027,X3026))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3027,X3026),tc_prod(X3027,X3026)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),esk71_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)),esk72_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027))),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3023),X3022))),c_Transitive__Closure_Ortrancl(tc_prod(X3027,X3026),X3021)))
| hBOOL(hAPP(hAPP(X3020,X3025),X3024))
| ~ hBOOL(hAPP(hAPP(X3020,X3023),X3022))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3027,X3026),tc_prod(X3027,X3026))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3027,X3026),tc_prod(X3027,X3026)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3025),X3024)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3023),X3022))),c_Transitive__Closure_Ortrancl(tc_prod(X3027,X3026),X3021))) )
& ( hBOOL(hAPP(hAPP(X3020,esk71_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)),esk72_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)))
| hBOOL(hAPP(hAPP(X3020,X3025),X3024))
| ~ hBOOL(hAPP(hAPP(X3020,X3023),X3022))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3027,X3026),tc_prod(X3027,X3026))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3027,X3026),tc_prod(X3027,X3026)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3025),X3024)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3023),X3022))),c_Transitive__Closure_Ortrancl(tc_prod(X3027,X3026),X3021))) )
& ( ~ hBOOL(hAPP(hAPP(X3020,esk69_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)),esk70_8(X3020,X3021,X3022,X3023,X3024,X3025,X3026,X3027)))
| hBOOL(hAPP(hAPP(X3020,X3025),X3024))
| ~ hBOOL(hAPP(hAPP(X3020,X3023),X3022))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3027,X3026),tc_prod(X3027,X3026))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3027,X3026),tc_prod(X3027,X3026)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3025),X3024)),hAPP(hAPP(c_Product__Type_OPair(X3027,X3026),X3023),X3022))),c_Transitive__Closure_Ortrancl(tc_prod(X3027,X3026),X3021))) ) ),
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_588,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_c____)),hAPP(v_F,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____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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),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____))),v_b____)),v_a____)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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),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____))),v_b____)),v_a____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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____)))) ) ),
inference(fof_nnf,[status(thm)],[fact_ac]) ).
fof(i_0_589,plain,
! [X3048,X3049,X3050,X3051,X3052,X3053,X3054] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3054,X3053),tc_prod(X3054,X3053))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3054,X3053),tc_prod(X3054,X3053)),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3052),X3051)),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),esk73_7(X3048,X3049,X3050,X3051,X3052,X3053,X3054)),esk74_7(X3048,X3049,X3050,X3051,X3052,X3053,X3054)))),X3048))
| hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3052),X3051) = hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3050),X3049)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3054,X3053),tc_prod(X3054,X3053))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3054,X3053),tc_prod(X3054,X3053)),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3052),X3051)),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3050),X3049))),c_Transitive__Closure_Ortrancl(tc_prod(X3054,X3053),X3048))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3054,X3053),tc_prod(X3054,X3053))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3054,X3053),tc_prod(X3054,X3053)),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),esk73_7(X3048,X3049,X3050,X3051,X3052,X3053,X3054)),esk74_7(X3048,X3049,X3050,X3051,X3052,X3053,X3054))),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3050),X3049))),c_Transitive__Closure_Ortrancl(tc_prod(X3054,X3053),X3048)))
| hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3052),X3051) = hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3050),X3049)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3054,X3053),tc_prod(X3054,X3053))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3054,X3053),tc_prod(X3054,X3053)),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3052),X3051)),hAPP(hAPP(c_Product__Type_OPair(X3054,X3053),X3050),X3049))),c_Transitive__Closure_Ortrancl(tc_prod(X3054,X3053),X3048))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_509])])])]) ).
fof(i_0_590,plain,
! [X3201,X3202,X3203,X3204,X3205,X3206] :
( ( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3206,tc_fun(X3205,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3206,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),X3206),c_COMBC(X3205,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_prod(X3206,X3205)),tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),X3206),hAPP(c_COMBB(tc_prod(X3206,X3205),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool),X3205),c_member(tc_prod(X3206,X3205)))),c_Product__Type_OPair(X3206,X3205)))),X3204),hAPP(hAPP(c_COMBC(X3206,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),X3206),c_COMBC(X3205,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_prod(X3206,X3205)),tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),X3206),hAPP(c_COMBB(tc_prod(X3206,X3205),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool),X3205),c_member(tc_prod(X3206,X3205)))),c_Product__Type_OPair(X3206,X3205)))),X3203)),X3202),X3201))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3206,X3205)),hAPP(hAPP(c_Product__Type_OPair(X3206,X3205),X3202),X3201)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),X3204,X3203))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3206,X3205)),hAPP(hAPP(c_Product__Type_OPair(X3206,X3205),X3202),X3201)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),X3204,X3203)))
| hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3206,tc_fun(X3205,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3206,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),X3206),c_COMBC(X3205,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_prod(X3206,X3205)),tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),X3206),hAPP(c_COMBB(tc_prod(X3206,X3205),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool),X3205),c_member(tc_prod(X3206,X3205)))),c_Product__Type_OPair(X3206,X3205)))),X3204),hAPP(hAPP(c_COMBC(X3206,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_fun(X3205,tc_HOL_Obool)),X3206),c_COMBC(X3205,tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3205,tc_prod(X3206,X3205)),tc_fun(X3205,tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool)),X3206),hAPP(c_COMBB(tc_prod(X3206,X3205),tc_fun(tc_fun(tc_prod(X3206,X3205),tc_HOL_Obool),tc_HOL_Obool),X3205),c_member(tc_prod(X3206,X3205)))),c_Product__Type_OPair(X3206,X3205)))),X3203)),X3202),X3201)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).
fof(i_0_591,plain,
! [X3686,X3687,X3688,X3689,X3690,X3691,X3692,X3694,X3695,X3696,X3697,X3701] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3689,X3689)),hAPP(hAPP(c_Product__Type_OPair(X3689,X3689),esk97_7(X3686,X3687,X3688,X3689,X3690,X3691,X3692)),X3692)),X3687))
| hAPP(hAPP(X3686,X3690),X3692) = hAPP(hAPP(X3686,X3691),X3692)
| ~ c_Recdef_Oadm__wf(X3689,X3688,X3687,X3686) )
& ( hAPP(X3690,esk97_7(X3686,X3687,X3688,X3689,X3690,X3691,X3692)) != hAPP(X3691,esk97_7(X3686,X3687,X3688,X3689,X3690,X3691,X3692))
| hAPP(hAPP(X3686,X3690),X3692) = hAPP(hAPP(X3686,X3691),X3692)
| ~ c_Recdef_Oadm__wf(X3689,X3688,X3687,X3686) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3697,X3697)),hAPP(hAPP(c_Product__Type_OPair(X3697,X3697),X3701),esk100_4(X3694,X3695,X3696,X3697))),X3695))
| hAPP(esk98_4(X3694,X3695,X3696,X3697),X3701) = hAPP(esk99_4(X3694,X3695,X3696,X3697),X3701)
| c_Recdef_Oadm__wf(X3697,X3696,X3695,X3694) )
& ( hAPP(hAPP(X3694,esk98_4(X3694,X3695,X3696,X3697)),esk100_4(X3694,X3695,X3696,X3697)) != hAPP(hAPP(X3694,esk99_4(X3694,X3695,X3696,X3697)),esk100_4(X3694,X3695,X3696,X3697))
| c_Recdef_Oadm__wf(X3697,X3696,X3695,X3694) ) ),
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_592,plain,
! [X2908,X2909,X2910] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2910,hAPP(hAPP(c_COMBC(X2910,tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_fun(X2910,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2910,tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_fun(X2910,tc_HOL_Obool)),X2910),c_COMBC(X2910,tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2910,tc_prod(X2910,X2910)),tc_fun(X2910,tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool)),X2910),hAPP(c_COMBB(tc_prod(X2910,X2910),tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool),X2910),c_member(tc_prod(X2910,X2910)))),c_Product__Type_OPair(X2910,X2910)))),X2909)),X2908))
| hBOOL(hAPP(hAPP(c_member(X2910),X2908),c_Wellfounded_Oacc(X2910,X2909))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2910),X2908),c_Wellfounded_Oacc(X2910,X2909)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2910,hAPP(hAPP(c_COMBC(X2910,tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_fun(X2910,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2910,tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_fun(X2910,tc_HOL_Obool)),X2910),c_COMBC(X2910,tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2910,tc_prod(X2910,X2910)),tc_fun(X2910,tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool)),X2910),hAPP(c_COMBB(tc_prod(X2910,X2910),tc_fun(tc_fun(tc_prod(X2910,X2910),tc_HOL_Obool),tc_HOL_Obool),X2910),c_member(tc_prod(X2910,X2910)))),c_Product__Type_OPair(X2910,X2910)))),X2909)),X2908)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).
fof(i_0_593,plain,
! [X3068,X3069,X3070,X3071] : c_List_Opartition(X3071,X3070,hAPP(hAPP(c_List_Olist_OCons(X3071),X3069),X3068)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3071),tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(hAPP(c_COMBS(tc_List_Olist(X3071),tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3071),tc_fun(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)))),tc_fun(tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)))),tc_List_Olist(X3071)),c_COMBS(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),tc_fun(tc_List_Olist(X3071),tc_fun(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)))),tc_List_Olist(X3071)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_fun(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),tc_List_Olist(X3071)),c_If(tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)),hAPP(X3070,X3069)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X3071),tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),tc_List_Olist(X3071)),c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071))),hAPP(c_List_Olist_OCons(X3071),X3069))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3071),tc_fun(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071))),tc_fun(tc_fun(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_fun(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)))),tc_List_Olist(X3071)),c_COMBB(tc_List_Olist(X3071),tc_prod(tc_List_Olist(X3071),tc_List_Olist(X3071)),tc_List_Olist(X3071))),c_Product__Type_OPair(tc_List_Olist(X3071),tc_List_Olist(X3071)))),hAPP(c_List_Olist_OCons(X3071),X3069)))),c_List_Opartition(X3071,X3070,X3068)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).
fof(i_0_594,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_F,v_P____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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____)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_F,v_P____))) ) ),
inference(fof_nnf,[status(thm)],[fact_ab]) ).
fof(i_0_595,plain,
! [X4009,X4010,X4011,X4012] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4012,tc_fun(X4011,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4012,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),X4012),c_COMBC(X4011,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_prod(X4012,X4011)),tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),X4012),hAPP(c_COMBB(tc_prod(X4012,X4011),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool),X4011),c_member(tc_prod(X4012,X4011)))),c_Product__Type_OPair(X4012,X4011)))),X4010),hAPP(hAPP(c_COMBC(X4012,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),X4012),c_COMBC(X4011,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_prod(X4012,X4011)),tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),X4012),hAPP(c_COMBB(tc_prod(X4012,X4011),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool),X4011),c_member(tc_prod(X4012,X4011)))),c_Product__Type_OPair(X4012,X4011)))),X4009))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),X4010,X4009) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),X4010,X4009)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4012,tc_fun(X4011,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X4012,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),X4012),c_COMBC(X4011,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_prod(X4012,X4011)),tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),X4012),hAPP(c_COMBB(tc_prod(X4012,X4011),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool),X4011),c_member(tc_prod(X4012,X4011)))),c_Product__Type_OPair(X4012,X4011)))),X4010),hAPP(hAPP(c_COMBC(X4012,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_fun(X4011,tc_HOL_Obool)),X4012),c_COMBC(X4011,tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4011,tc_prod(X4012,X4011)),tc_fun(X4011,tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool)),X4012),hAPP(c_COMBB(tc_prod(X4012,X4011),tc_fun(tc_fun(tc_prod(X4012,X4011),tc_HOL_Obool),tc_HOL_Obool),X4011),c_member(tc_prod(X4012,X4011)))),c_Product__Type_OPair(X4012,X4011)))),X4009)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_596,plain,
! [X3383,X3384,X3385,X3386,X3387,X3388] :
( ( X3388 = hAPP(hAPP(c_Product__Type_OPair(X3387,X3386),esk84_6(X3383,X3384,X3385,X3386,X3387,X3388)),esk85_6(X3383,X3384,X3385,X3386,X3387,X3388))
| hBOOL(hAPP(hAPP(c_member(X3385),X3384),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3387,X3386,tc_fun(X3385,tc_HOL_Obool)),X3383),X3388))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3385),X3384),hAPP(hAPP(X3383,esk84_6(X3383,X3384,X3385,X3386,X3387,X3388)),esk85_6(X3383,X3384,X3385,X3386,X3387,X3388))))
| hBOOL(hAPP(hAPP(c_member(X3385),X3384),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3387,X3386,tc_fun(X3385,tc_HOL_Obool)),X3383),X3388))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).
fof(i_0_597,plain,
! [X3635,X3636,X3637,X3638,X3639,X3640,X3641,X3642,X3643,X3644,X3645,X3646,X3647] :
( ( hAPP(hAPP(hAPP(c_Recdef_Ocut(X3640,X3639),X3638),X3637),X3636) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X3640,X3639),X3635),X3637),X3636)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3640,X3640)),hAPP(hAPP(c_Product__Type_OPair(X3640,X3640),X3641),X3636)),X3637))
| hAPP(X3638,X3641) = hAPP(X3635,X3641) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3647,X3647)),hAPP(hAPP(c_Product__Type_OPair(X3647,X3647),esk93_6(X3642,X3643,X3644,X3645,X3646,X3647)),X3643)),X3644))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X3647,X3646),X3645),X3644),X3643) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X3647,X3646),X3642),X3644),X3643) )
& ( hAPP(X3645,esk93_6(X3642,X3643,X3644,X3645,X3646,X3647)) != hAPP(X3642,esk93_6(X3642,X3643,X3644,X3645,X3646,X3647))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X3647,X3646),X3645),X3644),X3643) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X3647,X3646),X3642),X3644),X3643) ) ),
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_598,plain,
! [X2198,X2199,X2200,X2201,X2202,X2203] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2203),X2202)),hAPP(v_F,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),X2201),X2200)),hAPP(v_F,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),X2203),X2202)),hAPP(X2199,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2201),X2200)),hAPP(X2198,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| ~ 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))),X2198),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))),X2199),c_Arrow__Order__Mirabelle_OProf))
| X2202 = X2201
| X2203 = X2200
| X2201 = X2200
| X2203 = 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),X2201),X2200)),hAPP(v_F,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),X2203),X2202)),hAPP(v_F,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),X2203),X2202)),hAPP(X2199,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2201),X2200)),hAPP(X2198,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| ~ 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))),X2198),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))),X2199),c_Arrow__Order__Mirabelle_OProf))
| X2202 = X2201
| X2203 = X2200
| X2201 = X2200
| X2203 = 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),X2203),X2202)),hAPP(v_F,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),X2201),X2200)),hAPP(v_F,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),X2203),X2202)),hAPP(X2199,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2201),X2200)),hAPP(X2198,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| ~ 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))),X2198),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))),X2199),c_Arrow__Order__Mirabelle_OProf))
| X2202 = X2201
| X2203 = X2200
| X2201 = X2200
| X2203 = 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),X2201),X2200)),hAPP(v_F,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),X2203),X2202)),hAPP(v_F,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),X2203),X2202)),hAPP(X2199,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2201),X2200)),hAPP(X2198,esk5_6(X2198,X2199,X2200,X2201,X2202,X2203))))
| ~ 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))),X2198),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))),X2199),c_Arrow__Order__Mirabelle_OProf))
| X2202 = X2201
| X2203 = X2200
| X2201 = X2200
| X2203 = X2202 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_599,plain,
! [X2191,X2192,X2193,X2194,X2195,X2196] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2196),X2195)),hAPP(X2192,esk4_6(X2191,X2192,X2193,X2194,X2195,X2196))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2194),X2193)),hAPP(X2191,esk4_6(X2191,X2192,X2193,X2194,X2195,X2196))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2196),X2195)),hAPP(v_F,X2192)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2194),X2193)),hAPP(v_F,X2191)))
| ~ 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))),X2191),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))),X2192),c_Arrow__Order__Mirabelle_OProf))
| X2195 = X2194
| X2196 = X2193
| X2194 = X2193
| X2196 = 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),X2196),X2195)),hAPP(X2192,esk4_6(X2191,X2192,X2193,X2194,X2195,X2196))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2194),X2193)),hAPP(X2191,esk4_6(X2191,X2192,X2193,X2194,X2195,X2196))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2196),X2195)),hAPP(v_F,X2192)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2194),X2193)),hAPP(v_F,X2191)))
| ~ 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))),X2191),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))),X2192),c_Arrow__Order__Mirabelle_OProf))
| X2195 = X2194
| X2196 = X2193
| X2194 = X2193
| X2196 = X2195 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).
fof(i_0_600,plain,
! [X2608,X2609,X2610,X2611] :
( ( ~ c_List_Olistrelp(X2611,hAPP(hAPP(c_COMBC(X2611,tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_fun(X2611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2611,tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_fun(X2611,tc_HOL_Obool)),X2611),c_COMBC(X2611,tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2611,tc_prod(X2611,X2611)),tc_fun(X2611,tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool)),X2611),hAPP(c_COMBB(tc_prod(X2611,X2611),tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool),X2611),c_member(tc_prod(X2611,X2611)))),c_Product__Type_OPair(X2611,X2611)))),X2610),X2609,X2608)
| 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)),X2609),X2608)),c_List_Olistrel(X2611,X2610))) )
& ( ~ 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)),X2609),X2608)),c_List_Olistrel(X2611,X2610)))
| c_List_Olistrelp(X2611,hAPP(hAPP(c_COMBC(X2611,tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_fun(X2611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2611,tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_fun(X2611,tc_HOL_Obool)),X2611),c_COMBC(X2611,tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2611,tc_prod(X2611,X2611)),tc_fun(X2611,tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool)),X2611),hAPP(c_COMBB(tc_prod(X2611,X2611),tc_fun(tc_fun(tc_prod(X2611,X2611),tc_HOL_Obool),tc_HOL_Obool),X2611),c_member(tc_prod(X2611,X2611)))),c_Product__Type_OPair(X2611,X2611)))),X2610),X2609,X2608) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).
fof(i_0_601,plain,
! [X2894,X2895,X2896,X2897] :
( ( ~ c_Predicate_ODomainP(X2897,X2896,hAPP(hAPP(c_COMBC(X2897,tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_fun(X2896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2896,tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_fun(X2896,tc_HOL_Obool)),X2897),c_COMBC(X2896,tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2896,tc_prod(X2897,X2896)),tc_fun(X2896,tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool)),X2897),hAPP(c_COMBB(tc_prod(X2897,X2896),tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool),X2896),c_member(tc_prod(X2897,X2896)))),c_Product__Type_OPair(X2897,X2896)))),X2895),X2894)
| hBOOL(hAPP(hAPP(c_member(X2897),X2894),c_Relation_ODomain(X2897,X2896,X2895))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2897),X2894),c_Relation_ODomain(X2897,X2896,X2895)))
| c_Predicate_ODomainP(X2897,X2896,hAPP(hAPP(c_COMBC(X2897,tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_fun(X2896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2896,tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_fun(X2896,tc_HOL_Obool)),X2897),c_COMBC(X2896,tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2896,tc_prod(X2897,X2896)),tc_fun(X2896,tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool)),X2897),hAPP(c_COMBB(tc_prod(X2897,X2896),tc_fun(tc_fun(tc_prod(X2897,X2896),tc_HOL_Obool),tc_HOL_Obool),X2896),c_member(tc_prod(X2897,X2896)))),c_Product__Type_OPair(X2897,X2896)))),X2895),X2894) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).
fof(i_0_602,plain,
! [X2890,X2891,X2892,X2893] :
( ( ~ c_Predicate_ORangeP(X2893,X2892,hAPP(hAPP(c_COMBC(X2893,tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_fun(X2892,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2892,tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_fun(X2892,tc_HOL_Obool)),X2893),c_COMBC(X2892,tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2892,tc_prod(X2893,X2892)),tc_fun(X2892,tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool)),X2893),hAPP(c_COMBB(tc_prod(X2893,X2892),tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool),X2892),c_member(tc_prod(X2893,X2892)))),c_Product__Type_OPair(X2893,X2892)))),X2891),X2890)
| hBOOL(hAPP(hAPP(c_member(X2892),X2890),c_Relation_ORange(X2893,X2892,X2891))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2892),X2890),c_Relation_ORange(X2893,X2892,X2891)))
| c_Predicate_ORangeP(X2893,X2892,hAPP(hAPP(c_COMBC(X2893,tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_fun(X2892,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2892,tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_fun(X2892,tc_HOL_Obool)),X2893),c_COMBC(X2892,tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2892,tc_prod(X2893,X2892)),tc_fun(X2892,tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool)),X2893),hAPP(c_COMBB(tc_prod(X2893,X2892),tc_fun(tc_fun(tc_prod(X2893,X2892),tc_HOL_Obool),tc_HOL_Obool),X2892),c_member(tc_prod(X2893,X2892)))),c_Product__Type_OPair(X2893,X2892)))),X2891),X2890) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).
fof(i_0_603,plain,
! [X2205,X2206,X2207,X2208] :
( ( hAPP(hAPP(c_COMBC(X2208,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),X2208),c_COMBC(X2207,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_prod(X2208,X2207)),tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),X2208),hAPP(c_COMBB(tc_prod(X2208,X2207),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool),X2207),c_member(tc_prod(X2208,X2207)))),c_Product__Type_OPair(X2208,X2207)))),X2206) != hAPP(hAPP(c_COMBC(X2208,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),X2208),c_COMBC(X2207,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_prod(X2208,X2207)),tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),X2208),hAPP(c_COMBB(tc_prod(X2208,X2207),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool),X2207),c_member(tc_prod(X2208,X2207)))),c_Product__Type_OPair(X2208,X2207)))),X2205)
| X2206 = X2205 )
& ( X2206 != X2205
| hAPP(hAPP(c_COMBC(X2208,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),X2208),c_COMBC(X2207,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_prod(X2208,X2207)),tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),X2208),hAPP(c_COMBB(tc_prod(X2208,X2207),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool),X2207),c_member(tc_prod(X2208,X2207)))),c_Product__Type_OPair(X2208,X2207)))),X2206) = hAPP(hAPP(c_COMBC(X2208,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_fun(X2207,tc_HOL_Obool)),X2208),c_COMBC(X2207,tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2207,tc_prod(X2208,X2207)),tc_fun(X2207,tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool)),X2208),hAPP(c_COMBB(tc_prod(X2208,X2207),tc_fun(tc_fun(tc_prod(X2208,X2207),tc_HOL_Obool),tc_HOL_Obool),X2207),c_member(tc_prod(X2208,X2207)))),c_Product__Type_OPair(X2208,X2207)))),X2205) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_604,plain,
! [X3391,X3392,X3393,X3394,X3395,X3396] :
( ( X3391 = hAPP(hAPP(c_Product__Type_OPair(X3394,X3393),esk86_6(X3391,X3392,X3393,X3394,X3395,X3396)),esk87_6(X3391,X3392,X3393,X3394,X3395,X3396))
| ~ hBOOL(hAPP(hAPP(c_member(X3396),X3395),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3394,X3393,tc_fun(X3396,tc_HOL_Obool)),X3392),X3391))) )
& ( hBOOL(hAPP(hAPP(c_member(X3396),X3395),hAPP(hAPP(X3392,esk86_6(X3391,X3392,X3393,X3394,X3395,X3396)),esk87_6(X3391,X3392,X3393,X3394,X3395,X3396))))
| ~ hBOOL(hAPP(hAPP(c_member(X3396),X3395),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3394,X3393,tc_fun(X3396,tc_HOL_Obool)),X3392),X3391))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_510])])])]) ).
fof(i_0_605,plain,
! [X3061,X3062,X3063,X3064,X3065] :
( ( X3064 = hAPP(hAPP(c_List_Olist_OCons(X3065),X3063),esk76_5(X3061,X3062,X3063,X3064,X3065))
| X3064 = hAPP(hAPP(c_List_Olist_OCons(X3065),esk75_5(X3061,X3062,X3063,X3064,X3065)),X3062)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3065),tc_List_Olist(X3065))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3065),tc_List_Olist(X3065)),X3064),hAPP(hAPP(c_List_Olist_OCons(X3065),X3063),X3062))),c_List_Olistrel1(X3065,X3061))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3065),tc_List_Olist(X3065))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3065),tc_List_Olist(X3065)),esk76_5(X3061,X3062,X3063,X3064,X3065)),X3062)),c_List_Olistrel1(X3065,X3061)))
| X3064 = hAPP(hAPP(c_List_Olist_OCons(X3065),esk75_5(X3061,X3062,X3063,X3064,X3065)),X3062)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3065),tc_List_Olist(X3065))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3065),tc_List_Olist(X3065)),X3064),hAPP(hAPP(c_List_Olist_OCons(X3065),X3063),X3062))),c_List_Olistrel1(X3065,X3061))) )
& ( X3064 = hAPP(hAPP(c_List_Olist_OCons(X3065),X3063),esk76_5(X3061,X3062,X3063,X3064,X3065))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3065,X3065)),hAPP(hAPP(c_Product__Type_OPair(X3065,X3065),esk75_5(X3061,X3062,X3063,X3064,X3065)),X3063)),X3061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3065),tc_List_Olist(X3065))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3065),tc_List_Olist(X3065)),X3064),hAPP(hAPP(c_List_Olist_OCons(X3065),X3063),X3062))),c_List_Olistrel1(X3065,X3061))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3065),tc_List_Olist(X3065))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3065),tc_List_Olist(X3065)),esk76_5(X3061,X3062,X3063,X3064,X3065)),X3062)),c_List_Olistrel1(X3065,X3061)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3065,X3065)),hAPP(hAPP(c_Product__Type_OPair(X3065,X3065),esk75_5(X3061,X3062,X3063,X3064,X3065)),X3063)),X3061))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3065),tc_List_Olist(X3065))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3065),tc_List_Olist(X3065)),X3064),hAPP(hAPP(c_List_Olist_OCons(X3065),X3063),X3062))),c_List_Olistrel1(X3065,X3061))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_511])])])]) ).
fof(i_0_606,negated_conjecture,
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_512])])]) ).
fof(i_0_607,plain,
! [X3659,X3660,X3661,X3662] : c_Recdef_Oadm__wf(X3662,X3661,X3660,hAPP(hAPP(c_COMBC(tc_fun(X3662,X3661),tc_fun(X3662,X3662),tc_fun(X3662,X3661)),hAPP(hAPP(c_COMBB(tc_fun(X3662,tc_fun(X3662,X3661)),tc_fun(tc_fun(X3662,X3662),tc_fun(X3662,X3661)),tc_fun(X3662,X3661)),c_COMBS(X3662,X3662,X3661)),hAPP(hAPP(c_COMBB(tc_fun(X3662,tc_fun(X3662,X3661)),tc_fun(X3662,tc_fun(X3662,X3661)),tc_fun(X3662,X3661)),hAPP(c_COMBB(tc_fun(X3662,X3661),tc_fun(X3662,X3661),X3662),X3659)),hAPP(hAPP(c_COMBC(tc_fun(X3662,X3661),tc_fun(tc_prod(X3662,X3662),tc_HOL_Obool),tc_fun(X3662,tc_fun(X3662,X3661))),c_Recdef_Ocut(X3662,X3661)),X3660)))),c_COMBI(X3662))),
inference(variable_rename,[status(thm)],[fact_adm__lemma]) ).
fof(i_0_608,plain,
! [X2634,X2635,X2636,X2637,X2638] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2638),tc_List_Olist(X2638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2638),tc_List_Olist(X2638)),hAPP(hAPP(c_List_Oappend(X2638),X2637),X2636)),hAPP(hAPP(c_List_Oappend(X2638),X2637),X2635))),c_List_Olexord(X2638,X2634)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2638,X2638)),hAPP(hAPP(c_Product__Type_OPair(X2638,X2638),esk42_5(X2634,X2635,X2636,X2637,X2638)),esk42_5(X2634,X2635,X2636,X2637,X2638))),X2634))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2638),tc_List_Olist(X2638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2638),tc_List_Olist(X2638)),X2636),X2635)),c_List_Olexord(X2638,X2634))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_513])])]) ).
fof(i_0_609,plain,
! [X2379,X2380,X2381,X2382,X2383,X2384] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2382),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2381),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hBOOL(hAPP(hAPP(c_member(X2384),esk24_6(X2379,X2380,X2381,X2382,X2383,X2384)),X2383)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2381),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2382),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hBOOL(hAPP(hAPP(c_member(X2384),esk24_6(X2379,X2380,X2381,X2382,X2383,X2384)),X2383)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2382),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2381),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hAPP(X2382,esk24_6(X2379,X2380,X2381,X2382,X2383,X2384)) != hAPP(X2381,esk24_6(X2379,X2380,X2381,X2382,X2383,X2384)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2381),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2384,X2380)),X2382),c_FuncSet_OPi(X2384,X2380,X2383,X2379)))
| hAPP(X2382,esk24_6(X2379,X2380,X2381,X2382,X2383,X2384)) != hAPP(X2381,esk24_6(X2379,X2380,X2381,X2382,X2383,X2384)) ) ),
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,
! [X3519,X3520,X3521,X3522,X3523] :
( ( hBOOL(hAPP(hAPP(c_member(X3523),esk90_5(X3519,X3520,X3521,X3522,X3523)),X3522))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3523,X3521)),c_FuncSet_Orestrict(X3523,X3521,X3520,X3522)),c_FuncSet_OPi(X3523,X3521,X3522,X3519))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3521),hAPP(X3520,esk90_5(X3519,X3520,X3521,X3522,X3523))),hAPP(X3519,esk90_5(X3519,X3520,X3521,X3522,X3523))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3523,X3521)),c_FuncSet_Orestrict(X3523,X3521,X3520,X3522)),c_FuncSet_OPi(X3523,X3521,X3522,X3519))) ) ),
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,
! [X2373,X2374,X2375,X2376,X2377] :
( ( hBOOL(hAPP(hAPP(c_member(X2377),esk23_5(X2373,X2374,X2375,X2376,X2377)),X2376))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2377,X2375)),X2374),c_FuncSet_OPi(X2377,X2375,X2376,X2373))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2375),hAPP(X2374,esk23_5(X2373,X2374,X2375,X2376,X2377))),hAPP(X2373,esk23_5(X2373,X2374,X2375,X2376,X2377))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2377,X2375)),X2374),c_FuncSet_OPi(X2377,X2375,X2376,X2373))) ) ),
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,
! [X2347,X2348,X2349,X2350,X2351] :
( ( hBOOL(hAPP(hAPP(c_member(X2351),esk20_5(X2347,X2348,X2349,X2350,X2351)),X2350))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2351,X2349)),X2348),c_FuncSet_OPi(X2351,X2349,X2350,X2347))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2349),hAPP(X2348,esk20_5(X2347,X2348,X2349,X2350,X2351))),hAPP(X2347,esk20_5(X2347,X2348,X2349,X2350,X2351))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2351,X2349)),X2348),c_FuncSet_OPi(X2351,X2349,X2350,X2347))) ) ),
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,
! [X2720,X2721,X2722,X2723,X2724] :
( ( X2721 = hAPP(hAPP(c_List_Olist_OCons(X2724),X2723),esk44_5(X2720,X2721,X2722,X2723,X2724))
| X2721 = hAPP(hAPP(c_List_Olist_OCons(X2724),esk43_5(X2720,X2721,X2722,X2723,X2724)),X2722)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2724),tc_List_Olist(X2724))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2724),tc_List_Olist(X2724)),hAPP(hAPP(c_List_Olist_OCons(X2724),X2723),X2722)),X2721)),c_List_Olistrel1(X2724,X2720))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2724),tc_List_Olist(X2724))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2724),tc_List_Olist(X2724)),X2722),esk44_5(X2720,X2721,X2722,X2723,X2724))),c_List_Olistrel1(X2724,X2720)))
| X2721 = hAPP(hAPP(c_List_Olist_OCons(X2724),esk43_5(X2720,X2721,X2722,X2723,X2724)),X2722)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2724),tc_List_Olist(X2724))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2724),tc_List_Olist(X2724)),hAPP(hAPP(c_List_Olist_OCons(X2724),X2723),X2722)),X2721)),c_List_Olistrel1(X2724,X2720))) )
& ( X2721 = hAPP(hAPP(c_List_Olist_OCons(X2724),X2723),esk44_5(X2720,X2721,X2722,X2723,X2724))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2724,X2724)),hAPP(hAPP(c_Product__Type_OPair(X2724,X2724),X2723),esk43_5(X2720,X2721,X2722,X2723,X2724))),X2720))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2724),tc_List_Olist(X2724))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2724),tc_List_Olist(X2724)),hAPP(hAPP(c_List_Olist_OCons(X2724),X2723),X2722)),X2721)),c_List_Olistrel1(X2724,X2720))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2724),tc_List_Olist(X2724))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2724),tc_List_Olist(X2724)),X2722),esk44_5(X2720,X2721,X2722,X2723,X2724))),c_List_Olistrel1(X2724,X2720)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2724,X2724)),hAPP(hAPP(c_Product__Type_OPair(X2724,X2724),X2723),esk43_5(X2720,X2721,X2722,X2723,X2724))),X2720))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2724),tc_List_Olist(X2724))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2724),tc_List_Olist(X2724)),hAPP(hAPP(c_List_Olist_OCons(X2724),X2723),X2722)),X2721)),c_List_Olistrel1(X2724,X2720))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_514])])])]) ).
fof(i_0_614,plain,
! [X2619,X2620,X2621,X2622,X2623] :
( ( X2622 = hAPP(hAPP(c_List_Olist_OCons(X2623),esk36_5(X2619,X2620,X2621,X2622,X2623)),esk37_5(X2619,X2620,X2621,X2622,X2623))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2623),tc_List_Olist(X2623))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2623),tc_List_Olist(X2623)),X2622),hAPP(hAPP(c_List_Olist_OCons(X2623),X2621),X2620))),c_List_Olistrel(X2623,X2619))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2623,X2623)),hAPP(hAPP(c_Product__Type_OPair(X2623,X2623),esk36_5(X2619,X2620,X2621,X2622,X2623)),X2621)),X2619))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2623),tc_List_Olist(X2623))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2623),tc_List_Olist(X2623)),X2622),hAPP(hAPP(c_List_Olist_OCons(X2623),X2621),X2620))),c_List_Olistrel(X2623,X2619))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2623),tc_List_Olist(X2623))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2623),tc_List_Olist(X2623)),esk37_5(X2619,X2620,X2621,X2622,X2623)),X2620)),c_List_Olistrel(X2623,X2619)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2623),tc_List_Olist(X2623))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2623),tc_List_Olist(X2623)),X2622),hAPP(hAPP(c_List_Olist_OCons(X2623),X2621),X2620))),c_List_Olistrel(X2623,X2619))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_515])])])]) ).
fof(i_0_615,plain,
! [X2216,X2217,X2218,X2219,X2220,X2222,X2227,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),X2219),X2220)),hAPP(X2216,X2217)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2216,X2218)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2217,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2218,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| ~ 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))),X2218),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))),X2217),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(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),X2219),X2220)),hAPP(X2216,X2218)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2216,X2217)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2217,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2218,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| ~ 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))),X2218),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))),X2217),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(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),X2219),X2220)),hAPP(X2216,X2217)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2216,X2218)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2217,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2218,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| ~ 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))),X2218),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))),X2217),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(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),X2219),X2220)),hAPP(X2216,X2218)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2216,X2217)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2217,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2220)),hAPP(X2218,esk6_5(X2216,X2217,X2218,X2219,X2220))))
| ~ 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))),X2218),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))),X2217),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2216) )
& ( 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_1(X2222)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2222) )
& ( 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))),esk8_1(X2222)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2222) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X2222)),esk10_1(X2222))),hAPP(esk7_1(X2222),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),esk9_1(X2222)),esk10_1(X2222))),hAPP(esk8_1(X2222),X2227)))
| c_Arrow__Order__Mirabelle_OIIA(X2222) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X2222)),esk10_1(X2222))),hAPP(esk8_1(X2222),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),esk9_1(X2222)),esk10_1(X2222))),hAPP(esk7_1(X2222),X2228)))
| c_Arrow__Order__Mirabelle_OIIA(X2222) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X2222)),esk10_1(X2222))),hAPP(X2222,esk7_1(X2222))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X2222)),esk10_1(X2222))),hAPP(X2222,esk8_1(X2222))))
| c_Arrow__Order__Mirabelle_OIIA(X2222) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X2222)),esk10_1(X2222))),hAPP(X2222,esk7_1(X2222))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk9_1(X2222)),esk10_1(X2222))),hAPP(X2222,esk8_1(X2222))))
| c_Arrow__Order__Mirabelle_OIIA(X2222) ) ),
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,
! [X3525,X3526,X3527,X3528,X3529] :
( ( hBOOL(hAPP(hAPP(c_member(X3529),esk91_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,c_COMBK(tc_fun(X3527,tc_HOL_Obool),X3529,X3525)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3527),hAPP(X3526,esk91_5(X3525,X3526,X3527,X3528,X3529))),X3525))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3529,X3527)),c_FuncSet_Orestrict(X3529,X3527,X3526,X3528)),c_FuncSet_OPi(X3529,X3527,X3528,c_COMBK(tc_fun(X3527,tc_HOL_Obool),X3529,X3525)))) ) ),
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,
! [X2356,X2357,X2358,X2359,X2360] :
( ( hBOOL(hAPP(hAPP(c_member(X2360),esk22_5(X2356,X2357,X2358,X2359,X2360)),X2359))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2360,X2358)),X2357),c_FuncSet_OPi(X2360,X2358,X2359,c_COMBK(tc_fun(X2358,tc_HOL_Obool),X2360,X2356)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2358),hAPP(X2357,esk22_5(X2356,X2357,X2358,X2359,X2360))),X2356))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2360,X2358)),X2357),c_FuncSet_OPi(X2360,X2358,X2359,c_COMBK(tc_fun(X2358,tc_HOL_Obool),X2360,X2356)))) ) ),
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,
! [X3917,X3918,X3919,X3920] : c_Hilbert__Choice_OEps(tc_prod(X3920,X3919),hAPP(c_Product__Type_Oprod_Oprod__case(X3920,X3919,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3920,tc_fun(X3919,tc_HOL_Obool),tc_fun(X3919,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X3919,tc_HOL_Obool),tc_fun(X3919,tc_HOL_Obool)),X3920),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3919)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3920),c_fconj),hAPP(c_fequal,X3918)))),hAPP(c_fequal,X3917)))) = hAPP(hAPP(c_Product__Type_OPair(X3920,X3919),X3918),X3917),
inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).
fof(i_0_619,plain,
! [X3199,X3200] : c_Relation_OId__on(X3200,X3199) = hAPP(c_Product__Type_Oprod_Oprod__case(X3200,X3200,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X3200,tc_HOL_Obool,tc_fun(X3200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X3200,tc_HOL_Obool)),X3200),c_COMBC(X3200,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3200,tc_HOL_Obool),tc_fun(X3200,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3200),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3200),c_fconj)),c_fequal))),X3199)),
inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).
fof(i_0_620,plain,
! [X2612,X2613,X2614,X2615,X2616] :
( ( X2613 = hAPP(hAPP(c_List_Olist_OCons(X2616),esk34_5(X2612,X2613,X2614,X2615,X2616)),esk35_5(X2612,X2613,X2614,X2615,X2616))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2616),tc_List_Olist(X2616))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2616),tc_List_Olist(X2616)),hAPP(hAPP(c_List_Olist_OCons(X2616),X2615),X2614)),X2613)),c_List_Olistrel(X2616,X2612))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2616,X2616)),hAPP(hAPP(c_Product__Type_OPair(X2616,X2616),X2615),esk34_5(X2612,X2613,X2614,X2615,X2616))),X2612))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2616),tc_List_Olist(X2616))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2616),tc_List_Olist(X2616)),hAPP(hAPP(c_List_Olist_OCons(X2616),X2615),X2614)),X2613)),c_List_Olistrel(X2616,X2612))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2616),tc_List_Olist(X2616))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2616),tc_List_Olist(X2616)),X2614),esk35_5(X2612,X2613,X2614,X2615,X2616))),c_List_Olistrel(X2616,X2612)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2616),tc_List_Olist(X2616))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2616),tc_List_Olist(X2616)),hAPP(hAPP(c_List_Olist_OCons(X2616),X2615),X2614)),X2613)),c_List_Olistrel(X2616,X2612))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_516])])])]) ).
fof(i_0_621,plain,
! [X2428,X2429,X2430,X2431] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2431,X2431)),hAPP(hAPP(c_Product__Type_OPair(X2431,X2431),esk27_4(X2428,X2429,X2430,X2431)),esk28_4(X2428,X2429,X2430,X2431))),X2430))
| 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)),X2429),X2428)),c_List_Olexord(X2431,X2430)))
| X2429 = X2428
| 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)),X2428),X2429)),c_List_Olexord(X2431,X2430))) )
& ( esk27_4(X2428,X2429,X2430,X2431) != esk28_4(X2428,X2429,X2430,X2431)
| 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)),X2429),X2428)),c_List_Olexord(X2431,X2430)))
| X2429 = X2428
| 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)),X2428),X2429)),c_List_Olexord(X2431,X2430))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2431,X2431)),hAPP(hAPP(c_Product__Type_OPair(X2431,X2431),esk28_4(X2428,X2429,X2430,X2431)),esk27_4(X2428,X2429,X2430,X2431))),X2430))
| 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)),X2429),X2428)),c_List_Olexord(X2431,X2430)))
| X2429 = X2428
| 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)),X2428),X2429)),c_List_Olexord(X2431,X2430))) ) ),
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_517]) ).
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_518]) ).
fof(i_0_624,plain,
! [X3034,X3035,X3036,X3037] :
( ( hBOOL(hAPP(c_List_Olistsp(X3037,X3036),X3034))
| ~ hBOOL(hAPP(c_List_Olistsp(X3037,hAPP(hAPP(c_COMBS(X3037,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3037),c_fconj),X3036)),X3035)),X3034)) )
& ( hBOOL(hAPP(c_List_Olistsp(X3037,X3035),X3034))
| ~ hBOOL(hAPP(c_List_Olistsp(X3037,hAPP(hAPP(c_COMBS(X3037,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3037),c_fconj),X3036)),X3035)),X3034)) )
& ( ~ hBOOL(hAPP(c_List_Olistsp(X3037,X3036),X3034))
| ~ hBOOL(hAPP(c_List_Olistsp(X3037,X3035),X3034))
| hBOOL(hAPP(c_List_Olistsp(X3037,hAPP(hAPP(c_COMBS(X3037,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3037),c_fconj),X3036)),X3035)),X3034)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])]) ).
fof(i_0_625,plain,
! [X2578,X2579,X2580,X2581,X2582,X2583] :
( ( X2582 = X2580
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),X2582),X2580)),c_List_Olistrel1(X2583,X2578)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),hAPP(hAPP(c_List_Oappend(X2583),X2582),hAPP(hAPP(c_List_Olist_OCons(X2583),X2581),c_List_Olist_ONil(X2583)))),hAPP(hAPP(c_List_Oappend(X2583),X2580),hAPP(hAPP(c_List_Olist_OCons(X2583),X2579),c_List_Olist_ONil(X2583))))),c_List_Olistrel1(X2583,X2578))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2583,X2583)),hAPP(hAPP(c_Product__Type_OPair(X2583,X2583),X2581),X2579)),X2578))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),X2582),X2580)),c_List_Olistrel1(X2583,X2578)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),hAPP(hAPP(c_List_Oappend(X2583),X2582),hAPP(hAPP(c_List_Olist_OCons(X2583),X2581),c_List_Olist_ONil(X2583)))),hAPP(hAPP(c_List_Oappend(X2583),X2580),hAPP(hAPP(c_List_Olist_OCons(X2583),X2579),c_List_Olist_ONil(X2583))))),c_List_Olistrel1(X2583,X2578))) )
& ( X2582 = X2580
| X2581 = X2579
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),hAPP(hAPP(c_List_Oappend(X2583),X2582),hAPP(hAPP(c_List_Olist_OCons(X2583),X2581),c_List_Olist_ONil(X2583)))),hAPP(hAPP(c_List_Oappend(X2583),X2580),hAPP(hAPP(c_List_Olist_OCons(X2583),X2579),c_List_Olist_ONil(X2583))))),c_List_Olistrel1(X2583,X2578))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2583,X2583)),hAPP(hAPP(c_Product__Type_OPair(X2583,X2583),X2581),X2579)),X2578))
| X2581 = X2579
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),hAPP(hAPP(c_List_Oappend(X2583),X2582),hAPP(hAPP(c_List_Olist_OCons(X2583),X2581),c_List_Olist_ONil(X2583)))),hAPP(hAPP(c_List_Oappend(X2583),X2580),hAPP(hAPP(c_List_Olist_OCons(X2583),X2579),c_List_Olist_ONil(X2583))))),c_List_Olistrel1(X2583,X2578))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),X2582),X2580)),c_List_Olistrel1(X2583,X2578)))
| X2581 != X2579
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),hAPP(hAPP(c_List_Oappend(X2583),X2582),hAPP(hAPP(c_List_Olist_OCons(X2583),X2581),c_List_Olist_ONil(X2583)))),hAPP(hAPP(c_List_Oappend(X2583),X2580),hAPP(hAPP(c_List_Olist_OCons(X2583),X2579),c_List_Olist_ONil(X2583))))),c_List_Olistrel1(X2583,X2578))) )
& ( X2582 != X2580
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2583,X2583)),hAPP(hAPP(c_Product__Type_OPair(X2583,X2583),X2581),X2579)),X2578))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2583),tc_List_Olist(X2583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2583),tc_List_Olist(X2583)),hAPP(hAPP(c_List_Oappend(X2583),X2582),hAPP(hAPP(c_List_Olist_OCons(X2583),X2581),c_List_Olist_ONil(X2583)))),hAPP(hAPP(c_List_Oappend(X2583),X2580),hAPP(hAPP(c_List_Olist_OCons(X2583),X2579),c_List_Olist_ONil(X2583))))),c_List_Olistrel1(X2583,X2578))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).
fof(i_0_626,plain,
! [X4029,X4030,X4031,X4032,X4033] :
( ( hBOOL(hAPP(hAPP(c_member(X4033),esk104_5(X4029,X4030,X4031,X4032,X4033)),X4032))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4033,X4031),tc_HOL_Obool),c_FuncSet_OPi(X4033,X4031,X4032,X4030),c_FuncSet_OPi(X4033,X4031,X4032,X4029)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4031,tc_HOL_Obool),hAPP(X4030,esk104_5(X4029,X4030,X4031,X4032,X4033)),hAPP(X4029,esk104_5(X4029,X4030,X4031,X4032,X4033)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X4033,X4031),tc_HOL_Obool),c_FuncSet_OPi(X4033,X4031,X4032,X4030),c_FuncSet_OPi(X4033,X4031,X4032,X4029)) ) ),
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,
! [X2239,X2240,X2241,X2242,X2243,X2244,X2245,X2246] :
( ( X2244 = X2242
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2246,X2246)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2246),X2244),X2242)),X2240))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2246,X2245),tc_prod(X2246,X2245))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2246,X2245),tc_prod(X2246,X2245)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2244),X2243)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2242),X2241))),c_Wellfounded_Olex__prod(X2246,X2245,X2240,X2239))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2245,X2245)),hAPP(hAPP(c_Product__Type_OPair(X2245,X2245),X2243),X2241)),X2239))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2246,X2246)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2246),X2244),X2242)),X2240))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2246,X2245),tc_prod(X2246,X2245))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2246,X2245),tc_prod(X2246,X2245)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2244),X2243)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2242),X2241))),c_Wellfounded_Olex__prod(X2246,X2245,X2240,X2239))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2246,X2246)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2246),X2244),X2242)),X2240))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2246,X2245),tc_prod(X2246,X2245))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2246,X2245),tc_prod(X2246,X2245)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2244),X2243)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2242),X2241))),c_Wellfounded_Olex__prod(X2246,X2245,X2240,X2239))) )
& ( X2244 != X2242
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2245,X2245)),hAPP(hAPP(c_Product__Type_OPair(X2245,X2245),X2243),X2241)),X2239))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2246,X2245),tc_prod(X2246,X2245))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2246,X2245),tc_prod(X2246,X2245)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2244),X2243)),hAPP(hAPP(c_Product__Type_OPair(X2246,X2245),X2242),X2241))),c_Wellfounded_Olex__prod(X2246,X2245,X2240,X2239))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_628,plain,
! [X2308,X2309] :
( ( 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_2(X2308,X2309)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2309,X2308)
| ~ 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))),X2309),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)))) )
& ( esk16_2(X2308,X2309) != esk17_2(X2308,X2309)
| c_Arrow__Order__Mirabelle_Odictator(X2309,X2308)
| ~ 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))),X2309),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),esk16_2(X2308,X2309)),esk17_2(X2308,X2309))),hAPP(esk15_2(X2308,X2309),X2308)))
| c_Arrow__Order__Mirabelle_Odictator(X2309,X2308)
| ~ 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))),X2309),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),esk16_2(X2308,X2309)),esk17_2(X2308,X2309))),hAPP(X2309,esk15_2(X2308,X2309))))
| c_Arrow__Order__Mirabelle_Odictator(X2309,X2308)
| ~ 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))),X2309),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,
! [X3702,X3703,X3704,X3705,X3706] : hAPP(c_Hilbert__Choice_Oinv__into(X3706,X3705,X3704,X3703),X3702) = c_Hilbert__Choice_OEps(X3706,hAPP(hAPP(c_COMBS(X3706,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3706),c_fconj),hAPP(hAPP(c_COMBC(X3706,tc_fun(X3706,tc_HOL_Obool),tc_HOL_Obool),c_member(X3706)),X3704))),hAPP(hAPP(c_COMBC(X3706,X3705,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X3705,tc_fun(X3705,tc_HOL_Obool),X3706),c_fequal),X3703)),X3702))),
inference(variable_rename,[status(thm)],[fact_inv__into__def]) ).
fof(i_0_630,plain,
! [X2626,X2627,X2628,X2629] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2629,X2629)),hAPP(hAPP(c_Product__Type_OPair(X2629,X2629),esk38_4(X2626,X2627,X2628,X2629)),esk39_4(X2626,X2627,X2628,X2629))),X2626))
| ~ 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)),X2628),X2627)),c_List_Olistrel1(X2629,X2626))) )
& ( X2628 = hAPP(hAPP(c_List_Oappend(X2629),esk40_4(X2626,X2627,X2628,X2629)),hAPP(hAPP(c_List_Olist_OCons(X2629),esk38_4(X2626,X2627,X2628,X2629)),esk41_4(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)),X2628),X2627)),c_List_Olistrel1(X2629,X2626))) )
& ( X2627 = hAPP(hAPP(c_List_Oappend(X2629),esk40_4(X2626,X2627,X2628,X2629)),hAPP(hAPP(c_List_Olist_OCons(X2629),esk39_4(X2626,X2627,X2628,X2629)),esk41_4(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)),X2628),X2627)),c_List_Olistrel1(X2629,X2626))) ) ),
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_519]) ).
fof(i_0_632,plain,
! [X3057,X3058,X3059,X3060] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3060)),X3059),c_List_Olists(X3060,X3058)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3060)),X3059),c_List_Olists(X3060,X3057)))
| hBOOL(hAPP(c_List_Olistsp(X3060,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3060,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3060,tc_fun(X3060,tc_HOL_Obool),tc_HOL_Obool),c_member(X3060)),X3058),hAPP(hAPP(c_COMBC(X3060,tc_fun(X3060,tc_HOL_Obool),tc_HOL_Obool),c_member(X3060)),X3057))),X3059)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__IntI])]) ).
fof(i_0_633,plain,
! [X2144] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X2144)),v_c____),v_b____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X2144)),v_c____),v_b____)),v_b____),v_a____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X2144)),v_c____),v_b____)),v_b____),v_a____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X2144)),v_c____),v_b____))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096])]) ).
fof(i_0_634,plain,
! [X3617,X3618,X3619,X3620,X3621] :
( ( hBOOL(hAPP(hAPP(c_member(X3621),esk92_5(X3617,X3618,X3619,X3620,X3621)),X3618))
| X3619 = X3617
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3621,X3620)),X3617),c_FuncSet_Oextensional(X3621,X3620,X3618)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3621,X3620)),X3619),c_FuncSet_Oextensional(X3621,X3620,X3618))) )
& ( hAPP(X3619,esk92_5(X3617,X3618,X3619,X3620,X3621)) != hAPP(X3617,esk92_5(X3617,X3618,X3619,X3620,X3621))
| X3619 = X3617
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3621,X3620)),X3617),c_FuncSet_Oextensional(X3621,X3620,X3618)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3621,X3620)),X3619),c_FuncSet_Oextensional(X3621,X3620,X3618))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensionalityI])])])]) ).
fof(i_0_635,plain,
! [X2450,X2451,X2452,X2453,X2454,X2455,X2456] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2456,X2456)),hAPP(hAPP(c_Product__Type_OPair(X2456,X2456),X2455),X2454)),X2453))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2456),tc_List_Olist(X2456))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2456),tc_List_Olist(X2456)),hAPP(hAPP(c_List_Oappend(X2456),X2452),hAPP(hAPP(c_List_Olist_OCons(X2456),X2455),X2451))),hAPP(hAPP(c_List_Oappend(X2456),X2452),hAPP(hAPP(c_List_Olist_OCons(X2456),X2454),X2450)))),c_List_Olexord(X2456,X2453))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).
fof(i_0_636,plain,
! [X2162,X2163,X2164,X2165,X2166,X2167,X2168] :
( ~ hBOOL(hAPP(X2168,X2167))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2166,X2166)),hAPP(hAPP(c_Product__Type_OPair(X2166,X2166),X2165),X2164)),hAPP(X2163,X2167)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2162,X2166),tc_prod(X2162,X2166))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2162,X2166),tc_prod(X2162,X2166)),hAPP(hAPP(c_Product__Type_OPair(X2162,X2166),X2167),X2165)),hAPP(hAPP(c_Product__Type_OPair(X2162,X2166),X2167),X2164))),c_Recdef_Osame__fst(X2162,X2166,X2168,X2163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_637,plain,
! [X3147,X3148,X3149,X3150,X3151,X3152,X3153,X3154] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3154,X3153,X3152),X3151),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3150,X3149,tc_prod(X3154,X3153)),X3148),X3147)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3150,X3149,X3152),hAPP(hAPP(c_COMBB(tc_fun(X3149,tc_prod(X3154,X3153)),tc_fun(X3149,X3152),X3150),hAPP(c_COMBB(tc_prod(X3154,X3153),X3152,X3149),hAPP(c_Product__Type_Oprod_Oprod__case(X3154,X3153,X3152),X3151))),X3148)),X3147),
inference(variable_rename,[status(thm)],[fact_split__twice]) ).
fof(i_0_638,plain,
! [X2482,X2483,X2484,X2485,X2486,X2489,X2490,X2491,X2492,X2493,X2494,X2495] :
( ( hAPP(hAPP(c_List_Oappend(X2486),X2485),esk31_5(X2482,X2483,X2484,X2485,X2486)) = X2483
| X2485 = hAPP(hAPP(c_List_Oappend(X2486),X2483),esk30_5(X2482,X2483,X2484,X2485,X2486))
| hAPP(hAPP(c_List_Oappend(X2486),X2485),X2484) != hAPP(hAPP(c_List_Oappend(X2486),X2483),X2482) )
& ( X2484 = hAPP(hAPP(c_List_Oappend(X2486),esk31_5(X2482,X2483,X2484,X2485,X2486)),X2482)
| X2485 = hAPP(hAPP(c_List_Oappend(X2486),X2483),esk30_5(X2482,X2483,X2484,X2485,X2486))
| hAPP(hAPP(c_List_Oappend(X2486),X2485),X2484) != hAPP(hAPP(c_List_Oappend(X2486),X2483),X2482) )
& ( hAPP(hAPP(c_List_Oappend(X2486),X2485),esk31_5(X2482,X2483,X2484,X2485,X2486)) = X2483
| hAPP(hAPP(c_List_Oappend(X2486),esk30_5(X2482,X2483,X2484,X2485,X2486)),X2484) = X2482
| hAPP(hAPP(c_List_Oappend(X2486),X2485),X2484) != hAPP(hAPP(c_List_Oappend(X2486),X2483),X2482) )
& ( X2484 = hAPP(hAPP(c_List_Oappend(X2486),esk31_5(X2482,X2483,X2484,X2485,X2486)),X2482)
| hAPP(hAPP(c_List_Oappend(X2486),esk30_5(X2482,X2483,X2484,X2485,X2486)),X2484) = X2482
| hAPP(hAPP(c_List_Oappend(X2486),X2485),X2484) != hAPP(hAPP(c_List_Oappend(X2486),X2483),X2482) )
& ( X2492 != hAPP(hAPP(c_List_Oappend(X2493),X2490),X2494)
| hAPP(hAPP(c_List_Oappend(X2493),X2494),X2491) != X2489
| hAPP(hAPP(c_List_Oappend(X2493),X2492),X2491) = hAPP(hAPP(c_List_Oappend(X2493),X2490),X2489) )
& ( hAPP(hAPP(c_List_Oappend(X2493),X2492),X2495) != X2490
| X2491 != hAPP(hAPP(c_List_Oappend(X2493),X2495),X2489)
| hAPP(hAPP(c_List_Oappend(X2493),X2492),X2491) = hAPP(hAPP(c_List_Oappend(X2493),X2490),X2489) ) ),
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_639,plain,
! [X3140,X3141,X3142,X3143] :
( ( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3143,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3143,tc_fun(X3143,tc_HOL_Obool),tc_HOL_Obool),c_member(X3143)),X3142),hAPP(hAPP(c_COMBC(X3143,tc_fun(X3143,tc_HOL_Obool),tc_HOL_Obool),c_member(X3143)),X3141)),X3140))
| hBOOL(hAPP(hAPP(c_member(X3143),X3140),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3143,tc_HOL_Obool),X3142,X3141))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3143),X3140),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3143,tc_HOL_Obool),X3142,X3141)))
| hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3143,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3143,tc_fun(X3143,tc_HOL_Obool),tc_HOL_Obool),c_member(X3143)),X3142),hAPP(hAPP(c_COMBC(X3143,tc_fun(X3143,tc_HOL_Obool),tc_HOL_Obool),c_member(X3143)),X3141)),X3140)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).
fof(i_0_640,plain,
! [X2898,X2899,X2900,X2901] :
( ~ hBOOL(hAPP(hAPP(c_member(X2901),X2900),c_Relation_ORange(X2899,X2901,X2898)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2899,X2901)),hAPP(hAPP(c_Product__Type_OPair(X2899,X2901),esk55_4(X2898,X2899,X2900,X2901)),X2900)),X2898)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_520])])]) ).
fof(i_0_641,plain,
! [X2868,X2869,X2870,X2871,X2873,X2874,X2875,X2876,X2877] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2871),X2870),c_Relation_ORange(X2869,X2871,X2868)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2869,X2871)),hAPP(hAPP(c_Product__Type_OPair(X2869,X2871),esk53_4(X2868,X2869,X2870,X2871)),X2870)),X2868)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2874,X2876)),hAPP(hAPP(c_Product__Type_OPair(X2874,X2876),X2877),X2875)),X2873))
| hBOOL(hAPP(hAPP(c_member(X2876),X2875),c_Relation_ORange(X2874,X2876,X2873))) ) ),
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_642,plain,
! [X2602,X2603,X2604,X2605,X2606,X2607] :
( ( X2606 = X2604
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2607,X2607)),hAPP(hAPP(c_Product__Type_OPair(X2607,X2607),X2606),X2604)),X2602))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2606),X2605)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2604),X2603))),c_List_Olistrel1(X2607,X2602))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),X2605),X2603)),c_List_Olistrel1(X2607,X2602)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2607,X2607)),hAPP(hAPP(c_Product__Type_OPair(X2607,X2607),X2606),X2604)),X2602))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2606),X2605)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2604),X2603))),c_List_Olistrel1(X2607,X2602))) )
& ( X2606 = X2604
| X2605 = X2603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2606),X2605)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2604),X2603))),c_List_Olistrel1(X2607,X2602))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),X2605),X2603)),c_List_Olistrel1(X2607,X2602)))
| X2605 = X2603
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2606),X2605)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2604),X2603))),c_List_Olistrel1(X2607,X2602))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2607,X2607)),hAPP(hAPP(c_Product__Type_OPair(X2607,X2607),X2606),X2604)),X2602))
| X2605 != X2603
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2606),X2605)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2604),X2603))),c_List_Olistrel1(X2607,X2602))) )
& ( X2606 != X2604
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),X2605),X2603)),c_List_Olistrel1(X2607,X2602)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2607),tc_List_Olist(X2607))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2607),tc_List_Olist(X2607)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2606),X2605)),hAPP(hAPP(c_List_Olist_OCons(X2607),X2604),X2603))),c_List_Olistrel1(X2607,X2602))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).
fof(i_0_643,plain,
! [X2646,X2647,X2648,X2649,X2650,X2651] :
( ( X2650 = X2648
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2651,X2651)),hAPP(hAPP(c_Product__Type_OPair(X2651,X2651),X2650),X2648)),X2646))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2650),X2649)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2648),X2647))),c_List_Olex(X2651,X2646))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),X2649),X2647)),c_List_Olex(X2651,X2646)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2651,X2651)),hAPP(hAPP(c_Product__Type_OPair(X2651,X2651),X2650),X2648)),X2646))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2650),X2649)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2648),X2647))),c_List_Olex(X2651,X2646))) )
& ( X2650 = X2648
| c_Nat_Osize__class_Osize(tc_List_Olist(X2651),X2649) = c_Nat_Osize__class_Osize(tc_List_Olist(X2651),X2647)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2650),X2649)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2648),X2647))),c_List_Olex(X2651,X2646))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),X2649),X2647)),c_List_Olex(X2651,X2646)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2651),X2649) = c_Nat_Osize__class_Osize(tc_List_Olist(X2651),X2647)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2650),X2649)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2648),X2647))),c_List_Olex(X2651,X2646))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2651,X2651)),hAPP(hAPP(c_Product__Type_OPair(X2651,X2651),X2650),X2648)),X2646))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2651),X2649) != c_Nat_Osize__class_Osize(tc_List_Olist(X2651),X2647)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2650),X2649)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2648),X2647))),c_List_Olex(X2651,X2646))) )
& ( X2650 != X2648
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),X2649),X2647)),c_List_Olex(X2651,X2646)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2651),tc_List_Olist(X2651))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2651),tc_List_Olist(X2651)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2650),X2649)),hAPP(hAPP(c_List_Olist_OCons(X2651),X2648),X2647))),c_List_Olex(X2651,X2646))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).
fof(i_0_644,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_645,plain,
! [X2740,X2741,X2742,X2743,X2744,X2745] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2745,X2745)),hAPP(hAPP(c_Product__Type_OPair(X2745,X2745),X2744),X2743)),c_Transitive__Closure_Ortrancl(X2745,X2742)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2745),tc_List_Olist(X2745))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2745),tc_List_Olist(X2745)),X2741),X2740)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2745),c_List_Olistrel1(X2745,X2742))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2745),tc_List_Olist(X2745))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2745),tc_List_Olist(X2745)),hAPP(hAPP(c_List_Olist_OCons(X2745),X2744),X2741)),hAPP(hAPP(c_List_Olist_OCons(X2745),X2743),X2740))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2745),c_List_Olistrel1(X2745,X2742)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).
fof(i_0_646,plain,
! [X2444,X2445,X2446,X2447,X2448,X2449] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2449,X2449)),hAPP(hAPP(c_Product__Type_OPair(X2449,X2449),X2448),X2447)),X2446))
| ~ 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)),X2445),X2444)),c_List_Olistrel(X2449,X2446)))
| 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)),hAPP(hAPP(c_List_Olist_OCons(X2449),X2448),X2445)),hAPP(hAPP(c_List_Olist_OCons(X2449),X2447),X2444))),c_List_Olistrel(X2449,X2446))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).
fof(i_0_647,plain,
! [X3547,X3548,X3549,X3550,X3551] :
( c_Set_Oimage(X3551,X3550,X3549,X3548) != X3547
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3550,X3551)),c_FuncSet_Orestrict(X3550,X3551,c_Hilbert__Choice_Oinv__into(X3551,X3550,X3548,X3549),X3547)),c_FuncSet_OPi(X3550,X3551,X3547,c_COMBK(tc_fun(X3551,tc_HOL_Obool),X3550,X3548)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__funcset])]) ).
fof(i_0_648,plain,
! [X2229,X2230,X2231,X2232,X2234,X2238] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2229)
| ~ 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))),X2230),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),X2231),X2232)),hAPP(X2230,esk11_4(X2229,X2230,X2231,X2232))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2231),X2232)),hAPP(X2229,X2230))) )
& ( 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))),esk12_1(X2234)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2234) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk13_1(X2234)),esk14_1(X2234))),hAPP(esk12_1(X2234),X2238)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2234) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk13_1(X2234)),esk14_1(X2234))),hAPP(X2234,esk12_1(X2234))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2234) ) ),
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_649,plain,
! [X2749,X2750,X2751,X2752,X2753] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2753),tc_List_Olist(X2753))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2753),tc_List_Olist(X2753)),X2752),X2751)),c_List_Olistrel(X2753,c_Transitive__Closure_Ortrancl(X2753,X2750))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2753),tc_List_Olist(X2753))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2753),tc_List_Olist(X2753)),X2751),X2749)),c_List_Olistrel(X2753,c_Transitive__Closure_Ortrancl(X2753,X2750))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2753),tc_List_Olist(X2753))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2753),tc_List_Olist(X2753)),X2752),X2749)),c_List_Olistrel(X2753,c_Transitive__Closure_Ortrancl(X2753,X2750)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).
fof(i_0_650,plain,
! [X2754,X2755,X2756,X2757,X2758] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2758),tc_List_Olist(X2758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2758),tc_List_Olist(X2758)),X2757),X2756)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2758),c_List_Olistrel1(X2758,X2755))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2758),tc_List_Olist(X2758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2758),tc_List_Olist(X2758)),hAPP(hAPP(c_List_Olist_OCons(X2758),X2754),X2757)),hAPP(hAPP(c_List_Olist_OCons(X2758),X2754),X2756))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2758),c_List_Olistrel1(X2758,X2755)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).
fof(i_0_651,plain,
! [X2707,X2708,X2709,X2710,X2711] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2711),tc_List_Olist(X2711))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2711),tc_List_Olist(X2711)),X2710),X2709)),c_List_Olexord(X2711,X2708)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2711),tc_List_Olist(X2711))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2711),tc_List_Olist(X2711)),X2709),X2707)),c_List_Olexord(X2711,X2708)))
| ~ c_Relation_Otrans(X2711,X2708)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2711),tc_List_Olist(X2711))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2711),tc_List_Olist(X2711)),X2710),X2707)),c_List_Olexord(X2711,X2708))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__trans])]) ).
fof(i_0_652,plain,
! [X2535,X2536,X2537,X2538,X2539,X2540] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2540),tc_List_Olist(X2540))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2540),tc_List_Olist(X2540)),X2539),X2538)),c_List_Olistrel1(X2540,X2537)))
| X2536 != X2535
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2540),tc_List_Olist(X2540))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2540),tc_List_Olist(X2540)),hAPP(hAPP(c_List_Oappend(X2540),X2539),X2536)),hAPP(hAPP(c_List_Oappend(X2540),X2538),X2535))),c_List_Olistrel1(X2540,X2537))) )
& ( X2539 != X2538
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2540),tc_List_Olist(X2540))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2540),tc_List_Olist(X2540)),X2536),X2535)),c_List_Olistrel1(X2540,X2537)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2540),tc_List_Olist(X2540))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2540),tc_List_Olist(X2540)),hAPP(hAPP(c_List_Oappend(X2540),X2539),X2536)),hAPP(hAPP(c_List_Oappend(X2540),X2538),X2535))),c_List_Olistrel1(X2540,X2537))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).
fof(i_0_653,plain,
! [X2584,X2585,X2586,X2587,X2588] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2588),tc_List_Olist(X2588))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2588),tc_List_Olist(X2588)),X2587),X2586)),c_List_Olexord(X2588,X2585)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2588),tc_List_Olist(X2588))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2588),tc_List_Olist(X2588)),hAPP(hAPP(c_List_Oappend(X2588),X2584),X2587)),hAPP(hAPP(c_List_Oappend(X2588),X2584),X2586))),c_List_Olexord(X2588,X2585))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).
fof(i_0_654,plain,
! [X2589,X2590,X2591,X2592,X2593] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2593),tc_List_Olist(X2593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2593),tc_List_Olist(X2593)),X2592),X2591)),c_List_Olistrel1(X2593,X2590)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2593),tc_List_Olist(X2593))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2593),tc_List_Olist(X2593)),hAPP(hAPP(c_List_Olist_OCons(X2593),X2589),X2592)),hAPP(hAPP(c_List_Olist_OCons(X2593),X2589),X2591))),c_List_Olistrel1(X2593,X2590))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).
cnf(i_0_655,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_521]) ).
cnf(i_0_656,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_522]) ).
fof(i_0_657,plain,
! [X2278,X2279,X2280,X2281,X2282] :
( ( 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2278 != X2282
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 != X2282
| X2278 = X2281
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2278)),X2280))
| X2278 = X2282
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 = X2282
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),X2280))
| X2278 = X2282
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2278 != X2282
| X2278 = X2282
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 != X2282
| X2279 = X2282
| X2278 = X2282
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),X2280))
| X2279 = X2282
| X2278 = X2282
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 != X2282
| X2278 != X2281
| X2278 = X2282
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),X2280))
| X2278 != X2281
| X2278 = X2282
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 != X2282
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2278)),X2280))
| X2278 = X2282
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),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),X2278)),X2280))
| X2278 = X2282
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2278 != X2282
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2281)),X2280))
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 != X2282
| X2279 = X2282
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2281)),X2280))
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),X2280))
| X2279 = X2282
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2281)),X2280))
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 != X2282
| X2278 != X2281
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2281)),X2280))
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),X2280))
| X2278 != X2281
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2281)),X2280))
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( X2279 != X2282
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X2278)),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),X2279),X2281)),X2280))
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2279),X2278)),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),X2278)),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),X2279),X2281)),X2280))
| 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),X2279),X2278)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2280),X2282),X2281)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2280),c_Arrow__Order__Mirabelle_OLin))
| X2282 = X2281 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_658,plain,
! [X2295,X2296,X2297,X2298,X2299] :
( ( X2296 != X2295
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2296 != 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),X2299),X2295)),X2297))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 != X2298
| X2296 = X2299
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2299)),X2297))
| X2296 = 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),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 = 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),X2296),X2295)),X2297))
| X2296 = 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),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2296 != X2298
| X2296 = X2298
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 != X2298
| X2295 = X2298
| X2296 = X2298
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = 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),X2296),X2295)),X2297))
| X2295 = X2298
| X2296 = X2298
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 != X2298
| X2296 != X2299
| X2296 = X2298
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = 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),X2296),X2295)),X2297))
| X2296 != X2299
| X2296 = X2298
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 != 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),X2296),X2299)),X2297))
| X2296 = X2298
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = 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),X2296),X2295)),X2297))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2299)),X2297))
| X2296 = X2298
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2296 != 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),X2299),X2295)),X2297))
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 != X2298
| X2295 = 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),X2299),X2295)),X2297))
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = 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),X2296),X2295)),X2297))
| X2295 = 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),X2299),X2295)),X2297))
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 != X2298
| X2296 != X2299
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2299),X2295)),X2297))
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = 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),X2296),X2295)),X2297))
| X2296 != X2299
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2299),X2295)),X2297))
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 )
& ( X2295 != 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),X2296),X2299)),X2297))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2299),X2295)),X2297))
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = 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),X2296),X2295)),X2297))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2299)),X2297))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2299),X2295)),X2297))
| X2296 = X2295
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2296),X2295)),c_Arrow__Order__Mirabelle_Oabove(X2297,X2299,X2298)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2297),c_Arrow__Order__Mirabelle_OLin))
| X2299 = X2298 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_659,plain,
! [X2434,X2435,X2436] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2436,X2436)),hAPP(hAPP(c_Product__Type_OPair(X2436,X2436),esk29_3(X2434,X2435,X2436)),esk29_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_523])])]) ).
fof(i_0_660,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_661,plain,
! [X3668,X3669,X3670,X3671,X3672,X3673] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3673),X3672),X3671))
| c_Fun_Ooverride__on(X3673,X3670,X3669,X3668,X3671,X3672) = hAPP(X3668,X3672) )
& ( hBOOL(hAPP(hAPP(c_member(X3673),X3672),X3671))
| c_Fun_Ooverride__on(X3673,X3670,X3669,X3668,X3671,X3672) = hAPP(X3669,X3672) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).
fof(i_0_662,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(X3675,X3678) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])]) ).
fof(i_0_663,plain,
! [X3594,X3595,X3596,X3597,X3598] :
( ~ hBOOL(hAPP(hAPP(c_member(X3598),X3597),c_Set_Oimage(X3596,X3598,X3595,X3594)))
| hBOOL(hAPP(hAPP(c_member(X3596),hAPP(c_Hilbert__Choice_Oinv__into(X3596,X3598,X3594,X3595),X3597)),X3594)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
fof(i_0_664,plain,
! [X2457,X2458,X2459,X2460,X2461] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2461,X2461)),hAPP(hAPP(c_Product__Type_OPair(X2461,X2461),X2460),X2459)),X2458))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2461),tc_List_Olist(X2461))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2461),tc_List_Olist(X2461)),hAPP(hAPP(c_List_Olist_OCons(X2461),X2460),X2457)),hAPP(hAPP(c_List_Olist_OCons(X2461),X2459),X2457))),c_List_Olistrel1(X2461,X2458))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).
fof(i_0_665,plain,
! [X3921,X3922,X3923] : c_Hilbert__Choice_OEps(tc_prod(X3923,X3922),X3921) = c_Hilbert__Choice_OEps(tc_prod(X3923,X3922),hAPP(c_Product__Type_Oprod_Oprod__case(X3923,X3922,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X3922,tc_prod(X3923,X3922)),tc_fun(X3922,tc_HOL_Obool),X3923),hAPP(c_COMBB(tc_prod(X3923,X3922),tc_HOL_Obool,X3922),X3921)),c_Product__Type_OPair(X3923,X3922)))),
inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).
fof(i_0_666,plain,
! [X2817,X2818,X2819,X2820,X2821] :
( ~ c_Relation_Osingle__valued(X2821,X2821,X2820)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2821,X2821)),hAPP(hAPP(c_Product__Type_OPair(X2821,X2821),X2819),X2818)),c_Transitive__Closure_Ortrancl(X2821,X2820)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2821,X2821)),hAPP(hAPP(c_Product__Type_OPair(X2821,X2821),X2819),X2817)),c_Transitive__Closure_Ortrancl(X2821,X2820)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2821,X2821)),hAPP(hAPP(c_Product__Type_OPair(X2821,X2821),X2818),X2817)),c_Transitive__Closure_Ortrancl(X2821,X2820)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2821,X2821)),hAPP(hAPP(c_Product__Type_OPair(X2821,X2821),X2817),X2818)),c_Transitive__Closure_Ortrancl(X2821,X2820))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).
cnf(i_0_667,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_526]) ).
fof(i_0_668,plain,
! [X2903,X2904,X2905,X2906] :
( ~ hBOOL(hAPP(hAPP(c_member(X2906),X2905),c_Relation_ODomain(X2906,X2904,X2903)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2906,X2904)),hAPP(hAPP(c_Product__Type_OPair(X2906,X2904),X2905),esk56_4(X2903,X2904,X2905,X2906))),X2903)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])])]) ).
fof(i_0_669,plain,
! [X2858,X2859,X2860,X2861,X2863,X2864,X2865,X2866,X2867] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2861),X2860),c_Relation_ODomain(X2861,X2859,X2858)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2861,X2859)),hAPP(hAPP(c_Product__Type_OPair(X2861,X2859),X2860),esk52_4(X2858,X2859,X2860,X2861))),X2858)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2866,X2864)),hAPP(hAPP(c_Product__Type_OPair(X2866,X2864),X2865),X2867)),X2863))
| hBOOL(hAPP(hAPP(c_member(X2866),X2865),c_Relation_ODomain(X2866,X2864,X2863))) ) ),
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_670,plain,
! [X2553,X2554,X2555,X2556,X2557,X2559,X2560,X2561,X2562,X2563,X2564] :
( ( hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),esk33_5(X2553,X2554,X2555,X2556,X2557)) = X2554
| X2554 = c_List_Olist_ONil(X2557)
| hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),X2555) != hAPP(hAPP(c_List_Oappend(X2557),X2554),X2553) )
& ( X2555 = hAPP(hAPP(c_List_Oappend(X2557),esk33_5(X2553,X2554,X2555,X2556,X2557)),X2553)
| X2554 = c_List_Olist_ONil(X2557)
| hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),X2555) != hAPP(hAPP(c_List_Oappend(X2557),X2554),X2553) )
& ( hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),esk33_5(X2553,X2554,X2555,X2556,X2557)) = X2554
| hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),X2555) = X2553
| hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),X2555) != hAPP(hAPP(c_List_Oappend(X2557),X2554),X2553) )
& ( X2555 = hAPP(hAPP(c_List_Oappend(X2557),esk33_5(X2553,X2554,X2555,X2556,X2557)),X2553)
| hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),X2555) = X2553
| hAPP(hAPP(c_List_Olist_OCons(X2557),X2556),X2555) != hAPP(hAPP(c_List_Oappend(X2557),X2554),X2553) )
& ( X2560 != c_List_Olist_ONil(X2563)
| hAPP(hAPP(c_List_Olist_OCons(X2563),X2562),X2561) != X2559
| hAPP(hAPP(c_List_Olist_OCons(X2563),X2562),X2561) = hAPP(hAPP(c_List_Oappend(X2563),X2560),X2559) )
& ( hAPP(hAPP(c_List_Olist_OCons(X2563),X2562),X2564) != X2560
| X2561 != hAPP(hAPP(c_List_Oappend(X2563),X2564),X2559)
| hAPP(hAPP(c_List_Olist_OCons(X2563),X2562),X2561) = hAPP(hAPP(c_List_Oappend(X2563),X2560),X2559) ) ),
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_671,plain,
! [X2541,X2542,X2543,X2544,X2545,X2547,X2548,X2549,X2550,X2551,X2552] :
( ( X2544 = hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),esk32_5(X2541,X2542,X2543,X2544,X2545))
| X2544 = c_List_Olist_ONil(X2545)
| hAPP(hAPP(c_List_Oappend(X2545),X2544),X2543) != hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),X2541) )
& ( hAPP(hAPP(c_List_Oappend(X2545),esk32_5(X2541,X2542,X2543,X2544,X2545)),X2543) = X2541
| X2544 = c_List_Olist_ONil(X2545)
| hAPP(hAPP(c_List_Oappend(X2545),X2544),X2543) != hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),X2541) )
& ( X2544 = hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),esk32_5(X2541,X2542,X2543,X2544,X2545))
| X2543 = hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),X2541)
| hAPP(hAPP(c_List_Oappend(X2545),X2544),X2543) != hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),X2541) )
& ( hAPP(hAPP(c_List_Oappend(X2545),esk32_5(X2541,X2542,X2543,X2544,X2545)),X2543) = X2541
| X2543 = hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),X2541)
| hAPP(hAPP(c_List_Oappend(X2545),X2544),X2543) != hAPP(hAPP(c_List_Olist_OCons(X2545),X2542),X2541) )
& ( X2550 != c_List_Olist_ONil(X2551)
| X2549 != hAPP(hAPP(c_List_Olist_OCons(X2551),X2548),X2547)
| hAPP(hAPP(c_List_Oappend(X2551),X2550),X2549) = hAPP(hAPP(c_List_Olist_OCons(X2551),X2548),X2547) )
& ( X2550 != hAPP(hAPP(c_List_Olist_OCons(X2551),X2548),X2552)
| hAPP(hAPP(c_List_Oappend(X2551),X2552),X2549) != X2547
| hAPP(hAPP(c_List_Oappend(X2551),X2550),X2549) = hAPP(hAPP(c_List_Olist_OCons(X2551),X2548),X2547) ) ),
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_672,plain,
! [X3599,X3600,X3601,X3602,X3603,X3604] :
( hAPP(c_Hilbert__Choice_Oinv__into(X3604,X3603,X3602,X3601),X3600) != hAPP(c_Hilbert__Choice_Oinv__into(X3604,X3603,X3602,X3601),X3599)
| ~ hBOOL(hAPP(hAPP(c_member(X3603),X3600),c_Set_Oimage(X3604,X3603,X3601,X3602)))
| ~ hBOOL(hAPP(hAPP(c_member(X3603),X3599),c_Set_Oimage(X3604,X3603,X3601,X3602)))
| X3600 = X3599 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
fof(i_0_673,plain,
! [X3144,X3145,X3146] : c_List_Olistsp(X3146,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3146,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3146,tc_fun(X3146,tc_HOL_Obool),tc_HOL_Obool),c_member(X3146)),X3145),hAPP(hAPP(c_COMBC(X3146,tc_fun(X3146,tc_HOL_Obool),tc_HOL_Obool),c_member(X3146)),X3144))) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X3146),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X3146),tc_fun(tc_List_Olist(X3146),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X3146))),c_List_Olists(X3146,X3145)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3146),tc_fun(tc_List_Olist(X3146),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X3146))),c_List_Olists(X3146,X3144))),
inference(variable_rename,[status(thm)],[fact_lists__Int__eq]) ).
fof(i_0_674,plain,
! [X2652,X2653] : c_List_Orotate1(X2653,X2652) = c_List_Olist_Olist__case(tc_List_Olist(X2653),X2653,c_List_Olist_ONil(X2653),hAPP(hAPP(c_COMBB(tc_List_Olist(X2653),tc_fun(tc_List_Olist(X2653),tc_List_Olist(X2653)),X2653),hAPP(c_COMBC(tc_List_Olist(X2653),tc_List_Olist(X2653),tc_List_Olist(X2653)),c_List_Oappend(X2653))),hAPP(hAPP(c_COMBC(X2653,tc_List_Olist(X2653),tc_List_Olist(X2653)),c_List_Olist_OCons(X2653)),c_List_Olist_ONil(X2653))),X2652),
inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).
fof(i_0_675,plain,
! [X3005,X3006,X3007] :
( ( ~ hBOOL(hAPP(c_List_Olistsp(X3007,hAPP(hAPP(c_COMBC(X3007,tc_fun(X3007,tc_HOL_Obool),tc_HOL_Obool),c_member(X3007)),X3006)),X3005))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3007)),X3005),c_List_Olists(X3007,X3006))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3007)),X3005),c_List_Olists(X3007,X3006)))
| hBOOL(hAPP(c_List_Olistsp(X3007,hAPP(hAPP(c_COMBC(X3007,tc_fun(X3007,tc_HOL_Obool),tc_HOL_Obool),c_member(X3007)),X3006)),X3005)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])]) ).
fof(i_0_676,plain,
! [X4047,X4048,X4049,X4050,X4051] :
( ( hAPP(X4048,X4050) = hAPP(X4048,X4049)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4048,X4050),hAPP(X4048,X4049))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4051,X4051)),hAPP(hAPP(c_Product__Type_OPair(X4051,X4051),X4050),X4049)),c_List_Omeasures(X4051,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4051,tc_Nat_Onat)),X4048),X4047)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4051,X4051)),hAPP(hAPP(c_Product__Type_OPair(X4051,X4051),X4050),X4049)),c_List_Omeasures(X4051,X4047)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4048,X4050),hAPP(X4048,X4049))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4051,X4051)),hAPP(hAPP(c_Product__Type_OPair(X4051,X4051),X4050),X4049)),c_List_Omeasures(X4051,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4051,tc_Nat_Onat)),X4048),X4047)))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4048,X4050),hAPP(X4048,X4049))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4051,X4051)),hAPP(hAPP(c_Product__Type_OPair(X4051,X4051),X4050),X4049)),c_List_Omeasures(X4051,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4051,tc_Nat_Onat)),X4048),X4047)))) )
& ( hAPP(X4048,X4050) != hAPP(X4048,X4049)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4051,X4051)),hAPP(hAPP(c_Product__Type_OPair(X4051,X4051),X4050),X4049)),c_List_Omeasures(X4051,X4047)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4051,X4051)),hAPP(hAPP(c_Product__Type_OPair(X4051,X4051),X4050),X4049)),c_List_Omeasures(X4051,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4051,tc_Nat_Onat)),X4048),X4047)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).
fof(i_0_677,plain,
! [X2784,X2785,X2786,X2787,X2788] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2788,X2788)),hAPP(hAPP(c_Product__Type_OPair(X2788,X2788),X2787),X2786)),c_Transitive__Closure_Ortrancl(X2788,X2785)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2788,X2788)),hAPP(hAPP(c_Product__Type_OPair(X2788,X2788),X2786),X2784)),c_Transitive__Closure_Ortrancl(X2788,X2785)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2788,X2788)),hAPP(hAPP(c_Product__Type_OPair(X2788,X2788),X2787),X2784)),c_Transitive__Closure_Ortrancl(X2788,X2785))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).
fof(i_0_678,plain,
! [X2798,X2799,X2800,X2801,X2802] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2802,X2802)),hAPP(hAPP(c_Product__Type_OPair(X2802,X2802),X2801),X2800)),X2799))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2802,X2802)),hAPP(hAPP(c_Product__Type_OPair(X2802,X2802),X2800),X2798)),c_Transitive__Closure_Ortrancl(X2802,X2799)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2802,X2802)),hAPP(hAPP(c_Product__Type_OPair(X2802,X2802),X2801),X2798)),c_Transitive__Closure_Ortrancl(X2802,X2799))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).
fof(i_0_679,plain,
! [X2789,X2790,X2791,X2792,X2793] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2793,X2793)),hAPP(hAPP(c_Product__Type_OPair(X2793,X2793),X2792),X2791)),c_Transitive__Closure_Ortrancl(X2793,X2790)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2793,X2793)),hAPP(hAPP(c_Product__Type_OPair(X2793,X2793),X2791),X2789)),X2790))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2793,X2793)),hAPP(hAPP(c_Product__Type_OPair(X2793,X2793),X2792),X2789)),c_Transitive__Closure_Ortrancl(X2793,X2790))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).
fof(i_0_680,plain,
! [X2712,X2713,X2714,X2715] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2715),tc_List_Olist(X2715))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2715),tc_List_Olist(X2715)),X2714),X2713)),c_List_Olistrel(X2715,X2712)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2715),tc_List_Olist(X2715))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2715),tc_List_Olist(X2715)),X2714),X2713)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2715),c_List_Olistrel1(X2715,X2712)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).
fof(i_0_681,plain,
! [X2716,X2717,X2718,X2719] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2719),tc_List_Olist(X2719))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2719),tc_List_Olist(X2719)),X2718),X2717)),c_List_Olistrel1(X2719,X2716)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2719),tc_List_Olist(X2719))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2719),tc_List_Olist(X2719)),X2718),X2717)),c_List_Olistrel(X2719,c_Transitive__Closure_Ortrancl(X2719,X2716)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).
fof(i_0_682,plain,
! [X2687,X2688,X2689,X2690] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2690),tc_List_Olist(X2690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2690),tc_List_Olist(X2690)),X2689),X2688)),c_List_Olexord(X2690,X2687)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2690),tc_List_Olist(X2690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2690),tc_List_Olist(X2690)),X2689),X2688)),c_List_Olex(X2690,X2687))) )
& ( c_Nat_Osize__class_Osize(tc_List_Olist(X2690),X2689) = c_Nat_Osize__class_Osize(tc_List_Olist(X2690),X2688)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2690),tc_List_Olist(X2690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2690),tc_List_Olist(X2690)),X2689),X2688)),c_List_Olex(X2690,X2687))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2690),tc_List_Olist(X2690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2690),tc_List_Olist(X2690)),X2689),X2688)),c_List_Olexord(X2690,X2687)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2690),X2689) != c_Nat_Osize__class_Osize(tc_List_Olist(X2690),X2688)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2690),tc_List_Olist(X2690))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2690),tc_List_Olist(X2690)),X2689),X2688)),c_List_Olex(X2690,X2687))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).
cnf(i_0_683,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_528]) ).
fof(i_0_684,plain,
! [X2774,X2775,X2776,X2777,X2778,X2779,X2780] :
( ( ~ c_Relation_Otrans(X2775,X2774)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2775,X2775)),hAPP(hAPP(c_Product__Type_OPair(X2775,X2775),X2776),X2777)),X2774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2775,X2775)),hAPP(hAPP(c_Product__Type_OPair(X2775,X2775),X2777),X2778)),X2774))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2775,X2775)),hAPP(hAPP(c_Product__Type_OPair(X2775,X2775),X2776),X2778)),X2774)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2780,X2780)),hAPP(hAPP(c_Product__Type_OPair(X2780,X2780),esk45_2(X2779,X2780)),esk46_2(X2779,X2780))),X2779))
| c_Relation_Otrans(X2780,X2779) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2780,X2780)),hAPP(hAPP(c_Product__Type_OPair(X2780,X2780),esk46_2(X2779,X2780)),esk47_2(X2779,X2780))),X2779))
| c_Relation_Otrans(X2780,X2779) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2780,X2780)),hAPP(hAPP(c_Product__Type_OPair(X2780,X2780),esk45_2(X2779,X2780)),esk47_2(X2779,X2780))),X2779))
| c_Relation_Otrans(X2780,X2779) ) ),
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,
! [X2769,X2770,X2771,X2772,X2773] :
( ~ c_Relation_Otrans(X2773,X2772)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2771),X2770)),X2772))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2770),X2769)),X2772))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2771),X2769)),X2772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transD])]) ).
fof(i_0_686,plain,
! [X4013,X4014,X4015,X4016,X4017] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4017,X4016),hAPP(X4017,X4015))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4014,X4014)),hAPP(hAPP(c_Product__Type_OPair(X4014,X4014),X4016),X4015)),c_List_Omeasures(X4014,X4013)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4014,X4014)),hAPP(hAPP(c_Product__Type_OPair(X4014,X4014),X4016),X4015)),c_List_Omeasures(X4014,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4014,tc_Nat_Onat)),X4017),X4013)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).
fof(i_0_687,plain,
! [X3303,X3304,X3305,X3306,X3307,X3308,X3309] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3309,X3308)),hAPP(hAPP(c_Product__Type_OPair(X3309,X3308),X3307),X3306)),X3305))
| hBOOL(hAPP(hAPP(c_member(X3304),hAPP(hAPP(X3303,X3307),X3306)),c_Set_Oimage(tc_prod(X3309,X3308),X3304,hAPP(c_Product__Type_Oprod_Oprod__case(X3309,X3308,X3304),X3303),X3305))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).
fof(i_0_688,plain,
! [X2570,X2571,X2572,X2573,X2574,X2575,X2576,X2577] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2577,X2577)),hAPP(hAPP(c_Product__Type_OPair(X2577,X2577),X2576),X2575)),X2574))
| X2573 != hAPP(hAPP(c_List_Oappend(X2577),X2572),hAPP(hAPP(c_List_Olist_OCons(X2577),X2576),X2571))
| X2570 != hAPP(hAPP(c_List_Oappend(X2577),X2572),hAPP(hAPP(c_List_Olist_OCons(X2577),X2575),X2571))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2577),tc_List_Olist(X2577))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2577),tc_List_Olist(X2577)),X2573),X2570)),c_List_Olistrel1(X2577,X2574))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).
fof(i_0_689,plain,
! [X3365,X3366,X3367,X3368,X3369,X3371,X3372,X3373,X3374,X3375,X3376] :
( ( hBOOL(hAPP(hAPP(c_member(X3367),esk83_4(X3365,X3366,X3367,X3368)),X3365))
| ~ hBOOL(hAPP(hAPP(c_member(X3369),X3368),c_Set_Oimage(X3367,X3369,X3366,X3365))) )
& ( X3368 = hAPP(X3366,esk83_4(X3365,X3366,X3367,X3368))
| ~ hBOOL(hAPP(hAPP(c_member(X3369),X3368),c_Set_Oimage(X3367,X3369,X3366,X3365))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3373),X3375),X3371))
| X3374 != hAPP(X3372,X3375)
| hBOOL(hAPP(hAPP(c_member(X3376),X3374),c_Set_Oimage(X3373,X3376,X3372,X3371))) ) ),
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_690,plain,
! [X2268,X2269,X2270] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2269),X2268)),X2270))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2268),X2269)),X2270))
| X2269 = X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2270),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),X2268),X2269)),X2270))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2269),X2268)),X2270))
| X2269 = X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2270),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])])]) ).
fof(i_0_691,plain,
! [X2271,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_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2272),X2271)),X2273))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2271),X2272)),X2273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])]) ).
fof(i_0_692,plain,
! [X3072,X3073,X3074] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3074,X3073)),hAPP(hAPP(c_Product__Type_OPair(X3074,X3073),esk77_3(X3072,X3073,X3074)),esk78_3(X3072,X3073,X3074))),X3072))
| c_Relation_Osingle__valued(X3074,X3073,X3072) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3074,X3073)),hAPP(hAPP(c_Product__Type_OPair(X3074,X3073),esk77_3(X3072,X3073,X3074)),esk79_3(X3072,X3073,X3074))),X3072))
| c_Relation_Osingle__valued(X3074,X3073,X3072) )
& ( esk78_3(X3072,X3073,X3074) != esk79_3(X3072,X3073,X3074)
| c_Relation_Osingle__valued(X3074,X3073,X3072) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedI])])])]) ).
fof(i_0_693,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_694,plain,
! [X3417,X3418,X3419,X3420,X3421] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X3421,X3420,tc_HOL_Obool,X3419),X3418),X3417))
| hBOOL(hAPP(X3419,hAPP(hAPP(c_Product__Type_OPair(X3421,X3420),X3418),X3417))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryD])]) ).
fof(i_0_695,plain,
! [X3412,X3413,X3414,X3415,X3416] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X3416,X3415,tc_HOL_Obool,X3414),X3413),X3412))
| hBOOL(hAPP(X3414,hAPP(hAPP(c_Product__Type_OPair(X3416,X3415),X3413),X3412))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryE])]) ).
fof(i_0_696,plain,
! [X3932,X3933,X3934,X3935,X3936] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3936,X3935)),X3934),c_FuncSet_OPi(X3936,X3935,X3933,c_COMBK(tc_fun(X3935,tc_HOL_Obool),X3936,X3932))))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3935,tc_HOL_Obool),c_Set_Oimage(X3936,X3935,X3934,X3933),X3932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_697,plain,
! [X3884,X3885,X3886,X3887,X3888,X3890,X3891,X3892,X3893,X3894,X3895] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3886,tc_HOL_Obool),esk102_5(X3884,X3885,X3886,X3887,X3888),X3884)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3888,tc_HOL_Obool),X3887,c_Set_Oimage(X3886,X3888,X3885,X3884)) )
& ( X3887 = c_Set_Oimage(X3886,X3888,X3885,esk102_5(X3884,X3885,X3886,X3887,X3888))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3888,tc_HOL_Obool),X3887,c_Set_Oimage(X3886,X3888,X3885,X3884)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3892,tc_HOL_Obool),X3895,X3890)
| X3893 != c_Set_Oimage(X3892,X3894,X3891,X3895)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3894,tc_HOL_Obool),X3893,c_Set_Oimage(X3892,X3894,X3891,X3890)) ) ),
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_698,plain,
! [X3192,X3193,X3194,X3195,X3196,X3197,X3198] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3198,X3197,tc_fun(X3196,tc_HOL_Obool)),X3195),hAPP(hAPP(c_Product__Type_OPair(X3198,X3197),X3194),X3193)),X3192))
| hBOOL(hAPP(hAPP(hAPP(X3195,X3194),X3193),X3192)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).
fof(i_0_699,plain,
! [X2289,X2290,X2291,X2292,X2293,X2294] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2294,X2293)),X2292),c_FuncSet_OPi(X2294,X2293,X2291,c_COMBK(tc_fun(X2293,tc_HOL_Obool),X2294,X2290))))
| ~ hBOOL(hAPP(hAPP(c_member(X2294),X2289),X2291))
| hBOOL(hAPP(hAPP(c_member(X2293),hAPP(X2292,X2289)),X2290)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_700,plain,
! [X2840,X2841,X2842,X2843,X2844,X2845] :
( ~ c_Relation_Osingle__valued(X2845,X2844,X2843)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2845,X2844)),hAPP(hAPP(c_Product__Type_OPair(X2845,X2844),X2842),X2841)),X2843))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2845,X2844)),hAPP(hAPP(c_Product__Type_OPair(X2845,X2844),X2842),X2840)),X2843))
| X2841 = X2840 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).
fof(i_0_701,plain,
! [X4018,X4019,X4020,X4021,X4022] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4020,X4021),X4019,X4018)
| c_Orderings_Oord__class_Oless__eq(X4021,hAPP(X4019,X4022),hAPP(X4018,X4022))
| ~ class_Orderings_Oord(X4021) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4021,hAPP(X4019,esk103_4(X4018,X4019,X4020,X4021)),hAPP(X4018,esk103_4(X4018,X4019,X4020,X4021)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4020,X4021),X4019,X4018)
| ~ class_Orderings_Oord(X4021) ) ),
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_702,plain,
! [X2143] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2143)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X2143)),v_c____),v_b____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X2143)),v_c____),v_b____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2143))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096])]) ).
fof(i_0_703,plain,
! [X2418,X2419,X2420,X2423,X2424,X2425,X2426,X2427] :
( ( ~ 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)),c_List_Olist_ONil(X2420)),X2419)),c_List_Olexord(X2420,X2418)))
| X2419 = hAPP(hAPP(c_List_Olist_OCons(X2420),esk25_3(X2418,X2419,X2420)),esk26_3(X2418,X2419,X2420)) )
& ( X2424 != hAPP(hAPP(c_List_Olist_OCons(X2425),X2426),X2427)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2425),tc_List_Olist(X2425))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2425),tc_List_Olist(X2425)),c_List_Olist_ONil(X2425)),X2424)),c_List_Olexord(X2425,X2423))) ) ),
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_704,plain,
! [X2277] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2277),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,X2277)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_705,plain,
! [X4024,X4025,X4026,X4027,X4028] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4028,X4027),hAPP(X4028,X4026))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4025,X4025)),hAPP(hAPP(c_Product__Type_OPair(X4025,X4025),X4027),X4026)),X4024))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4025,X4025)),hAPP(hAPP(c_Product__Type_OPair(X4025,X4025),X4027),X4026)),c_Wellfounded_Omlex__prod(X4025,X4028,X4024))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_706,plain,
! [X3901,X3902,X3903,X3904,X3905] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3905,tc_HOL_Obool),c_Set_Oimage(X3904,X3905,X3903,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3904,tc_HOL_Obool),X3902,X3901)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3905,tc_HOL_Obool),c_Set_Oimage(X3904,X3905,X3903,X3902),c_Set_Oimage(X3904,X3905,X3903,X3901))),
inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).
fof(i_0_707,plain,
! [X2157,X2158,X2159,X2160,X2161] :
( ( ~ c_FunDef_Oin__rel(X2161,X2160,X2159,X2158,X2157)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2161,X2160)),hAPP(hAPP(c_Product__Type_OPair(X2161,X2160),X2158),X2157)),X2159)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2161,X2160)),hAPP(hAPP(c_Product__Type_OPair(X2161,X2160),X2158),X2157)),X2159))
| c_FunDef_Oin__rel(X2161,X2160,X2159,X2158,X2157) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_708,plain,
! [X2695,X2696,X2697,X2698,X2699] :
( ( c_Nat_Osize__class_Osize(tc_List_Olist(X2699),X2698) = X2695
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2699),tc_List_Olist(X2699))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2699),tc_List_Olist(X2699)),X2698),X2697)),c_List_Olexn(X2699,X2696,X2695))) )
& ( c_Nat_Osize__class_Osize(tc_List_Olist(X2699),X2697) = X2695
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2699),tc_List_Olist(X2699))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2699),tc_List_Olist(X2699)),X2698),X2697)),c_List_Olexn(X2699,X2696,X2695))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).
fof(i_0_709,plain,
! [X2961,X2962,X2963] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2963,X2963)),hAPP(hAPP(c_Product__Type_OPair(X2963,X2963),esk61_3(X2961,X2962,X2963)),X2962)),X2961))
| hBOOL(hAPP(hAPP(c_member(X2963),X2962),c_Wellfounded_Oacc(X2963,X2961))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2963),esk61_3(X2961,X2962,X2963)),c_Wellfounded_Oacc(X2963,X2961)))
| hBOOL(hAPP(hAPP(c_member(X2963),X2962),c_Wellfounded_Oacc(X2963,X2961))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])])])]) ).
fof(i_0_710,plain,
! [X2957,X2958,X2959] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2959,X2959)),hAPP(hAPP(c_Product__Type_OPair(X2959,X2959),esk60_3(X2957,X2958,X2959)),X2958)),X2957))
| hBOOL(hAPP(hAPP(c_member(X2959),X2958),c_Wellfounded_Oacc(X2959,X2957))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2959),esk60_3(X2957,X2958,X2959)),c_Wellfounded_Oacc(X2959,X2957)))
| hBOOL(hAPP(hAPP(c_member(X2959),X2958),c_Wellfounded_Oacc(X2959,X2957))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).
fof(i_0_711,plain,
! [X2882,X2883,X2884,X2885,X2886,X2887,X2888] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2884),X2883),c_Wellfounded_Oacc(X2884,X2882)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2884,X2884)),hAPP(hAPP(c_Product__Type_OPair(X2884,X2884),X2885),X2883)),X2882))
| hBOOL(hAPP(hAPP(c_member(X2884),X2885),c_Wellfounded_Oacc(X2884,X2882))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2888,X2888)),hAPP(hAPP(c_Product__Type_OPair(X2888,X2888),esk54_3(X2886,X2887,X2888)),X2887)),X2886))
| hBOOL(hAPP(hAPP(c_member(X2888),X2887),c_Wellfounded_Oacc(X2888,X2886))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2888),esk54_3(X2886,X2887,X2888)),c_Wellfounded_Oacc(X2888,X2886)))
| hBOOL(hAPP(hAPP(c_member(X2888),X2887),c_Wellfounded_Oacc(X2888,X2886))) ) ),
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_712,plain,
! [X3155,X3156,X3157,X3158] : hAPP(c_Product__Type_Oprod_Oprod__case(X3158,X3157,X3156),hAPP(hAPP(c_COMBB(tc_fun(X3157,tc_prod(X3158,X3157)),tc_fun(X3157,X3156),X3158),hAPP(c_COMBB(tc_prod(X3158,X3157),X3156,X3157),X3155)),c_Product__Type_OPair(X3158,X3157))) = X3155,
inference(variable_rename,[status(thm)],[fact_split__eta]) ).
fof(i_0_713,plain,
! [X2759,X2760,X2761,X2762] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2762),tc_List_Olist(X2762))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2762),tc_List_Olist(X2762)),X2761),X2760)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2762),c_List_Olistrel1(X2762,X2759))))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2762),X2761) = c_Nat_Osize__class_Osize(tc_List_Olist(X2762),X2760) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).
fof(i_0_714,plain,
! [X2462,X2463,X2464] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2464),tc_List_Olist(X2464))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2464),tc_List_Olist(X2464)),c_List_Olist_ONil(X2464)),X2463)),c_List_Olistrel(X2464,X2462)))
| X2463 = c_List_Olist_ONil(X2464) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).
fof(i_0_715,plain,
! [X2594,X2595,X2596] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2596),tc_List_Olist(X2596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2596),tc_List_Olist(X2596)),c_List_Olist_ONil(X2596)),X2595)),c_List_Olistrel1(X2596,X2594))),
inference(variable_rename,[status(thm)],[i_0_532]) ).
fof(i_0_716,plain,
! [X2441,X2442,X2443] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2443),tc_List_Olist(X2443))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2443),tc_List_Olist(X2443)),c_List_Olist_ONil(X2443)),X2442)),c_List_Olex(X2443,X2441))),
inference(variable_rename,[status(thm)],[i_0_533]) ).
fof(i_0_717,plain,
! [X3589,X3590,X3591,X3592,X3593] :
( ~ hBOOL(hAPP(hAPP(c_member(X3593),X3592),c_Set_Oimage(X3591,X3593,X3590,X3589)))
| hAPP(X3590,hAPP(c_Hilbert__Choice_Oinv__into(X3591,X3593,X3589,X3590),X3592)) = X3592 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
fof(i_0_718,plain,
! [X2465,X2466,X2467] :
( ~ 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)),X2466),c_List_Olist_ONil(X2467))),c_List_Olistrel(X2467,X2465)))
| X2466 = c_List_Olist_ONil(X2467) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).
fof(i_0_719,plain,
! [X2597,X2598,X2599] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2599),tc_List_Olist(X2599))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2599),tc_List_Olist(X2599)),X2598),c_List_Olist_ONil(X2599))),c_List_Olistrel1(X2599,X2597))),
inference(variable_rename,[status(thm)],[i_0_534]) ).
fof(i_0_720,plain,
! [X2438,X2439,X2440] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2440),tc_List_Olist(X2440))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2440),tc_List_Olist(X2440)),X2439),c_List_Olist_ONil(X2440))),c_List_Olex(X2440,X2438))),
inference(variable_rename,[status(thm)],[i_0_535]) ).
fof(i_0_721,plain,
! [X2401,X2402,X2403] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2403),tc_List_Olist(X2403))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2403),tc_List_Olist(X2403)),X2402),c_List_Olist_ONil(X2403))),c_List_Olexord(X2403,X2401))),
inference(variable_rename,[status(thm)],[i_0_536]) ).
fof(i_0_722,plain,
! [X2679,X2680,X2681,X2682] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2682),tc_List_Olist(X2682))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2682),tc_List_Olist(X2682)),X2681),X2680)),c_List_Olistrel1(X2682,X2679)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2682),X2681) = c_Nat_Osize__class_Osize(tc_List_Olist(X2682),X2680) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).
fof(i_0_723,plain,
! [X2683,X2684,X2685,X2686] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2686),tc_List_Olist(X2686))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2686),tc_List_Olist(X2686)),X2685),X2684)),c_List_Olistrel(X2686,X2683)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2686),X2685) = c_Nat_Osize__class_Osize(tc_List_Olist(X2686),X2684) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).
fof(i_0_724,plain,
! [X3207,X3208,X3209,X3211,X3212,X3213,X3214,X3215,X3218] :
( ( ~ hBOOL(hAPP(X3209,esk80_3(X3207,X3208,X3209)))
| hBOOL(hAPP(X3209,hAPP(hAPP(c_Product__Type_OPair(X3208,X3207),X3211),X3212))) )
& ( ~ hBOOL(hAPP(X3215,hAPP(hAPP(c_Product__Type_OPair(X3214,X3213),esk81_3(X3213,X3214,X3215)),esk82_3(X3213,X3214,X3215))))
| hBOOL(hAPP(X3215,X3218)) ) ),
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_725,plain,
! [X3407,X3408,X3409,X3410,X3411] :
( ~ hBOOL(hAPP(X3411,hAPP(hAPP(c_Product__Type_OPair(X3410,X3409),X3408),X3407)))
| hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X3410,X3409,tc_HOL_Obool,X3411),X3408),X3407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).
fof(i_0_726,plain,
! [X3663,X3664] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3664,X3664)),hAPP(hAPP(c_Product__Type_OPair(X3664,X3664),esk94_2(X3663,X3664)),esk95_2(X3663,X3664))),X3663))
| c_Relation_Otrans(X3664,X3663) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3664,X3664)),hAPP(hAPP(c_Product__Type_OPair(X3664,X3664),esk95_2(X3663,X3664)),esk96_2(X3663,X3664))),X3663))
| c_Relation_Otrans(X3664,X3663) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3664,X3664)),hAPP(hAPP(c_Product__Type_OPair(X3664,X3664),esk94_2(X3663,X3664)),esk96_2(X3663,X3664))),X3663))
| c_Relation_Otrans(X3664,X3663) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transI])])])]) ).
fof(i_0_727,plain,
! [X2169,X2170,X2171,X2172,X2173] :
( ( ~ c_Nitpick_Orefl_H(X2170,X2169)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2170,X2170)),hAPP(hAPP(c_Product__Type_OPair(X2170,X2170),X2171),X2171)),X2169)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2173,X2173)),hAPP(hAPP(c_Product__Type_OPair(X2173,X2173),esk2_2(X2172,X2173)),esk2_2(X2172,X2173))),X2172))
| c_Nitpick_Orefl_H(X2173,X2172) ) ),
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_728,plain,
! [X3180,X3181,X3182,X3183,X3184,X3185,X3186] :
( ~ hBOOL(hAPP(hAPP(c_member(X3186),X3185),hAPP(hAPP(X3184,X3183),X3182)))
| hBOOL(hAPP(hAPP(c_member(X3186),X3185),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3181,X3180,tc_fun(X3186,tc_HOL_Obool)),X3184),hAPP(hAPP(c_Product__Type_OPair(X3181,X3180),X3183),X3182)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).
fof(i_0_729,plain,
! [X2640,X2641,X2642,X2643,X2644,X2645] :
( X2643 != hAPP(hAPP(c_List_Olist_OCons(X2642),X2644),X2645)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2642),tc_List_Olist(X2642))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2642),tc_List_Olist(X2642)),X2641),hAPP(hAPP(c_List_Oappend(X2642),X2641),X2643))),c_List_Olexord(X2642,X2640))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).
cnf(i_0_730,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_537]) ).
fof(i_0_731,plain,
! [X3510,X3511,X3512,X3513] : hBOOL(hAPP(hAPP(c_member(tc_fun(X3513,X3512)),c_FuncSet_Orestrict(X3513,X3512,X3511,X3510)),c_FuncSet_Oextensional(X3513,X3512,X3510))),
inference(variable_rename,[status(thm)],[fact_restrict__extensional]) ).
fof(i_0_732,plain,
! [X2300,X2301,X2302,X2303,X2304,X2305] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2305,X2304)),X2303),c_FuncSet_OPi(X2305,X2304,X2302,X2301)))
| ~ hBOOL(hAPP(hAPP(c_member(X2305),X2300),X2302))
| hBOOL(hAPP(hAPP(c_member(X2304),hAPP(X2303,X2300)),hAPP(X2301,X2300))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_733,plain,
! [X2283,X2284,X2285,X2286,X2287,X2288] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2288,X2287)),X2286),c_FuncSet_OPi(X2288,X2287,X2285,X2284)))
| hBOOL(hAPP(hAPP(c_member(X2287),hAPP(X2286,X2283)),hAPP(X2284,X2283)))
| ~ hBOOL(hAPP(hAPP(c_member(X2288),X2283),X2285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])]) ).
fof(i_0_734,plain,
! [X3623,X3624,X3625,X3626,X3627,X3628] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3628,X3627)),X3626),c_FuncSet_Oextensional__funcset(X3628,X3627,X3625,X3624)))
| ~ hBOOL(hAPP(hAPP(c_member(X3628),X3623),X3625))
| hBOOL(hAPP(hAPP(c_member(X3627),hAPP(X3626,X3623)),X3624)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__funcset__mem])]) ).
fof(i_0_735,plain,
! [X3810,X3811,X3812] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3812,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3812,tc_fun(X3812,tc_HOL_Obool),tc_HOL_Obool),c_member(X3812)),X3811),hAPP(hAPP(c_COMBC(X3812,tc_fun(X3812,tc_HOL_Obool),tc_HOL_Obool),c_member(X3812)),X3810))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3812,tc_HOL_Obool),X3811,X3810) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3812,tc_HOL_Obool),X3811,X3810)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3812,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3812,tc_fun(X3812,tc_HOL_Obool),tc_HOL_Obool),c_member(X3812)),X3811),hAPP(hAPP(c_COMBC(X3812,tc_fun(X3812,tc_HOL_Obool),tc_HOL_Obool),c_member(X3812)),X3810)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_736,plain,
! [X4052,X4053,X4054,X4055,X4056] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4056,X4055),hAPP(X4056,X4054))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4053,X4053)),hAPP(hAPP(c_Product__Type_OPair(X4053,X4053),X4055),X4054)),c_List_Omeasures(X4053,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X4053,tc_Nat_Onat)),X4056),X4052)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).
fof(i_0_737,plain,
! [X2149,X2150,X2151,X2152] :
( ( X2151 != X2149
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),c_Arrow__Order__Mirabelle_Omkbot(X2150,X2149))) )
& ( X2152 != X2149
| X2152 != X2151
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),c_Arrow__Order__Mirabelle_Omkbot(X2150,X2149))) )
& ( X2152 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),X2150))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),c_Arrow__Order__Mirabelle_Omkbot(X2150,X2149))) )
& ( X2152 != X2149
| X2152 = X2149
| X2151 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),c_Arrow__Order__Mirabelle_Omkbot(X2150,X2149))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),X2150))
| X2152 = X2149
| X2151 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),c_Arrow__Order__Mirabelle_Omkbot(X2150,X2149))) )
& ( X2152 != X2149
| X2152 = X2151
| X2151 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),c_Arrow__Order__Mirabelle_Omkbot(X2150,X2149))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),X2150))
| X2152 = X2151
| X2151 = X2149
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2152),X2151)),c_Arrow__Order__Mirabelle_Omkbot(X2150,X2149))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_738,plain,
! [X2153,X2154,X2155,X2156] :
( ( X2156 != X2153
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),c_Arrow__Order__Mirabelle_Omktop(X2154,X2153))) )
& ( X2155 != X2153
| X2156 != X2155
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),c_Arrow__Order__Mirabelle_Omktop(X2154,X2153))) )
& ( X2155 = X2153
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),X2154))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),c_Arrow__Order__Mirabelle_Omktop(X2154,X2153))) )
& ( X2155 != X2153
| X2155 = X2153
| X2156 = X2153
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),c_Arrow__Order__Mirabelle_Omktop(X2154,X2153))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),X2154))
| X2155 = X2153
| X2156 = X2153
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),c_Arrow__Order__Mirabelle_Omktop(X2154,X2153))) )
& ( X2155 != X2153
| X2156 = X2155
| X2156 = X2153
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),c_Arrow__Order__Mirabelle_Omktop(X2154,X2153))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),X2154))
| X2156 = X2155
| X2156 = X2153
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2156),X2155)),c_Arrow__Order__Mirabelle_Omktop(X2154,X2153))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_739,plain,
! [X2142] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2142)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2142))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2142)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2142))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iff])]) ).
fof(i_0_740,plain,
! [X3906,X3907,X3908,X3909,X3910,X3911] :
( c_Set_Oimage(X3911,X3910,X3909,X3908) != X3907
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3910,tc_HOL_Obool),X3906,X3907)
| c_Set_Oimage(X3911,X3910,X3909,c_Set_Oimage(X3910,X3911,c_Hilbert__Choice_Oinv__into(X3911,X3910,X3908,X3909),X3906)) = X3906 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_741,plain,
! [X2247,X2248,X2249] :
( X2249 = X2248
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2247),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,X2247),X2249),X2248)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_742,plain,
! [X3611,X3612,X3613,X3614,X3615,X3616] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3616,X3615)),X3614),c_FuncSet_Oextensional__funcset(X3616,X3615,X3613,X3612)))
| hBOOL(hAPP(hAPP(c_member(X3616),X3611),X3613))
| hAPP(X3614,X3611) = c_HOL_Oundefined(X3615) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])]) ).
fof(i_0_743,plain,
! [X2813,X2814,X2815,X2816] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2816,X2816)),hAPP(hAPP(c_Product__Type_OPair(X2816,X2816),X2815),X2814)),c_Transitive__Closure_Ortrancl(X2816,X2813)))
| ~ hBOOL(hAPP(hAPP(c_member(X2816),X2814),c_Wellfounded_Oacc(X2816,X2813)))
| hBOOL(hAPP(hAPP(c_member(X2816),X2815),c_Wellfounded_Oacc(X2816,X2813))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).
fof(i_0_744,plain,
! [X2809,X2810,X2811,X2812] :
( ~ hBOOL(hAPP(hAPP(c_member(X2812),X2811),c_Wellfounded_Oacc(X2812,X2810)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2812,X2812)),hAPP(hAPP(c_Product__Type_OPair(X2812,X2812),X2809),X2811)),c_Transitive__Closure_Ortrancl(X2812,X2810)))
| hBOOL(hAPP(hAPP(c_member(X2812),X2809),c_Wellfounded_Oacc(X2812,X2810))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).
fof(i_0_745,plain,
! [X2316,X2317,X2318,X2319,X2320] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2317,X2316)
| ~ 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))),X2318),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2317,X2318) = hAPP(X2318,X2316) )
& ( 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))),esk19_2(X2319,X2320)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2320,X2319) )
& ( hAPP(X2320,esk19_2(X2319,X2320)) != hAPP(esk19_2(X2319,X2320),X2319)
| c_Arrow__Order__Mirabelle_Odictator(X2320,X2319) ) ),
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_746,plain,
! [X3649,X3650,X3651,X3652,X3653,X3654] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3654,X3654)),hAPP(hAPP(c_Product__Type_OPair(X3654,X3654),X3653),X3652)),X3651))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3654,X3650),X3649),X3651),X3652),X3653) = hAPP(X3649,X3653) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut__apply])]) ).
fof(i_0_747,plain,
! [X3629,X3630,X3631,X3632,X3633,X3634] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3632,X3632)),hAPP(hAPP(c_Product__Type_OPair(X3632,X3632),X3631),X3630)),X3634))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3632,X3629),X3633),X3634),X3630),X3631) = hAPP(X3633,X3631) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__cut__apply])]) ).
fof(i_0_748,plain,
! [X3605,X3606,X3607,X3608,X3609,X3610] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3610,X3610)),hAPP(hAPP(c_Product__Type_OPair(X3610,X3610),X3609),X3608)),X3607))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3610,X3606),X3605),X3607),X3608),X3609) = hAPP(X3605,X3609) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3610,X3610)),hAPP(hAPP(c_Product__Type_OPair(X3610,X3610),X3609),X3608)),X3607))
| hAPP(hAPP(hAPP(hAPP(c_Recdef_Ocut(X3610,X3606),X3605),X3607),X3608),X3609) = c_HOL_Oundefined(X3606) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])]) ).
fof(i_0_749,plain,
! [X2878,X2879,X2880,X2881] :
( ~ hBOOL(hAPP(hAPP(c_member(X2881),X2880),c_Wellfounded_Oacc(X2881,X2879)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2881,X2881)),hAPP(hAPP(c_Product__Type_OPair(X2881,X2881),X2878),X2880)),X2879))
| hBOOL(hAPP(hAPP(c_member(X2881),X2878),c_Wellfounded_Oacc(X2881,X2879))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).
fof(i_0_750,plain,
! [X2370,X2371,X2372] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2372,X2372)),hAPP(hAPP(c_Product__Type_OPair(X2372,X2372),X2371),X2370)),c_List_Omeasures(X2372,c_List_Olist_ONil(tc_fun(X2372,tc_Nat_Onat))))),
inference(variable_rename,[status(thm)],[i_0_541]) ).
fof(i_0_751,plain,
! [X2822,X2823,X2824,X2825] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2825,X2825)),hAPP(hAPP(c_Product__Type_OPair(X2825,X2825),X2824),X2822)),c_Transitive__Closure_Ortrancl(X2825,X2823)))
| X2824 = X2822
| hBOOL(hAPP(hAPP(c_member(X2825),X2824),c_Relation_ODomain(X2825,X2825,X2823))) )
& ( X2824 != X2822
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2825,X2825)),hAPP(hAPP(c_Product__Type_OPair(X2825,X2825),X2824),X2822)),c_Transitive__Closure_Ortrancl(X2825,X2823)))
| hBOOL(hAPP(hAPP(c_member(X2825),X2824),c_Relation_ODomain(X2825,X2825,X2823))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])])]) ).
fof(i_0_752,plain,
! [X2338,X2339,X2340] :
( X2340 = X2339
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2338),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(X2338,X2340,X2339)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_753,plain,
! [X2831,X2832,X2833,X2834,X2835] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2835,X2834)),hAPP(hAPP(c_Product__Type_OPair(X2835,X2834),X2833),X2832)),X2831))
| hBOOL(hAPP(hAPP(c_member(X2835),X2833),c_Relation_ODomain(X2835,X2834,X2831))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).
fof(i_0_754,plain,
! [X2826,X2827,X2828,X2829,X2830] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2830,X2829)),hAPP(hAPP(c_Product__Type_OPair(X2830,X2829),X2828),X2827)),X2826))
| hBOOL(hAPP(hAPP(c_member(X2829),X2827),c_Relation_ORange(X2830,X2829,X2826))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).
fof(i_0_755,plain,
! [X2306,X2307] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2307,X2307)),c_COMBI(X2307)),c_FuncSet_OPi(X2307,X2307,X2306,c_COMBK(tc_fun(X2307,tc_HOL_Obool),X2307,X2306)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_756,plain,
! [X2600,X2601] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2601),tc_List_Olist(X2601))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2601),tc_List_Olist(X2601)),c_List_Olist_ONil(X2601)),c_List_Olist_ONil(X2601))),c_List_Olistrel(X2601,X2600))),
inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).
fof(i_0_757,plain,
! [X2987,X2988,X2989,X2990] :
( ( X2989 = X2988
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2990,X2990)),hAPP(hAPP(c_Product__Type_OPair(X2990,X2990),X2989),X2988)),c_Relation_OId__on(X2990,X2987))) )
& ( hBOOL(hAPP(hAPP(c_member(X2990),X2989),X2987))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2990,X2990)),hAPP(hAPP(c_Product__Type_OPair(X2990,X2990),X2989),X2988)),c_Relation_OId__on(X2990,X2987))) )
& ( X2989 != X2988
| ~ hBOOL(hAPP(hAPP(c_member(X2990),X2989),X2987))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2990,X2990)),hAPP(hAPP(c_Product__Type_OPair(X2990,X2990),X2989),X2988)),c_Relation_OId__on(X2990,X2987))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).
fof(i_0_758,plain,
! [X4207,X4208,X4209,X4210] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4210,X4210)),hAPP(hAPP(c_Product__Type_OPair(X4210,X4210),X4209),X4208)),c_Wellfounded_Omeasure(X4210,X4207)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4207,X4209),hAPP(X4207,X4208)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4207,X4209),hAPP(X4207,X4208))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4210,X4210)),hAPP(hAPP(c_Product__Type_OPair(X4210,X4210),X4209),X4208)),c_Wellfounded_Omeasure(X4210,X4207))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_759,plain,
! [X3316,X3317,X3318,X3319,X3320,X3321] :
( ( hBOOL(hAPP(hAPP(X3319,X3317),X3316))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3321,tc_fun(X3320,tc_HOL_Obool)),X3319,X3318),X3317),X3316)) )
& ( hBOOL(hAPP(hAPP(X3318,X3317),X3316))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3321,tc_fun(X3320,tc_HOL_Obool)),X3319,X3318),X3317),X3316)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])])]) ).
fof(i_0_760,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_761,plain,
! [X3334,X3335,X3336,X3337,X3338,X3339] :
( ~ hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3339,tc_fun(X3338,tc_HOL_Obool)),X3337,X3336),X3335),X3334))
| hBOOL(hAPP(hAPP(X3336,X3335),X3334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).
fof(i_0_762,plain,
! [X2731,X2732,X2733] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2733),tc_List_Olist(X2733))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2733),tc_List_Olist(X2733)),X2732),X2732)),c_List_Olistrel(X2733,c_Transitive__Closure_Ortrancl(X2733,X2731)))),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).
cnf(i_0_763,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_544]) ).
fof(i_0_764,plain,
! [X2803,X2804,X2805,X2806,X2807] :
( ( ~ c_Relation_Oirrefl(X2804,X2803)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2804,X2804)),hAPP(hAPP(c_Product__Type_OPair(X2804,X2804),X2805),X2805)),X2803)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2807,X2807)),hAPP(hAPP(c_Product__Type_OPair(X2807,X2807),esk48_2(X2806,X2807)),esk48_2(X2806,X2807))),X2806))
| c_Relation_Oirrefl(X2807,X2806) ) ),
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_545])])])])]) ).
fof(i_0_765,plain,
! [X2250,X2251] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2251),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(X2251,X2250)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_766,plain,
! [X2252,X2253] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2253),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(X2253,X2252)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_767,plain,
! [X3531,X3532] :
( X3532 = c_List_Olist_ONil(X3531)
| ~ c_List_Odistinct(X3531,X3532)
| c_List_OtakeWhile(X3531,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3531),c_fNot),hAPP(hAPP(c_COMBC(X3531,X3531,tc_HOL_Obool),c_fequal),c_List_Olast(X3531,X3532))),X3532) = c_List_Obutlast(X3531,X3532) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last])]) ).
fof(i_0_768,plain,
! [X2836,X2837,X2838,X2839] :
( ~ hBOOL(hAPP(hAPP(c_member(X2839),X2838),c_Wellfounded_Oacc(X2839,X2837)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2839)),X2836),c_Wellfounded_Oacc(tc_List_Olist(X2839),c_List_Olistrel1(X2839,X2837))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2839)),hAPP(hAPP(c_List_Olist_OCons(X2839),X2838),X2836)),c_Wellfounded_Oacc(tc_List_Olist(X2839),c_List_Olistrel1(X2839,X2837)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).
fof(i_0_769,plain,
! [X3377,X3378,X3379,X3380,X3381,X3382] : c_Set_Oimage(X3382,X3381,X3380,c_Set_Oimage(X3379,X3382,X3378,X3377)) = c_Set_Oimage(X3379,X3381,hAPP(hAPP(c_COMBB(X3382,X3381,X3379),X3380),X3378),X3377),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_770,plain,
! [X3912,X3913,X3914,X3915,X3916] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3916,X3915)),X3914),c_FuncSet_Oextensional(X3916,X3915,X3913)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3916,tc_HOL_Obool),X3913,X3912)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3916,X3915)),X3914),c_FuncSet_Oextensional(X3916,X3915,X3912))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__subset])]) ).
fof(i_0_771,plain,
! [X3187,X3188,X3189,X3190,X3191] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3191,X3190,tc_HOL_Obool),X3189),hAPP(hAPP(c_Product__Type_OPair(X3191,X3190),X3188),X3187)))
| hBOOL(hAPP(hAPP(X3189,X3188),X3187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).
fof(i_0_772,plain,
! [X3294,X3295,X3296,X3297,X3298,X3299] : c_Product__Type_Oprod_Oprod__rec(X3299,X3298,X3297,X3296,hAPP(hAPP(c_Product__Type_OPair(X3299,X3298),X3295),X3294)) = hAPP(hAPP(X3296,X3295),X3294),
inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).
fof(i_0_773,plain,
! [X4202,X4203,X4204,X4205,X4206] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X4206,X4205),hAPP(X4206,X4204))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4203,X4203)),hAPP(hAPP(c_Product__Type_OPair(X4203,X4203),X4205),X4204)),c_Wellfounded_Omlex__prod(X4203,X4206,X4202))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_774,plain,
! [X3360,X3361,X3362,X3363,X3364] :
( ~ hBOOL(hAPP(hAPP(c_member(X3364),X3363),X3362))
| hBOOL(hAPP(hAPP(c_member(X3361),hAPP(X3360,X3363)),c_Set_Oimage(X3364,X3361,X3360,X3362))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_775,plain,
! [X2341,X2342,X2343,X2344,X2345,X2346] : c_List_Olist_Olist__case(X2346,X2345,X2344,X2343,hAPP(hAPP(c_List_Olist_OCons(X2345),X2342),X2341)) = hAPP(hAPP(X2343,X2342),X2341),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).
fof(i_0_776,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_777,plain,
! [X3328,X3329,X3330,X3331,X3332,X3333] :
( X3333 != hAPP(X3332,X3331)
| ~ hBOOL(hAPP(hAPP(c_member(X3330),X3331),X3329))
| hBOOL(hAPP(hAPP(c_member(X3328),X3333),c_Set_Oimage(X3330,X3328,X3332,X3329))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_778,plain,
! [X3354,X3355,X3356,X3357,X3358,X3359] :
( ~ hBOOL(hAPP(hAPP(c_member(X3359),X3358),X3357))
| X3356 != hAPP(X3355,X3358)
| hBOOL(hAPP(hAPP(c_member(X3354),X3356),c_Set_Oimage(X3359,X3354,X3355,X3357))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_779,plain,
! [X3655,X3656,X3657,X3658] : c_FuncSet_Oextensional__funcset(X3658,X3657,X3656,X3655) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X3658,X3657),tc_HOL_Obool),c_FuncSet_OPi(X3658,X3657,X3656,c_COMBK(tc_fun(X3657,tc_HOL_Obool),X3658,X3655)),c_FuncSet_Oextensional(X3658,X3657,X3656)),
inference(variable_rename,[status(thm)],[fact_extensional__funcset__def]) ).
fof(i_0_780,plain,
! [X3928,X3929,X3930,X3931] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3931,tc_HOL_Obool),c_Relation_ORange(X3930,X3931,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3930,X3931),tc_HOL_Obool),X3929,X3928)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3931,tc_HOL_Obool),c_Relation_ORange(X3930,X3931,X3929),c_Relation_ORange(X3930,X3931,X3928))),
inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).
fof(i_0_781,plain,
! [X3924,X3925,X3926,X3927] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3927,tc_HOL_Obool),c_Relation_ODomain(X3927,X3926,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3927,X3926),tc_HOL_Obool),X3925,X3924)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3927,tc_HOL_Obool),c_Relation_ODomain(X3927,X3926,X3925),c_Relation_ODomain(X3927,X3926,X3924))),
inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).
fof(i_0_782,plain,
! [X2979,X2980,X2981,X2982] :
( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2982)),X2981),c_List_Olists(X2982,X2979)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2982)),hAPP(hAPP(c_List_Oappend(X2982),X2981),X2980)),c_List_Olists(X2982,X2979))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2982)),X2980),c_List_Olists(X2982,X2979)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2982)),hAPP(hAPP(c_List_Oappend(X2982),X2981),X2980)),c_List_Olists(X2982,X2979))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2982)),X2981),c_List_Olists(X2982,X2979)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2982)),X2980),c_List_Olists(X2982,X2979)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2982)),hAPP(hAPP(c_List_Oappend(X2982),X2981),X2980)),c_List_Olists(X2982,X2979))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).
fof(i_0_783,plain,
! [X2965,X2966,X2967,X2968] :
( X2968 != X2967
| ~ hBOOL(hAPP(hAPP(c_member(X2966),X2968),X2965))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2966,X2966)),hAPP(hAPP(c_Product__Type_OPair(X2966,X2966),X2968),X2967)),c_Relation_OId__on(X2966,X2965))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).
fof(i_0_784,plain,
! [X3847,X3848,X3849,X3850,X3851] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3851,tc_HOL_Obool),X3850,X3849)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3851,X3848),tc_HOL_Obool),c_FuncSet_OPi(X3851,X3848,X3849,X3847),c_FuncSet_OPi(X3851,X3848,X3850,X3847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_785,plain,
! [X3422,X3423,X3424,X3425,X3426,X3427] : hAPP(hAPP(c_Product__Type_Ocurry(X3427,X3426,X3425,X3424),X3423),X3422) = hAPP(X3424,hAPP(hAPP(c_Product__Type_OPair(X3427,X3426),X3423),X3422)),
inference(variable_rename,[status(thm)],[fact_curry__conv]) ).
fof(i_0_786,plain,
! [X3401,X3402,X3403,X3404,X3405,X3406] : hAPP(hAPP(c_Product__Type_Ocurry(X3406,X3405,X3404,X3403),X3402),X3401) = hAPP(X3403,hAPP(hAPP(c_Product__Type_OPair(X3406,X3405),X3402),X3401)),
inference(variable_rename,[status(thm)],[fact_curry__def]) ).
fof(i_0_787,plain,
! [X2325,X2326,X2327,X2328] : c_List_Olist_Olist__case(X2328,X2327,X2326,X2325,c_List_Olist_ONil(X2327)) = X2326,
inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).
fof(i_0_788,plain,
! [X3896,X3897,X3898,X3899,X3900] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3900,tc_HOL_Obool),X3899,X3898)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3897,tc_HOL_Obool),c_Set_Oimage(X3900,X3897,X3896,X3899),c_Set_Oimage(X3900,X3897,X3896,X3898)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_789,plain,
! [X2983,X2984,X2985,X2986] :
( ( hBOOL(hAPP(hAPP(c_member(X2986),X2985),X2983))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2986)),hAPP(hAPP(c_List_Olist_OCons(X2986),X2985),X2984)),c_List_Olists(X2986,X2983))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2986)),X2984),c_List_Olists(X2986,X2983)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2986)),hAPP(hAPP(c_List_Olist_OCons(X2986),X2985),X2984)),c_List_Olists(X2986,X2983))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2986),X2985),X2983))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2986)),X2984),c_List_Olists(X2986,X2983)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2986)),hAPP(hAPP(c_List_Olist_OCons(X2986),X2985),X2984)),c_List_Olists(X2986,X2983))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).
fof(i_0_790,plain,
! [X3001,X3002,X3003] :
( ( hBOOL(hAPP(hAPP(c_member(X3003),esk64_3(X3001,X3002,X3003)),X3001))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3003,X3003)),X3002),c_Relation_OId__on(X3003,X3001))) )
& ( X3002 = hAPP(hAPP(c_Product__Type_OPair(X3003,X3003),esk64_3(X3001,X3002,X3003)),esk64_3(X3001,X3002,X3003))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3003,X3003)),X3002),c_Relation_OId__on(X3003,X3001))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).
fof(i_0_791,plain,
! [X2274,X2275,X2276] :
( ( hAPP(hAPP(c_COMBC(X2276,tc_fun(X2276,tc_HOL_Obool),tc_HOL_Obool),c_member(X2276)),X2275) != hAPP(hAPP(c_COMBC(X2276,tc_fun(X2276,tc_HOL_Obool),tc_HOL_Obool),c_member(X2276)),X2274)
| X2275 = X2274 )
& ( X2275 != X2274
| hAPP(hAPP(c_COMBC(X2276,tc_fun(X2276,tc_HOL_Obool),tc_HOL_Obool),c_member(X2276)),X2275) = hAPP(hAPP(c_COMBC(X2276,tc_fun(X2276,tc_HOL_Obool),tc_HOL_Obool),c_member(X2276)),X2274) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_792,plain,
! [X2763,X2764,X2765] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2765,X2765)),hAPP(hAPP(c_Product__Type_OPair(X2765,X2765),X2764),X2764)),c_Transitive__Closure_Ortrancl(X2765,X2763))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
fof(i_0_793,plain,
! [X2313,X2314] :
( X2314 = X2313
| c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X2314),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X2313),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),esk18_2(X2313,X2314)),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_794,plain,
! [X3506,X3507,X3508,X3509] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3509,X3508)),X3507),c_FuncSet_Oextensional(X3509,X3508,X3506)))
| c_FuncSet_Orestrict(X3509,X3508,X3507,X3506) = X3507 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_extensional__restrict])]) ).
fof(i_0_795,plain,
! [X3175,X3176,X3177,X3178,X3179] :
( ~ hBOOL(hAPP(hAPP(X3179,X3178),X3177))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3176,X3175,tc_HOL_Obool),X3179),hAPP(hAPP(c_Product__Type_OPair(X3176,X3175),X3178),X3177))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).
fof(i_0_796,plain,
! [X3170,X3171,X3172,X3173,X3174] :
( ~ hBOOL(hAPP(hAPP(X3174,X3173),X3172))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3171,X3170,tc_HOL_Obool),X3174),hAPP(hAPP(c_Product__Type_OPair(X3171,X3170),X3173),X3172))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).
fof(i_0_797,plain,
! [X3488,X3489,X3490,X3491] : c_Set_Oimage(X3491,X3490,c_FuncSet_Orestrict(X3491,X3490,X3489,X3488),X3488) = c_Set_Oimage(X3491,X3490,X3489,X3488),
inference(variable_rename,[status(thm)],[fact_image__restrict__eq]) ).
fof(i_0_798,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_799,plain,
! [X2663,X2664,X2665,X2666,X2667,X2668] :
( ~ hBOOL(hAPP(hAPP(X2668,X2667),X2666))
| ~ c_List_Olistrelp(X2665,X2668,X2664,X2663)
| c_List_Olistrelp(X2665,X2668,hAPP(hAPP(c_List_Olist_OCons(X2665),X2667),X2664),hAPP(hAPP(c_List_Olist_OCons(X2665),X2666),X2663)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).
fof(i_0_800,plain,
! [X2991,X2992,X2993,X2996,X2997,X2998,X2999,X3000] :
( ( X2992 = hAPP(hAPP(c_List_Olist_OCons(X2993),esk62_3(X2991,X2992,X2993)),esk63_3(X2991,X2992,X2993))
| X2992 = c_List_Olist_ONil(X2993)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2993)),X2992),c_List_Olists(X2993,X2991))) )
& ( hBOOL(hAPP(hAPP(c_member(X2993),esk62_3(X2991,X2992,X2993)),X2991))
| X2992 = c_List_Olist_ONil(X2993)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2993)),X2992),c_List_Olists(X2993,X2991))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2993)),esk63_3(X2991,X2992,X2993)),c_List_Olists(X2993,X2991)))
| X2992 = c_List_Olist_ONil(X2993)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2993)),X2992),c_List_Olists(X2993,X2991))) )
& ( X2997 != c_List_Olist_ONil(X2998)
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2998)),X2997),c_List_Olists(X2998,X2996))) )
& ( X2997 != hAPP(hAPP(c_List_Olist_OCons(X2998),X2999),X3000)
| ~ hBOOL(hAPP(hAPP(c_member(X2998),X2999),X2996))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2998)),X3000),c_List_Olists(X2998,X2996)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2998)),X2997),c_List_Olists(X2998,X2996))) ) ),
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_801,plain,
! [X3557,X3558,X3559,X3560,X3561] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3561,X3560)),X3559),c_FuncSet_Oextensional(X3561,X3560,X3558)))
| hBOOL(hAPP(hAPP(c_member(X3561),X3557),X3558))
| hAPP(X3559,X3557) = c_HOL_Oundefined(X3560) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).
fof(i_0_802,plain,
! [X3136,X3137,X3138,X3139] :
( ~ hBOOL(hAPP(c_List_Olistsp(X3139,X3138),X3137))
| ~ hBOOL(hAPP(c_List_Olistsp(X3139,X3136),X3137))
| hBOOL(hAPP(c_List_Olistsp(X3139,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3139,tc_HOL_Obool),X3138,X3136)),X3137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])]) ).
fof(i_0_803,plain,
! [X2353,X2354] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk21_2(X2353,X2354)),c_Arrow__Order__Mirabelle_OLin))
| X2354 = X2353 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2354),X2353)),esk21_2(X2353,X2354)))
| X2354 = X2353 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_complete__Lin])])])]) ).
fof(i_0_804,plain,
! [X2700,X2701,X2702,X2703,X2704] : c_List_Omaps(X2704,X2703,X2702,hAPP(hAPP(c_List_Olist_OCons(X2704),X2701),X2700)) = hAPP(hAPP(c_List_Oappend(X2703),hAPP(X2702,X2701)),c_List_Omaps(X2704,X2703,X2702,X2700)),
inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J]) ).
fof(i_0_805,plain,
! [X2766,X2767,X2768] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2768,X2768)),X2767),X2766))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2768,X2768)),X2767),c_Transitive__Closure_Ortrancl(X2768,X2766))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).
fof(i_0_806,plain,
! [X2954,X2955,X2956] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2956)),X2955),c_Wellfounded_Oacc(tc_List_Olist(X2956),c_List_Olistrel1(X2956,X2954))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2956)),X2955),c_List_Olists(X2956,c_Wellfounded_Oacc(X2956,X2954)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).
fof(i_0_807,plain,
! [X2951,X2952,X2953] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2953)),X2952),c_List_Olists(X2953,c_Wellfounded_Oacc(X2953,X2951))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2953)),X2952),c_Wellfounded_Oacc(tc_List_Olist(X2953),c_List_Olistrel1(X2953,X2951)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).
fof(i_0_808,plain,
! [X3101,X3102,X3103,X3104] :
( ~ hBOOL(hAPP(hAPP(c_member(X3104),X3103),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3104,tc_HOL_Obool),X3102,X3101)))
| hBOOL(hAPP(hAPP(c_member(X3104),X3103),X3102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).
fof(i_0_809,plain,
! [X3097,X3098,X3099,X3100] :
( ( hBOOL(hAPP(hAPP(c_member(X3100),X3099),X3098))
| ~ hBOOL(hAPP(hAPP(c_member(X3100),X3099),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3100,tc_HOL_Obool),X3098,X3097))) )
& ( hBOOL(hAPP(hAPP(c_member(X3100),X3099),X3097))
| ~ hBOOL(hAPP(hAPP(c_member(X3100),X3099),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3100,tc_HOL_Obool),X3098,X3097))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3100),X3099),X3098))
| ~ hBOOL(hAPP(hAPP(c_member(X3100),X3099),X3097))
| hBOOL(hAPP(hAPP(c_member(X3100),X3099),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3100,tc_HOL_Obool),X3098,X3097))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).
fof(i_0_810,plain,
! [X3086,X3087,X3088,X3089] :
( ( hBOOL(hAPP(hAPP(c_member(X3089),X3088),X3087))
| ~ hBOOL(hAPP(hAPP(c_member(X3089),X3088),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3089,tc_HOL_Obool),X3087,X3086))) )
& ( hBOOL(hAPP(hAPP(c_member(X3089),X3088),X3086))
| ~ hBOOL(hAPP(hAPP(c_member(X3089),X3088),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3089,tc_HOL_Obool),X3087,X3086))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])])]) ).
fof(i_0_811,plain,
! [X3105,X3106,X3107,X3108] :
( ~ hBOOL(hAPP(hAPP(c_member(X3108),X3107),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3108,tc_HOL_Obool),X3106,X3105)))
| hBOOL(hAPP(hAPP(c_member(X3108),X3107),X3105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).
fof(i_0_812,plain,
! [X3090,X3091,X3092,X3093] :
( ~ hBOOL(hAPP(hAPP(c_member(X3093),X3092),X3091))
| ~ hBOOL(hAPP(hAPP(c_member(X3093),X3092),X3090))
| hBOOL(hAPP(hAPP(c_member(X3093),X3092),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3093,tc_HOL_Obool),X3091,X3090))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).
fof(i_0_813,plain,
! [X3552,X3553,X3554,X3555,X3556] :
( ( X3554 = hAPP(hAPP(c_List_Oappend(X3556),c_List_OtakeWhile(X3556,X3555,X3554)),hAPP(hAPP(c_List_Olist_OCons(X3556),X3553),X3552))
| c_List_OdropWhile(X3556,X3555,X3554) != hAPP(hAPP(c_List_Olist_OCons(X3556),X3553),X3552) )
& ( ~ hBOOL(hAPP(X3555,X3553))
| c_List_OdropWhile(X3556,X3555,X3554) != hAPP(hAPP(c_List_Olist_OCons(X3556),X3553),X3552) )
& ( X3554 != hAPP(hAPP(c_List_Oappend(X3556),c_List_OtakeWhile(X3556,X3555,X3554)),hAPP(hAPP(c_List_Olist_OCons(X3556),X3553),X3552))
| hBOOL(hAPP(X3555,X3553))
| c_List_OdropWhile(X3556,X3555,X3554) = hAPP(hAPP(c_List_Olist_OCons(X3556),X3553),X3552) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])])]) ).
fof(i_0_814,plain,
! [X3579,X3580,X3581,X3582,X3583] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3583),X3582),X3581))
| hAPP(c_FuncSet_Orestrict(X3583,X3580,X3579,X3581),X3582) = hAPP(X3579,X3582) )
& ( hBOOL(hAPP(hAPP(c_member(X3583),X3582),X3581))
| hAPP(c_FuncSet_Orestrict(X3583,X3580,X3579,X3581),X3582) = c_HOL_Oundefined(X3580) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])]) ).
fof(i_0_815,plain,
! [X3574,X3575,X3576,X3577,X3578] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3578),X3577),X3576))
| hAPP(c_FuncSet_Orestrict(X3578,X3575,X3574,X3576),X3577) = hAPP(X3574,X3577) )
& ( hBOOL(hAPP(hAPP(c_member(X3578),X3577),X3576))
| hAPP(c_FuncSet_Orestrict(X3578,X3575,X3574,X3576),X3577) = c_HOL_Oundefined(X3575) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).
fof(i_0_816,plain,
! [X3732,X3733,X3734,X3735,X3736] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3736,tc_HOL_Obool),X3735,X3734)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3736,tc_HOL_Obool),X3733,X3732)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3736,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3736,tc_HOL_Obool),X3735,X3733),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3736,tc_HOL_Obool),X3734,X3732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).
fof(i_0_817,plain,
! [X2329,X2330,X2331,X2332,X2333] : c_List_Osplice(X2333,hAPP(hAPP(c_List_Olist_OCons(X2333),X2332),X2331),hAPP(hAPP(c_List_Olist_OCons(X2333),X2330),X2329)) = hAPP(hAPP(c_List_Olist_OCons(X2333),X2332),hAPP(hAPP(c_List_Olist_OCons(X2333),X2330),c_List_Osplice(X2333,X2331,X2329))),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).
fof(i_0_818,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_551])])]) ).
fof(i_0_819,plain,
! [X3432,X3433,X3434,X3435] : hAPP(c_Product__Type_Oprod_Oprod__case(X3435,X3434,X3433),c_Product__Type_Ocurry(X3435,X3434,X3433,X3432)) = X3432,
inference(variable_rename,[status(thm)],[fact_split__curry]) ).
fof(i_0_820,plain,
! [X2939,X2940,X2941,X2942,X2943,X2944,X2945] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2941,X2940),X2939))
| ~ hBOOL(hAPP(hAPP(X2940,X2942),X2939))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2941,X2940),X2942)) )
& ( hBOOL(hAPP(hAPP(X2944,esk59_3(X2943,X2944,X2945)),X2943))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2945,X2944),X2943)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2945,X2944),esk59_3(X2943,X2944,X2945)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2945,X2944),X2943)) ) ),
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_821,plain,
! [X2931,X2932,X2933,X2934,X2935,X2936,X2937] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2933,X2932),X2931))
| ~ hBOOL(hAPP(hAPP(X2932,X2934),X2931))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2933,X2932),X2934)) )
& ( hBOOL(hAPP(hAPP(X2936,esk58_3(X2935,X2936,X2937)),X2935))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2937,X2936),X2935)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2937,X2936),esk58_3(X2935,X2936,X2937)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2937,X2936),X2935)) ) ),
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_822,plain,
! [X4273,X4274,X4275,X4276,X4277,X4278] : hAPP(hAPP(hAPP(c_COMBS(X4278,X4277,X4276),X4275),X4274),X4273) = hAPP(hAPP(X4275,X4273),hAPP(X4274,X4273)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_823,plain,
! [X2727,X2728,X2729,X2730] :
( ~ c_Relation_Otrans(X2730,X2729)
| ~ c_Relation_Otrans(X2728,X2727)
| c_Relation_Otrans(tc_prod(X2730,X2728),c_Wellfounded_Olex__prod(X2730,X2728,X2729,X2727)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__lex__prod])]) ).
fof(i_0_824,plain,
! [X2921,X2922,X2923,X2924,X2926,X2927,X2928,X2929,X2930] :
( ( ~ c_Predicate_ORangeP(X2924,X2923,X2922,X2921)
| hBOOL(hAPP(hAPP(X2922,esk57_2(X2921,X2922)),X2921)) )
& ( ~ hBOOL(hAPP(hAPP(X2927,X2928),X2926))
| c_Predicate_ORangeP(X2930,X2929,X2927,X2926) ) ),
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_825,plain,
! [X4267,X4268,X4269,X4270,X4271,X4272] : hAPP(hAPP(hAPP(c_COMBC(X4272,X4271,X4270),X4269),X4268),X4267) = hAPP(hAPP(X4269,X4267),X4268),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_826,plain,
! [X4261,X4262,X4263,X4264,X4265,X4266] : hAPP(hAPP(hAPP(c_COMBB(X4266,X4265,X4264),X4263),X4262),X4261) = hAPP(X4263,hAPP(X4262,X4261)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_827,plain,
! [X3078,X3079,X3080,X3081] :
( ( hBOOL(hAPP(X3080,X3078))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3081,tc_HOL_Obool),X3080,X3079),X3078)) )
& ( hBOOL(hAPP(X3079,X3078))
| ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3081,tc_HOL_Obool),X3080,X3079),X3078)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])])]) ).
fof(i_0_828,plain,
! [X3113,X3114,X3115,X3116] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3116,tc_HOL_Obool),X3115,X3114),X3113))
| hBOOL(hAPP(X3115,X3113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).
fof(i_0_829,plain,
! [X3109,X3110,X3111,X3112] :
( ~ hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3112,tc_HOL_Obool),X3111,X3110),X3109))
| hBOOL(hAPP(X3110,X3109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).
fof(i_0_830,plain,
! [X3044,X3045,X3046,X3047] :
( ( hBOOL(hAPP(c_List_Olistsp(X3047,X3046),X3045))
| ~ hBOOL(hAPP(c_List_Olistsp(X3047,X3046),hAPP(hAPP(c_List_Oappend(X3047),X3045),X3044))) )
& ( hBOOL(hAPP(c_List_Olistsp(X3047,X3046),X3044))
| ~ hBOOL(hAPP(c_List_Olistsp(X3047,X3046),hAPP(hAPP(c_List_Oappend(X3047),X3045),X3044))) )
& ( ~ hBOOL(hAPP(c_List_Olistsp(X3047,X3046),X3045))
| ~ hBOOL(hAPP(c_List_Olistsp(X3047,X3046),X3044))
| hBOOL(hAPP(c_List_Olistsp(X3047,X3046),hAPP(hAPP(c_List_Oappend(X3047),X3045),X3044))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])]) ).
fof(i_0_831,plain,
! [X3038,X3039,X3040,X3041] :
( ( hBOOL(hAPP(X3040,X3039))
| ~ hBOOL(hAPP(c_List_Olistsp(X3041,X3040),hAPP(hAPP(c_List_Olist_OCons(X3041),X3039),X3038))) )
& ( hBOOL(hAPP(c_List_Olistsp(X3041,X3040),X3038))
| ~ hBOOL(hAPP(c_List_Olistsp(X3041,X3040),hAPP(hAPP(c_List_Olist_OCons(X3041),X3039),X3038))) )
& ( ~ hBOOL(hAPP(X3040,X3039))
| ~ hBOOL(hAPP(c_List_Olistsp(X3041,X3040),X3038))
| hBOOL(hAPP(c_List_Olistsp(X3041,X3040),hAPP(hAPP(c_List_Olist_OCons(X3041),X3039),X3038))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])]) ).
fof(i_0_832,plain,
! [X2565,X2566,X2567,X2568,X2569] :
( ( X2568 = X2566
| hAPP(hAPP(c_List_Oappend(X2569),X2568),hAPP(hAPP(c_List_Olist_OCons(X2569),X2567),c_List_Olist_ONil(X2569))) != hAPP(hAPP(c_List_Oappend(X2569),X2566),hAPP(hAPP(c_List_Olist_OCons(X2569),X2565),c_List_Olist_ONil(X2569))) )
& ( X2567 = X2565
| hAPP(hAPP(c_List_Oappend(X2569),X2568),hAPP(hAPP(c_List_Olist_OCons(X2569),X2567),c_List_Olist_ONil(X2569))) != hAPP(hAPP(c_List_Oappend(X2569),X2566),hAPP(hAPP(c_List_Olist_OCons(X2569),X2565),c_List_Olist_ONil(X2569))) )
& ( X2568 != X2566
| X2567 != X2565
| hAPP(hAPP(c_List_Oappend(X2569),X2568),hAPP(hAPP(c_List_Olist_OCons(X2569),X2567),c_List_Olist_ONil(X2569))) = hAPP(hAPP(c_List_Oappend(X2569),X2566),hAPP(hAPP(c_List_Olist_OCons(X2569),X2565),c_List_Olist_ONil(X2569))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).
fof(i_0_833,plain,
! [X3436,X3437,X3438,X3441,X3442,X3443,X3444,X3445] :
( ( X3436 = hAPP(hAPP(c_List_Olist_OCons(X3438),esk88_3(X3436,X3437,X3438)),esk89_3(X3436,X3437,X3438))
| X3436 = c_List_Olist_ONil(X3438)
| ~ hBOOL(hAPP(c_List_Olistsp(X3438,X3437),X3436)) )
& ( hBOOL(hAPP(X3437,esk88_3(X3436,X3437,X3438)))
| X3436 = c_List_Olist_ONil(X3438)
| ~ hBOOL(hAPP(c_List_Olistsp(X3438,X3437),X3436)) )
& ( hBOOL(hAPP(c_List_Olistsp(X3438,X3437),esk89_3(X3436,X3437,X3438)))
| X3436 = c_List_Olist_ONil(X3438)
| ~ hBOOL(hAPP(c_List_Olistsp(X3438,X3437),X3436)) )
& ( X3441 != c_List_Olist_ONil(X3443)
| hBOOL(hAPP(c_List_Olistsp(X3443,X3442),X3441)) )
& ( X3441 != hAPP(hAPP(c_List_Olist_OCons(X3443),X3444),X3445)
| ~ hBOOL(hAPP(X3442,X3444))
| ~ hBOOL(hAPP(c_List_Olistsp(X3443,X3442),X3445))
| hBOOL(hAPP(c_List_Olistsp(X3443,X3442),X3441)) ) ),
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_834,plain,
! [X3789,X3790] : c_Hilbert__Choice_OEps(X3790,hAPP(hAPP(c_COMBC(X3790,X3790,tc_HOL_Obool),c_fequal),X3789)) = X3789,
inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).
fof(i_0_835,plain,
! [X3837,X3838,X3839,X3840] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3840,X3839),tc_HOL_Obool),X3838,X3837)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3840,tc_HOL_Obool),c_Relation_ODomain(X3840,X3839,X3838),c_Relation_ODomain(X3840,X3839,X3837)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).
fof(i_0_836,plain,
! [X3428,X3429,X3430,X3431] : c_Product__Type_Ocurry(X3431,X3430,X3429,hAPP(c_Product__Type_Oprod_Oprod__case(X3431,X3430,X3429),X3428)) = X3428,
inference(variable_rename,[status(thm)],[fact_curry__split]) ).
fof(i_0_837,plain,
! [X3816,X3817,X3818] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3818,X3818),tc_HOL_Obool),X3817,X3816)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3818,X3818),tc_HOL_Obool),X3816,c_Transitive__Closure_Ortrancl(X3818,X3817))
| c_Transitive__Closure_Ortrancl(X3818,X3816) = c_Transitive__Closure_Ortrancl(X3818,X3817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).
cnf(i_0_838,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_553]) ).
cnf(i_0_839,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_554]) ).
fof(i_0_840,plain,
! [X3288,X3289,X3290,X3291,X3292,X3293] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3293,X3292,X3291),X3290),hAPP(hAPP(c_Product__Type_OPair(X3293,X3292),X3289),X3288)) = hAPP(hAPP(X3290,X3289),X3288),
inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(i_0_841,plain,
! [X3164,X3165,X3166,X3167,X3168,X3169] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3169,X3168,X3167),X3166),hAPP(hAPP(c_Product__Type_OPair(X3169,X3168),X3165),X3164)) = hAPP(hAPP(X3166,X3165),X3164),
inference(variable_rename,[status(thm)],[fact_split__conv]) ).
fof(i_0_842,plain,
! [X3728,X3729,X3730,X3731] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3731,tc_HOL_Obool),X3730,X3729)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3731,tc_HOL_Obool),X3730,X3728)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3731,tc_HOL_Obool),X3730,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3731,tc_HOL_Obool),X3729,X3728)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).
fof(i_0_843,plain,
! [X3117,X3118,X3119,X3120] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3120,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3120,tc_HOL_Obool),X3119,X3118),X3117) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3120,tc_HOL_Obool),X3119,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3120,tc_HOL_Obool),X3118,X3117)),
inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).
fof(i_0_844,plain,
! [X3121,X3122,X3123,X3124] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3124,tc_HOL_Obool),X3123,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3124,tc_HOL_Obool),X3122,X3121)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3124,tc_HOL_Obool),X3122,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3124,tc_HOL_Obool),X3123,X3121)),
inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).
fof(i_0_845,plain,
! [X3741,X3742,X3743,X3744,X3745] :
( ~ class_Lattices_Osemilattice__inf(X3745)
| ~ c_Orderings_Oord__class_Oless__eq(X3745,X3744,X3743)
| ~ c_Orderings_Oord__class_Oless__eq(X3745,X3742,X3741)
| c_Orderings_Oord__class_Oless__eq(X3745,c_Lattices_Osemilattice__inf__class_Oinf(X3745,X3744,X3742),c_Lattices_Osemilattice__inf__class_Oinf(X3745,X3743,X3741)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).
fof(i_0_846,plain,
! [X3542,X3543,X3544,X3545,X3546] :
( hBOOL(hAPP(X3546,X3545))
| c_List_OtakeWhile(X3544,X3546,hAPP(hAPP(c_List_Oappend(X3544),X3543),hAPP(hAPP(c_List_Olist_OCons(X3544),X3545),X3542))) = c_List_OtakeWhile(X3544,X3546,X3543) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).
fof(i_0_847,plain,
! [X3841,X3842,X3843] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3843,X3843),tc_HOL_Obool),X3842,X3841)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3843),tc_List_Olist(X3843)),tc_HOL_Obool),c_List_Olistrel1(X3843,X3842),c_List_Olistrel1(X3843,X3841)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).
fof(i_0_848,plain,
! [X3844,X3845,X3846] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3846,X3846),tc_HOL_Obool),X3845,X3844)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3846),tc_List_Olist(X3846)),tc_HOL_Obool),c_List_Olistrel(X3846,X3845),c_List_Olistrel(X3846,X3844)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).
fof(i_0_849,plain,
! [X3082,X3083,X3084,X3085] :
( ~ hBOOL(hAPP(X3085,X3084))
| ~ hBOOL(hAPP(X3083,X3084))
| hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3082,tc_HOL_Obool),X3085,X3083),X3084)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).
fof(i_0_850,plain,
! [X3813,X3814,X3815] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3815,X3815),tc_HOL_Obool),X3814,c_Transitive__Closure_Ortrancl(X3815,X3813))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3815,X3815),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3815,X3814),c_Transitive__Closure_Ortrancl(X3815,X3813)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).
fof(i_0_851,plain,
! [X2496,X2497,X2498,X2499] : hAPP(hAPP(c_List_Oappend(X2499),hAPP(hAPP(c_List_Oappend(X2499),X2498),X2497)),X2496) = hAPP(hAPP(c_List_Oappend(X2499),X2498),hAPP(hAPP(c_List_Oappend(X2499),X2497),X2496)),
inference(variable_rename,[status(thm)],[fact_append__assoc]) ).
fof(i_0_852,plain,
! [X2500,X2501,X2502,X2503] : hAPP(hAPP(c_List_Oappend(X2503),hAPP(hAPP(c_List_Olist_OCons(X2503),X2502),X2501)),X2500) = hAPP(hAPP(c_List_Olist_OCons(X2503),X2502),hAPP(hAPP(c_List_Oappend(X2503),X2501),X2500)),
inference(variable_rename,[status(thm)],[fact_append__Cons]) ).
fof(i_0_853,plain,
! [X4035,X4036,X4037,X4038,X4039,X4040] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4040,tc_fun(X4039,tc_HOL_Obool)),X4038,X4037)
| ~ hBOOL(hAPP(hAPP(X4038,X4036),X4035))
| hBOOL(hAPP(hAPP(X4037,X4036),X4035)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_854,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_855,plain,
! [X3829,X3830,X3831,X3832] :
( ~ hBOOL(hAPP(hAPP(c_member(X3832),X3831),X3830))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3832,tc_HOL_Obool),X3830,X3829)
| hBOOL(hAPP(hAPP(c_member(X3832),X3831),X3829)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_856,plain,
! [X4234,X4235,X4236,X4237] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X4237,tc_HOL_Obool),X4236,X4235)
| ~ hBOOL(hAPP(hAPP(c_member(X4237),X4234),X4236))
| hBOOL(hAPP(hAPP(c_member(X4237),X4234),X4235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_857,plain,
! [X3833,X3834,X3835,X3836] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3836,tc_HOL_Obool),X3835,X3834)
| ~ hBOOL(hAPP(hAPP(c_member(X3836),X3833),X3835))
| hBOOL(hAPP(hAPP(c_member(X3836),X3833),X3834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_858,plain,
! [X3825,X3826,X3827,X3828] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3828,tc_HOL_Obool),X3827,X3826)
| ~ hBOOL(hAPP(hAPP(c_member(X3828),X3825),X3827))
| hBOOL(hAPP(hAPP(c_member(X3828),X3825),X3826)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_859,plain,
! [X3712,X3713,X3714,X3715] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3715,tc_HOL_Obool),X3714,X3713)
| ~ hBOOL(hAPP(hAPP(c_member(X3715),X3712),X3714))
| hBOOL(hAPP(hAPP(c_member(X3715),X3712),X3713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_860,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_861,plain,
! [X2916,X2917,X2918,X2919,X2920] :
( ~ hBOOL(hAPP(hAPP(X2920,X2919),X2918))
| c_Predicate_ODomainP(X2917,X2916,X2920,X2919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).
fof(i_0_862,plain,
! [X2911,X2912,X2913,X2914,X2915] :
( ~ hBOOL(hAPP(hAPP(X2915,X2914),X2913))
| c_Predicate_ORangeP(X2912,X2911,X2915,X2913) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).
fof(i_0_863,plain,
! [X3571,X3572,X3573] : hAPP(hAPP(c_List_Oappend(X3573),c_List_OtakeWhile(X3573,X3572,X3571)),c_List_OdropWhile(X3573,X3572,X3571)) = X3571,
inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id]) ).
fof(i_0_864,plain,
! [X3538,X3539,X3540,X3541] :
( ( ~ hBOOL(hAPP(X3541,X3540))
| c_List_OtakeWhile(X3539,X3541,hAPP(hAPP(c_List_Olist_OCons(X3539),X3540),X3538)) = hAPP(hAPP(c_List_Olist_OCons(X3539),X3540),c_List_OtakeWhile(X3539,X3541,X3538)) )
& ( hBOOL(hAPP(X3541,X3540))
| c_List_OtakeWhile(X3539,X3541,hAPP(hAPP(c_List_Olist_OCons(X3539),X3540),X3538)) = c_List_Olist_ONil(X3539) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])]) ).
fof(i_0_865,plain,
! [X3937,X3938] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3938),tc_List_Olist(X3938)),tc_HOL_Obool),c_List_Olistrel1(X3938,c_Transitive__Closure_Ortrancl(X3938,X3937)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X3938),c_List_Olistrel1(X3938,X3937))),
inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).
fof(i_0_866,plain,
! [X3514,X3515,X3516] : c_List_Obutlast(X3516,hAPP(hAPP(c_List_Oappend(X3516),X3515),hAPP(hAPP(c_List_Olist_OCons(X3516),X3514),c_List_Olist_ONil(X3516)))) = X3515,
inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).
fof(i_0_867,plain,
! [X3446,X3447,X3448] : c_List_Olast(X3448,hAPP(hAPP(c_List_Oappend(X3448),X3447),hAPP(hAPP(c_List_Olist_OCons(X3448),X3446),c_List_Olist_ONil(X3448)))) = X3446,
inference(variable_rename,[status(thm)],[fact_last__snoc]) ).
fof(i_0_868,plain,
! [X3806,X3807,X3808,X3809] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3809,X3808),tc_HOL_Obool),X3807,X3806)
| ~ c_Relation_Osingle__valued(X3809,X3808,X3806)
| c_Relation_Osingle__valued(X3809,X3808,X3807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).
fof(i_0_869,plain,
! [X3961,X3962,X3963] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3963),c_List_OdropWhile(X3963,X3962,X3961)),c_Nat_Osize__class_Osize(tc_List_Olist(X3963),X3961)),
inference(variable_rename,[status(thm)],[fact_length__dropWhile__le]) ).
fof(i_0_870,plain,
! [X3958,X3959,X3960] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3960),c_List_OtakeWhile(X3960,X3959,X3958)),c_Nat_Osize__class_Osize(tc_List_Olist(X3960),X3958)),
inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).
fof(i_0_871,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) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3771,X3770,X3769)
| ~ 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)],[fact_le__inf__iff])])]) ).
fof(i_0_872,plain,
! [X3750,X3751,X3752,X3753] :
( ~ class_Lattices_Osemilattice__inf(X3753)
| ~ c_Orderings_Oord__class_Oless__eq(X3753,X3752,X3751)
| ~ c_Orderings_Oord__class_Oless__eq(X3753,X3752,X3750)
| c_Orderings_Oord__class_Oless__eq(X3753,X3752,c_Lattices_Osemilattice__inf__class_Oinf(X3753,X3751,X3750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).
fof(i_0_873,plain,
! [X3746,X3747,X3748,X3749] :
( ~ class_Lattices_Osemilattice__inf(X3749)
| ~ c_Orderings_Oord__class_Oless__eq(X3749,X3748,X3747)
| ~ c_Orderings_Oord__class_Oless__eq(X3749,X3748,X3746)
| c_Orderings_Oord__class_Oless__eq(X3749,X3748,c_Lattices_Osemilattice__inf__class_Oinf(X3749,X3747,X3746)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).
fof(i_0_874,plain,
! [X2947,X2948,X2949,X2950] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2950,X2949),X2948))
| ~ hBOOL(hAPP(hAPP(X2949,X2947),X2948))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2950,X2949),X2947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).
fof(i_0_875,plain,
! [X3878,X3879,X3880] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3880,X3880),tc_HOL_Obool),X3879,X3878)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3880,tc_HOL_Obool),c_Wellfounded_Oacc(X3880,X3878),c_Wellfounded_Oacc(X3880,X3879)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).
fof(i_0_876,plain,
! [X3239,X3240,X3241,X3242] :
( ~ class_Lattices_Osemilattice__inf(X3242)
| c_Lattices_Osemilattice__inf__class_Oinf(X3242,c_Lattices_Osemilattice__inf__class_Oinf(X3242,X3241,X3240),X3239) = c_Lattices_Osemilattice__inf__class_Oinf(X3242,X3241,c_Lattices_Osemilattice__inf__class_Oinf(X3242,X3240,X3239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).
fof(i_0_877,plain,
! [X3231,X3232,X3233,X3234] :
( ~ class_Lattices_Osemilattice__inf(X3234)
| c_Lattices_Osemilattice__inf__class_Oinf(X3234,c_Lattices_Osemilattice__inf__class_Oinf(X3234,X3233,X3232),X3231) = c_Lattices_Osemilattice__inf__class_Oinf(X3234,X3233,c_Lattices_Osemilattice__inf__class_Oinf(X3234,X3232,X3231)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).
fof(i_0_878,plain,
! [X3235,X3236,X3237,X3238] :
( ~ class_Lattices_Olattice(X3238)
| c_Lattices_Osemilattice__inf__class_Oinf(X3238,c_Lattices_Osemilattice__inf__class_Oinf(X3238,X3237,X3236),X3235) = c_Lattices_Osemilattice__inf__class_Oinf(X3238,X3237,c_Lattices_Osemilattice__inf__class_Oinf(X3238,X3236,X3235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).
fof(i_0_879,plain,
! [X3251,X3252,X3253,X3254] :
( ~ class_Lattices_Osemilattice__inf(X3254)
| c_Lattices_Osemilattice__inf__class_Oinf(X3254,X3253,c_Lattices_Osemilattice__inf__class_Oinf(X3254,X3252,X3251)) = c_Lattices_Osemilattice__inf__class_Oinf(X3254,X3252,c_Lattices_Osemilattice__inf__class_Oinf(X3254,X3253,X3251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).
fof(i_0_880,plain,
! [X3243,X3244,X3245,X3246] :
( ~ class_Lattices_Osemilattice__inf(X3246)
| c_Lattices_Osemilattice__inf__class_Oinf(X3246,X3245,c_Lattices_Osemilattice__inf__class_Oinf(X3246,X3244,X3243)) = c_Lattices_Osemilattice__inf__class_Oinf(X3246,X3244,c_Lattices_Osemilattice__inf__class_Oinf(X3246,X3245,X3243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).
fof(i_0_881,plain,
! [X3247,X3248,X3249,X3250] :
( ~ class_Lattices_Olattice(X3250)
| c_Lattices_Osemilattice__inf__class_Oinf(X3250,X3249,c_Lattices_Osemilattice__inf__class_Oinf(X3250,X3248,X3247)) = c_Lattices_Osemilattice__inf__class_Oinf(X3250,X3248,c_Lattices_Osemilattice__inf__class_Oinf(X3250,X3249,X3247)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).
fof(i_0_882,plain,
! [X3517,X3518] :
( X3518 = c_List_Olist_ONil(X3517)
| hAPP(hAPP(c_List_Oappend(X3517),c_List_Obutlast(X3517,X3518)),hAPP(hAPP(c_List_Olist_OCons(X3517),c_List_Olast(X3517,X3518)),c_List_Olist_ONil(X3517))) = X3518 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).
fof(i_0_883,plain,
! [X3951,X3952,X3953] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3953,tc_fun(X3953,tc_HOL_Obool)),X3952,X3951)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3953,tc_HOL_Obool),c_Wellfounded_Oaccp(X3953,X3951),c_Wellfounded_Oaccp(X3953,X3952)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).
fof(i_0_884,plain,
! [X4226,X4227,X4228,X4229] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4229,tc_HOL_Obool),X4228,X4227)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4229,tc_HOL_Obool),X4227,X4226)
| c_Orderings_Oord__class_Oless(tc_fun(X4229,tc_HOL_Obool),X4228,X4226) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_885,plain,
! [X4222,X4223,X4224,X4225] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X4225,tc_HOL_Obool),X4224,X4223)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4225,tc_HOL_Obool),X4223,X4222)
| c_Orderings_Oord__class_Oless(tc_fun(X4225,tc_HOL_Obool),X4224,X4222) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_886,plain,
! [X3863,X3864,X3865,X3866] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3866,tc_HOL_Obool),X3865,X3864)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3866,tc_HOL_Obool),X3864,X3863)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3866,tc_HOL_Obool),X3865,X3863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_887,plain,
! [X3133,X3134,X3135] :
( ~ c_Relation_Otrans(X3135,X3134)
| ~ c_Relation_Otrans(X3135,X3133)
| c_Relation_Otrans(X3135,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3135,X3135),tc_HOL_Obool),X3134,X3133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__Int])]) ).
fof(i_0_888,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) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])])]) ).
fof(i_0_889,plain,
! [X3094,X3095,X3096] : c_List_Olistsp(X3096,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3096,tc_HOL_Obool),X3095,X3094)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X3096),tc_HOL_Obool),c_List_Olistsp(X3096,X3095),c_List_Olistsp(X3096,X3094)),
inference(variable_rename,[status(thm)],[fact_listsp__inf__eq]) ).
fof(i_0_890,plain,
! [X3125,X3126,X3127] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3127,tc_HOL_Obool),X3126,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3127,tc_HOL_Obool),X3126,X3125)) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3127,tc_HOL_Obool),X3126,X3125),
inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).
fof(i_0_891,plain,
! [X4230,X4231,X4232,X4233] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4232,X4233),X4231,X4230)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4232,X4233),X4231,X4230)
| ~ class_Orderings_Oord(X4233) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4232,X4233),X4230,X4231)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4232,X4233),X4231,X4230)
| ~ class_Orderings_Oord(X4233) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4232,X4233),X4231,X4230)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4232,X4233),X4230,X4231)
| c_Orderings_Oord__class_Oless(tc_fun(X4232,X4233),X4231,X4230)
| ~ class_Orderings_Oord(X4233) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])])]) ).
fof(i_0_892,plain,
! [X3707,X3708] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3708),tc_List_Olist(X3708)),tc_HOL_Obool),c_List_Olistrel(X3708,X3707),c_Transitive__Closure_Ortrancl(tc_List_Olist(X3708),c_List_Olistrel1(X3708,X3707))),
inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).
fof(i_0_893,plain,
! [X3225,X3226,X3227,X3228,X3229,X3230] :
( ( X3228 = X3226
| hAPP(hAPP(c_Product__Type_OPair(X3230,X3229),X3228),X3227) != hAPP(hAPP(c_Product__Type_OPair(X3230,X3229),X3226),X3225) )
& ( X3227 = X3225
| hAPP(hAPP(c_Product__Type_OPair(X3230,X3229),X3228),X3227) != hAPP(hAPP(c_Product__Type_OPair(X3230,X3229),X3226),X3225) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).
fof(i_0_894,plain,
! [X3219,X3220,X3221,X3222,X3223,X3224] :
( ( X3222 = X3220
| hAPP(hAPP(c_Product__Type_OPair(X3224,X3223),X3222),X3221) != hAPP(hAPP(c_Product__Type_OPair(X3224,X3223),X3220),X3219) )
& ( X3221 = X3219
| hAPP(hAPP(c_Product__Type_OPair(X3224,X3223),X3222),X3221) != hAPP(hAPP(c_Product__Type_OPair(X3224,X3223),X3220),X3219) )
& ( X3222 != X3220
| X3221 != X3219
| hAPP(hAPP(c_Product__Type_OPair(X3224,X3223),X3222),X3221) = hAPP(hAPP(c_Product__Type_OPair(X3224,X3223),X3220),X3219) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).
fof(i_0_895,plain,
! [X3954,X3955,X3956,X3957] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3957),X3956),c_Nat_Osize__class_Osize(tc_List_Olist(X3957),X3955))
| X3956 != hAPP(hAPP(c_List_Olist_OCons(X3957),X3954),X3955) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).
fof(i_0_896,plain,
! [X3283,X3284,X3285,X3286,X3287] :
( ~ class_Lattices_Olattice(X3287)
| hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3286,X3287),X3285,X3284),X3283) = c_Lattices_Osemilattice__inf__class_Oinf(X3287,hAPP(X3285,X3283),hAPP(X3284,X3283)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).
fof(i_0_897,plain,
! [X3159,X3160,X3161,X3162,X3163] :
( ~ class_Lattices_Olattice(X3163)
| hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3162,X3163),X3161,X3160),X3159) = c_Lattices_Osemilattice__inf__class_Oinf(X3163,hAPP(X3161,X3159),hAPP(X3160,X3159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).
fof(i_0_898,plain,
! [X2691,X2692,X2693,X2694] :
( c_List_Orotate1(X2694,c_List_Olist_ONil(X2694)) = c_List_Olist_ONil(X2694)
& c_List_Orotate1(X2693,hAPP(hAPP(c_List_Olist_OCons(X2693),X2692),X2691)) = hAPP(hAPP(c_List_Oappend(X2693),X2691),hAPP(hAPP(c_List_Olist_OCons(X2693),X2692),c_List_Olist_ONil(X2693))) ),
inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).
fof(i_0_899,plain,
! [X3483,X3484,X3485,X3486] :
( ( X3483 != c_List_Olist_ONil(X3486)
| hAPP(hAPP(c_List_Oappend(X3486),X3485),hAPP(hAPP(c_List_Olist_OCons(X3486),X3484),c_List_Olist_ONil(X3486))) != X3483 )
& ( c_List_Obutlast(X3486,X3483) = X3485
| hAPP(hAPP(c_List_Oappend(X3486),X3485),hAPP(hAPP(c_List_Olist_OCons(X3486),X3484),c_List_Olist_ONil(X3486))) != X3483 )
& ( c_List_Olast(X3486,X3483) = X3484
| hAPP(hAPP(c_List_Oappend(X3486),X3485),hAPP(hAPP(c_List_Olist_OCons(X3486),X3484),c_List_Olist_ONil(X3486))) != X3483 )
& ( X3483 = c_List_Olist_ONil(X3486)
| c_List_Obutlast(X3486,X3483) != X3485
| c_List_Olast(X3486,X3483) != X3484
| hAPP(hAPP(c_List_Oappend(X3486),X3485),hAPP(hAPP(c_List_Olist_OCons(X3486),X3484),c_List_Olist_ONil(X3486))) = X3483 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).
fof(i_0_900,plain,
! [X2468,X2469,X2470,X2471,X2472,X2473] :
( hAPP(hAPP(c_List_Oappend(X2473),X2472),X2471) != X2470
| X2469 != hAPP(hAPP(c_List_Oappend(X2473),X2471),X2468)
| hAPP(hAPP(c_List_Oappend(X2473),X2472),X2469) = hAPP(hAPP(c_List_Oappend(X2473),X2470),X2468) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).
fof(i_0_901,plain,
! [X2504,X2505,X2506,X2507,X2508,X2509] :
( hAPP(hAPP(c_List_Olist_OCons(X2509),X2508),X2507) != X2506
| X2505 != hAPP(hAPP(c_List_Oappend(X2509),X2507),X2504)
| hAPP(hAPP(c_List_Olist_OCons(X2509),X2508),X2505) = hAPP(hAPP(c_List_Oappend(X2509),X2506),X2504) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).
fof(i_0_902,plain,
! [X3881,X3882,X3883] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3883,tc_HOL_Obool),X3882,X3881)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X3883),tc_HOL_Obool),c_List_Olistsp(X3883,X3882),c_List_Olistsp(X3883,X3881)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])]) ).
fof(i_0_903,plain,
! [X3822,X3823,X3824] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3824,tc_HOL_Obool),X3823,X3822)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X3824),tc_HOL_Obool),c_List_Olists(X3824,X3823),c_List_Olists(X3824,X3822)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).
fof(i_0_904,plain,
! [X2677,X2678] : c_List_Olistrelp(X2678,X2677,c_List_Olist_ONil(X2678),c_List_Olist_ONil(X2678)),
inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).
fof(i_0_905,plain,
! [X2675,X2676] : c_List_Olistrelp(X2676,X2675,c_List_Olist_ONil(X2676),c_List_Olist_ONil(X2676)),
inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).
fof(i_0_906,plain,
! [X3562,X3563,X3564,X3565] :
( ( ~ hBOOL(hAPP(X3565,X3564))
| c_List_OdropWhile(X3563,X3565,hAPP(hAPP(c_List_Olist_OCons(X3563),X3564),X3562)) = c_List_OdropWhile(X3563,X3565,X3562) )
& ( hBOOL(hAPP(X3565,X3564))
| c_List_OdropWhile(X3563,X3565,hAPP(hAPP(c_List_Olist_OCons(X3563),X3564),X3562)) = hAPP(hAPP(c_List_Olist_OCons(X3563),X3564),X3562) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])]) ).
fof(i_0_907,plain,
! [X2746,X2747,X2748] : c_List_Omaps(X2748,X2747,X2746,c_List_Olist_ONil(X2748)) = c_List_Olist_ONil(X2747),
inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J]) ).
fof(i_0_908,plain,
! [X4126,X4127,X4128,X4129] :
( ~ class_Lattices_Osemilattice__inf(X4129)
| ~ c_Orderings_Oord__class_Oless(X4129,X4128,X4127)
| c_Orderings_Oord__class_Oless(X4129,c_Lattices_Osemilattice__inf__class_Oinf(X4129,X4128,X4126),X4127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).
fof(i_0_909,plain,
! [X4130,X4131,X4132,X4133] :
( ~ class_Lattices_Osemilattice__inf(X4133)
| ~ c_Orderings_Oord__class_Oless(X4133,X4132,X4131)
| c_Orderings_Oord__class_Oless(X4133,c_Lattices_Osemilattice__inf__class_Oinf(X4133,X4130,X4132),X4131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).
fof(i_0_910,plain,
! [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,c_Lattices_Osemilattice__inf__class_Oinf(X3767,X3766,X3764),X3765) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).
fof(i_0_911,plain,
! [X3760,X3761,X3762,X3763] :
( ~ class_Lattices_Osemilattice__inf(X3763)
| ~ c_Orderings_Oord__class_Oless__eq(X3763,X3762,X3761)
| c_Orderings_Oord__class_Oless__eq(X3763,c_Lattices_Osemilattice__inf__class_Oinf(X3763,X3760,X3762),X3761) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).
fof(i_0_912,plain,
! [X3399,X3400] : c_Set_Oimage(X3400,X3400,c_COMBI(X3400),X3399) = X3399,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_913,plain,
! [X3854,X3855,X3856] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3854,tc_HOL_Obool),X3856,X3855)
| X3856 != X3855 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3854,tc_HOL_Obool),X3855,X3856)
| X3856 != X3855 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3854,tc_HOL_Obool),X3856,X3855)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3854,tc_HOL_Obool),X3855,X3856)
| X3856 = X3855 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_914,plain,
! [X3709,X3710,X3711] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3711,tc_HOL_Obool),X3710,X3709)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3711,tc_HOL_Obool),X3709,X3710)
| X3710 = X3709 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_915,plain,
! [X2254,X2255,X2256] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2256),X2255),hAPP(c_fequal,X2254)))
| X2255 = X2254 )
& ( X2255 != X2254
| hBOOL(hAPP(hAPP(c_member(X2256),X2255),hAPP(c_fequal,X2254))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_916,plain,
! [X3946,X3947,X3948,X3949,X3950] :
( ~ class_Orderings_Oord(X3950)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3949,X3950),X3948,X3947)
| c_Orderings_Oord__class_Oless__eq(X3950,hAPP(X3948,X3946),hAPP(X3947,X3946)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_917,plain,
! [X3941,X3942,X3943,X3944,X3945] :
( ~ class_Orderings_Oord(X3945)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3944,X3945),X3943,X3942)
| c_Orderings_Oord__class_Oless__eq(X3945,hAPP(X3943,X3941),hAPP(X3942,X3941)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_918,plain,
! [X4144,X4145,X4146,X4147] :
( ~ class_Orderings_Opreorder(X4147)
| ~ c_Orderings_Oord__class_Oless(X4147,X4146,X4145)
| ~ c_Orderings_Oord__class_Oless(X4147,X4145,X4144)
| c_Orderings_Oord__class_Oless(X4147,X4146,X4144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_919,plain,
! [X4063,X4064,X4065,X4066] :
( ~ class_Orderings_Opreorder(X4066)
| ~ c_Orderings_Oord__class_Oless__eq(X4066,X4065,X4064)
| ~ c_Orderings_Oord__class_Oless(X4066,X4064,X4063)
| c_Orderings_Oord__class_Oless(X4066,X4065,X4063) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_920,plain,
! [X4071,X4072,X4073,X4074] :
( ~ class_Orderings_Opreorder(X4074)
| ~ c_Orderings_Oord__class_Oless(X4074,X4073,X4072)
| ~ c_Orderings_Oord__class_Oless__eq(X4074,X4072,X4071)
| c_Orderings_Oord__class_Oless(X4074,X4073,X4071) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_921,plain,
! [X4140,X4141,X4142,X4143] :
( ~ class_Orderings_Oorder(X4143)
| ~ c_Orderings_Oord__class_Oless(X4143,X4142,X4141)
| ~ c_Orderings_Oord__class_Oless(X4143,X4140,X4142)
| c_Orderings_Oord__class_Oless(X4143,X4140,X4141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_922,plain,
! [X4059,X4060,X4061,X4062] :
( ~ class_Orderings_Oorder(X4062)
| ~ c_Orderings_Oord__class_Oless__eq(X4062,X4061,X4060)
| ~ c_Orderings_Oord__class_Oless(X4062,X4059,X4061)
| c_Orderings_Oord__class_Oless(X4062,X4059,X4060) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_923,plain,
! [X4067,X4068,X4069,X4070] :
( ~ class_Orderings_Oorder(X4070)
| ~ c_Orderings_Oord__class_Oless(X4070,X4069,X4068)
| ~ c_Orderings_Oord__class_Oless__eq(X4070,X4067,X4069)
| c_Orderings_Oord__class_Oless(X4070,X4067,X4068) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_924,plain,
! [X3995,X3996,X3997,X3998] :
( ~ class_Orderings_Opreorder(X3998)
| ~ c_Orderings_Oord__class_Oless__eq(X3998,X3997,X3996)
| ~ c_Orderings_Oord__class_Oless__eq(X3998,X3996,X3995)
| c_Orderings_Oord__class_Oless__eq(X3998,X3997,X3995) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_925,plain,
! [X4002,X4003,X4004,X4005] :
( ~ class_Orderings_Oorder(X4005)
| ~ c_Orderings_Oord__class_Oless__eq(X4005,X4004,X4003)
| ~ c_Orderings_Oord__class_Oless__eq(X4005,X4002,X4004)
| c_Orderings_Oord__class_Oless__eq(X4005,X4002,X4003) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_926,plain,
! [X2969,X2970] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2970)),c_List_Olist_ONil(X2970)),c_List_Olists(X2970,X2969))),
inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).
fof(i_0_927,plain,
! [X3716,X3717,X3718] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3718,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3718,tc_HOL_Obool),X3717,X3716),X3717),
inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).
fof(i_0_928,plain,
! [X3719,X3720,X3721] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3721,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3721,tc_HOL_Obool),X3720,X3719),X3719),
inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).
fof(i_0_929,plain,
! [X3261,X3262,X3263] :
( ~ class_Lattices_Osemilattice__inf(X3263)
| c_Lattices_Osemilattice__inf__class_Oinf(X3263,X3262,c_Lattices_Osemilattice__inf__class_Oinf(X3263,X3262,X3261)) = c_Lattices_Osemilattice__inf__class_Oinf(X3263,X3262,X3261) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).
fof(i_0_930,plain,
! [X3255,X3256,X3257] :
( ~ class_Lattices_Osemilattice__inf(X3257)
| c_Lattices_Osemilattice__inf__class_Oinf(X3257,X3256,c_Lattices_Osemilattice__inf__class_Oinf(X3257,X3256,X3255)) = c_Lattices_Osemilattice__inf__class_Oinf(X3257,X3256,X3255) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).
fof(i_0_931,plain,
! [X3258,X3259,X3260] :
( ~ class_Lattices_Olattice(X3260)
| c_Lattices_Osemilattice__inf__class_Oinf(X3260,X3259,c_Lattices_Osemilattice__inf__class_Oinf(X3260,X3259,X3258)) = c_Lattices_Osemilattice__inf__class_Oinf(X3260,X3259,X3258) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).
fof(i_0_932,plain,
! [X2705,X2706] : c_List_Opartition(X2706,X2705,c_List_Olist_ONil(X2706)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2706),tc_List_Olist(X2706)),c_List_Olist_ONil(X2706)),c_List_Olist_ONil(X2706)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).
fof(i_0_933,plain,
! [X2322,X2323,X2324] : c_List_Osplice(X2324,hAPP(hAPP(c_List_Olist_OCons(X2324),X2323),X2322),c_List_Olist_ONil(X2324)) = hAPP(hAPP(c_List_Olist_OCons(X2324),X2323),X2322),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).
fof(i_0_934,plain,
! [X3791,X3792,X3794,X3795,X3796] :
( ( ~ hBOOL(hAPP(X3792,c_Hilbert__Choice_OEps(X3791,X3792)))
| hBOOL(hAPP(X3792,esk101_2(X3791,X3792))) )
& ( ~ hBOOL(hAPP(X3795,X3796))
| hBOOL(hAPP(X3795,c_Hilbert__Choice_OEps(X3794,X3795))) ) ),
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_935,plain,
! [X4111,X4112,X4113] :
( ( c_Orderings_Oord__class_Oless__eq(X4113,X4112,X4111)
| ~ c_Orderings_Oord__class_Oless(X4113,X4112,X4111)
| ~ class_Orderings_Opreorder(X4113) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4113,X4111,X4112)
| ~ c_Orderings_Oord__class_Oless(X4113,X4112,X4111)
| ~ class_Orderings_Opreorder(X4113) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4113,X4112,X4111)
| c_Orderings_Oord__class_Oless__eq(X4113,X4111,X4112)
| c_Orderings_Oord__class_Oless(X4113,X4112,X4111)
| ~ class_Orderings_Opreorder(X4113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])])]) ).
fof(i_0_936,plain,
! [X4216,X4217,X4218] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4218,tc_HOL_Obool),X4217,X4216)
| c_Orderings_Oord__class_Oless(tc_fun(X4218,tc_HOL_Obool),X4217,X4216)
| X4217 = X4216 )
& ( ~ c_Orderings_Oord__class_Oless(tc_fun(X4218,tc_HOL_Obool),X4217,X4216)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4218,tc_HOL_Obool),X4217,X4216) )
& ( X4217 != X4216
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4218,tc_HOL_Obool),X4217,X4216) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_937,plain,
! [X4213,X4214,X4215] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4215,tc_HOL_Obool),X4214,X4213)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4215,tc_HOL_Obool),X4214,X4213) )
& ( X4214 != X4213
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4215,tc_HOL_Obool),X4214,X4213) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4215,tc_HOL_Obool),X4214,X4213)
| X4214 = X4213
| c_Orderings_Oord__class_Oless(tc_fun(X4215,tc_HOL_Obool),X4214,X4213) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_938,plain,
! [X3722,X3723,X3724] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3724,tc_HOL_Obool),X3723,X3722)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3724,tc_HOL_Obool),X3723,X3722) = X3723 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).
fof(i_0_939,plain,
! [X3725,X3726,X3727] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3727,tc_HOL_Obool),X3726,X3725)
| c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3727,tc_HOL_Obool),X3725,X3726) = X3726 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).
fof(i_0_940,plain,
! [X3874,X3875,X3876,X3877] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3877,tc_HOL_Obool),X3876,X3875)
| ~ hBOOL(hAPP(X3876,X3874))
| hBOOL(hAPP(X3875,X3874)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_941,plain,
! [X3870,X3871,X3872,X3873] :
( ~ hBOOL(hAPP(X3873,X3872))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3871,tc_HOL_Obool),X3873,X3870)
| hBOOL(hAPP(X3870,X3872)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_942,plain,
! [X4219,X4220,X4221] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X4221,tc_HOL_Obool),X4220,X4219)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4221,tc_HOL_Obool),X4220,X4219) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_943,plain,
! [X3501,X3502,X3503] :
( ( X3503 != c_List_Olist_ONil(X3502)
| c_List_Obutlast(X3502,hAPP(hAPP(c_List_Oappend(X3502),X3501),X3503)) = c_List_Obutlast(X3502,X3501) )
& ( X3503 = c_List_Olist_ONil(X3502)
| c_List_Obutlast(X3502,hAPP(hAPP(c_List_Oappend(X3502),X3501),X3503)) = hAPP(hAPP(c_List_Oappend(X3502),X3501),c_List_Obutlast(X3502,X3503)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).
fof(i_0_944,plain,
! [X3498,X3499,X3500] :
( ( X3500 != c_List_Olist_ONil(X3499)
| c_List_Obutlast(X3499,hAPP(hAPP(c_List_Olist_OCons(X3499),X3498),X3500)) = c_List_Olist_ONil(X3499) )
& ( X3500 = c_List_Olist_ONil(X3499)
| c_List_Obutlast(X3499,hAPP(hAPP(c_List_Olist_OCons(X3499),X3498),X3500)) = hAPP(hAPP(c_List_Olist_OCons(X3499),X3498),c_List_Obutlast(X3499,X3500)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).
fof(i_0_945,plain,
! [X2187,X2188,X2189] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2189),X2188),X2187))
| hBOOL(hAPP(X2187,X2188)) )
& ( ~ hBOOL(hAPP(X2187,X2188))
| hBOOL(hAPP(hAPP(c_member(X2189),X2188),X2187)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_946,plain,
! [X4238,X4239,X4240] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4239,X4240)
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| X4240 = X4239
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4240,X4239) )
& ( ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| X4240 = X4239
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4240,X4239) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4239,X4240)
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4240,X4239) )
& ( ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4240,X4239) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4239,X4240)
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| X4240 = X4239
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240)) )
& ( ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| X4240 = X4239
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4239,X4240)
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240)) )
& ( ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240))
| ~ hBOOL(hAPP(hAPP(X4238,X4239),X4240)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_947,plain,
! [X4084,X4085,X4086] :
( ( c_Orderings_Oord__class_Oless(X4086,X4085,X4084)
| X4085 = X4084
| ~ c_Orderings_Oord__class_Oless__eq(X4086,X4085,X4084)
| ~ class_Orderings_Olinorder(X4086) )
& ( X4085 != X4084
| ~ c_Orderings_Oord__class_Oless(X4086,X4085,X4084)
| ~ c_Orderings_Oord__class_Oless__eq(X4086,X4085,X4084)
| ~ class_Orderings_Olinorder(X4086) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])]) ).
fof(i_0_948,plain,
! [X3999,X4000,X4001] :
( ~ class_Orderings_Oorder(X4001)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,X4000,X3999)
| ~ c_Orderings_Oord__class_Oless__eq(X4001,X3999,X4000)
| X3999 = X4000 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_949,plain,
! [X3992,X3993,X3994] :
( ~ class_Orderings_Oorder(X3994)
| ~ c_Orderings_Oord__class_Oless__eq(X3994,X3993,X3992)
| ~ c_Orderings_Oord__class_Oless__eq(X3994,X3992,X3993)
| X3993 = X3992 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_950,plain,
! [X3973,X3974,X3975] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3975,X3973,X3974)
| X3973 = X3974
| ~ c_Orderings_Oord__class_Oless__eq(X3975,X3974,X3973)
| ~ class_Orderings_Oorder(X3975) )
& ( X3973 != X3974
| c_Orderings_Oord__class_Oless__eq(X3975,X3973,X3974)
| ~ c_Orderings_Oord__class_Oless__eq(X3975,X3974,X3973)
| ~ class_Orderings_Oorder(X3975) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_951,plain,
! [X3967,X3968,X3969] :
( ( c_Orderings_Oord__class_Oless__eq(X3969,X3968,X3967)
| X3968 != X3967
| ~ class_Orderings_Oorder(X3969) )
& ( c_Orderings_Oord__class_Oless__eq(X3969,X3967,X3968)
| X3968 != X3967
| ~ class_Orderings_Oorder(X3969) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3969,X3968,X3967)
| ~ c_Orderings_Oord__class_Oless__eq(X3969,X3967,X3968)
| X3968 = X3967
| ~ class_Orderings_Oorder(X3969) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_952,plain,
! [X4164,X4165,X4166] :
( ~ class_Orderings_Oorder(X4166)
| ~ c_Orderings_Oord__class_Oless(X4166,X4165,X4164)
| ~ c_Orderings_Oord__class_Oless(X4166,X4164,X4165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])]) ).
fof(i_0_953,plain,
! [X4194,X4195,X4196] :
( ( c_Orderings_Oord__class_Oless(X4196,X4195,X4194)
| c_Orderings_Oord__class_Oless(X4196,X4194,X4195)
| X4195 = X4194
| ~ class_Orderings_Olinorder(X4196) )
& ( ~ c_Orderings_Oord__class_Oless(X4196,X4194,X4195)
| ~ c_Orderings_Oord__class_Oless(X4196,X4195,X4194)
| ~ class_Orderings_Olinorder(X4196) )
& ( X4195 != X4194
| ~ c_Orderings_Oord__class_Oless(X4196,X4195,X4194)
| ~ class_Orderings_Olinorder(X4196) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])])]) ).
fof(i_0_954,plain,
! [X4123,X4124,X4125] :
( ( c_Orderings_Oord__class_Oless(X4125,X4124,X4123)
| c_Orderings_Oord__class_Oless__eq(X4125,X4123,X4124)
| ~ class_Orderings_Olinorder(X4125) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4125,X4123,X4124)
| ~ c_Orderings_Oord__class_Oless(X4125,X4124,X4123)
| ~ class_Orderings_Olinorder(X4125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])])]) ).
fof(i_0_955,plain,
! [X4090,X4091,X4092] :
( ~ class_Orderings_Olinorder(X4092)
| ~ c_Orderings_Oord__class_Oless__eq(X4092,X4091,X4090)
| ~ c_Orderings_Oord__class_Oless(X4092,X4090,X4091) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).
fof(i_0_956,plain,
! [X4120,X4121,X4122] :
( ( c_Orderings_Oord__class_Oless__eq(X4122,X4121,X4120)
| c_Orderings_Oord__class_Oless(X4122,X4120,X4121)
| ~ class_Orderings_Olinorder(X4122) )
& ( ~ c_Orderings_Oord__class_Oless(X4122,X4120,X4121)
| ~ c_Orderings_Oord__class_Oless__eq(X4122,X4121,X4120)
| ~ class_Orderings_Olinorder(X4122) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])])]) ).
fof(i_0_957,plain,
! [X4179,X4180,X4181] :
( ~ class_Orderings_Opreorder(X4181)
| ~ c_Orderings_Oord__class_Oless(X4181,X4180,X4179)
| ~ c_Orderings_Oord__class_Oless(X4181,X4179,X4180) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_958,plain,
! [X4176,X4177,X4178] :
( ~ class_Orderings_Opreorder(X4178)
| ~ c_Orderings_Oord__class_Oless(X4178,X4177,X4176)
| ~ c_Orderings_Oord__class_Oless(X4178,X4176,X4177) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_959,plain,
! [X4167,X4168,X4169] :
( ~ class_Orderings_Opreorder(X4169)
| ~ c_Orderings_Oord__class_Oless(X4169,X4168,X4167)
| ~ c_Orderings_Oord__class_Oless(X4169,X4167,X4168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_960,plain,
! [X4137,X4138,X4139] :
( ~ class_Orderings_Opreorder(X4139)
| ~ c_Orderings_Oord__class_Oless(X4139,X4138,X4137)
| ~ c_Orderings_Oord__class_Oless(X4139,X4137,X4138) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).
fof(i_0_961,plain,
! [X3781,X3782,X3783] :
( ~ class_Lattices_Osemilattice__inf(X3783)
| c_Orderings_Oord__class_Oless__eq(X3783,c_Lattices_Osemilattice__inf__class_Oinf(X3783,X3782,X3781),X3782) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).
fof(i_0_962,plain,
! [X3784,X3785,X3786] :
( ~ class_Lattices_Olattice(X3786)
| c_Orderings_Oord__class_Oless__eq(X3786,c_Lattices_Osemilattice__inf__class_Oinf(X3786,X3785,X3784),X3785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).
fof(i_0_963,plain,
! [X3775,X3776,X3777] :
( ~ class_Lattices_Osemilattice__inf(X3777)
| c_Orderings_Oord__class_Oless__eq(X3777,c_Lattices_Osemilattice__inf__class_Oinf(X3777,X3776,X3775),X3775) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).
fof(i_0_964,plain,
! [X3778,X3779,X3780] :
( ~ class_Lattices_Olattice(X3780)
| c_Orderings_Oord__class_Oless__eq(X3780,c_Lattices_Osemilattice__inf__class_Oinf(X3780,X3779,X3778),X3778) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).
fof(i_0_965,plain,
! [X2257,X2258,X2259,X2260,X2261] :
( ( X2260 = X2258
| hAPP(hAPP(c_List_Olist_OCons(X2261),X2260),X2259) != hAPP(hAPP(c_List_Olist_OCons(X2261),X2258),X2257) )
& ( X2259 = X2257
| hAPP(hAPP(c_List_Olist_OCons(X2261),X2260),X2259) != hAPP(hAPP(c_List_Olist_OCons(X2261),X2258),X2257) )
& ( X2260 != X2258
| X2259 != X2257
| hAPP(hAPP(c_List_Olist_OCons(X2261),X2260),X2259) = hAPP(hAPP(c_List_Olist_OCons(X2261),X2258),X2257) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).
fof(i_0_966,plain,
! [X2474,X2475,X2476,X2477] :
( ( hAPP(hAPP(c_List_Oappend(X2477),X2476),X2475) != hAPP(hAPP(c_List_Oappend(X2477),X2474),X2475)
| X2476 = X2474 )
& ( X2476 != X2474
| hAPP(hAPP(c_List_Oappend(X2477),X2476),X2475) = hAPP(hAPP(c_List_Oappend(X2477),X2474),X2475) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).
fof(i_0_967,plain,
! [X2478,X2479,X2480,X2481] :
( ( hAPP(hAPP(c_List_Oappend(X2481),X2480),X2479) != hAPP(hAPP(c_List_Oappend(X2481),X2480),X2478)
| X2479 = X2478 )
& ( X2479 != X2478
| hAPP(hAPP(c_List_Oappend(X2481),X2480),X2479) = hAPP(hAPP(c_List_Oappend(X2481),X2480),X2478) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).
fof(i_0_968,plain,
! [X3128,X3129,X3130] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3130,tc_HOL_Obool),X3129,X3128) = c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3130,tc_HOL_Obool),X3128,X3129),
inference(variable_rename,[status(thm)],[fact_Int__commute]) ).
fof(i_0_969,plain,
! [X4114,X4115,X4116] :
( ( c_Orderings_Oord__class_Oless__eq(X4116,X4115,X4114)
| ~ c_Orderings_Oord__class_Oless(X4116,X4115,X4114)
| ~ class_Orderings_Oorder(X4116) )
& ( X4115 != X4114
| ~ c_Orderings_Oord__class_Oless(X4116,X4115,X4114)
| ~ class_Orderings_Oorder(X4116) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4116,X4115,X4114)
| X4115 = X4114
| c_Orderings_Oord__class_Oless(X4116,X4115,X4114)
| ~ class_Orderings_Oorder(X4116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_970,plain,
! [X4108,X4109,X4110] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4110,X4109,X4108)
| c_Orderings_Oord__class_Oless(X4110,X4109,X4108)
| X4109 = X4108
| ~ class_Orderings_Oorder(X4110) )
& ( ~ c_Orderings_Oord__class_Oless(X4110,X4109,X4108)
| c_Orderings_Oord__class_Oless__eq(X4110,X4109,X4108)
| ~ class_Orderings_Oorder(X4110) )
& ( X4109 != X4108
| c_Orderings_Oord__class_Oless__eq(X4110,X4109,X4108)
| ~ class_Orderings_Oorder(X4110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_971,plain,
! [X4096,X4097,X4098] :
( ~ class_Orderings_Oorder(X4098)
| X4097 = X4096
| ~ c_Orderings_Oord__class_Oless__eq(X4098,X4097,X4096)
| c_Orderings_Oord__class_Oless(X4098,X4097,X4096) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_972,plain,
! [X4081,X4082,X4083] :
( ~ class_Orderings_Oorder(X4083)
| ~ c_Orderings_Oord__class_Oless__eq(X4083,X4082,X4081)
| c_Orderings_Oord__class_Oless(X4083,X4082,X4081)
| X4082 = X4081 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_973,plain,
! [X4078,X4079,X4080] :
( ~ class_Orderings_Oorder(X4080)
| ~ c_Orderings_Oord__class_Oless__eq(X4080,X4079,X4078)
| X4079 = X4078
| c_Orderings_Oord__class_Oless(X4080,X4079,X4078) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_974,plain,
! [X4075,X4076,X4077] :
( ~ class_Orderings_Oorder(X4077)
| ~ c_Orderings_Oord__class_Oless__eq(X4077,X4076,X4075)
| X4075 = X4076
| c_Orderings_Oord__class_Oless(X4077,X4076,X4075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_975,plain,
! [X4099,X4100,X4101] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4101,X4100,X4099)
| X4100 = X4099
| c_Orderings_Oord__class_Oless(X4101,X4100,X4099)
| ~ class_Orderings_Olinorder(X4101) )
& ( X4100 != X4099
| c_Orderings_Oord__class_Oless__eq(X4101,X4100,X4099)
| c_Orderings_Oord__class_Oless(X4101,X4100,X4099)
| ~ class_Orderings_Olinorder(X4101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])])]) ).
fof(i_0_976,plain,
! [X4093,X4094,X4095] :
( ~ class_Orderings_Oorder(X4095)
| X4094 = X4093
| ~ c_Orderings_Oord__class_Oless__eq(X4095,X4093,X4094)
| c_Orderings_Oord__class_Oless(X4095,X4093,X4094) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_977,plain,
! [X3772,X3773,X3774] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3774,X3773,X3772)
| c_Lattices_Osemilattice__inf__class_Oinf(X3774,X3773,X3772) = X3773
| ~ class_Lattices_Osemilattice__inf(X3774) )
& ( c_Lattices_Osemilattice__inf__class_Oinf(X3774,X3773,X3772) != X3773
| c_Orderings_Oord__class_Oless__eq(X3774,X3773,X3772)
| ~ class_Lattices_Osemilattice__inf(X3774) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).
fof(i_0_978,plain,
! [X3757,X3758,X3759] :
( ~ class_Lattices_Osemilattice__inf(X3759)
| ~ c_Orderings_Oord__class_Oless__eq(X3759,X3758,X3757)
| c_Lattices_Osemilattice__inf__class_Oinf(X3759,X3758,X3757) = X3758 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).
fof(i_0_979,plain,
! [X3754,X3755,X3756] :
( ~ class_Lattices_Osemilattice__inf(X3756)
| ~ c_Orderings_Oord__class_Oless__eq(X3756,X3755,X3754)
| c_Lattices_Osemilattice__inf__class_Oinf(X3756,X3754,X3755) = X3755 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).
fof(i_0_980,plain,
! [X4087,X4088,X4089] :
( ~ class_Orderings_Opreorder(X4089)
| ~ c_Orderings_Oord__class_Oless(X4089,X4088,X4087)
| c_Orderings_Oord__class_Oless__eq(X4089,X4088,X4087) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_981,plain,
! [X3568,X3569,X3570] :
( ~ c_List_Odistinct(X3570,X3569)
| c_List_Odistinct(X3570,c_List_OdropWhile(X3570,X3568,X3569)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile])]) ).
fof(i_0_982,plain,
! [X3535,X3536,X3537] :
( ~ c_List_Odistinct(X3537,X3536)
| c_List_Odistinct(X3537,c_List_OtakeWhile(X3537,X3535,X3536)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).
fof(i_0_983,plain,
! [X2404,X2405,X2406] :
( ~ c_List_Odistinct(X2406,X2405)
| c_List_Odistinct(X2406,c_List_Oinsert(X2406,X2404,X2405)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])]) ).
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,
! [X3464,X3465,X3466] :
( X3466 != c_List_Olist_ONil(X3465)
| c_List_Olast(X3465,hAPP(hAPP(c_List_Oappend(X3465),X3464),X3466)) = c_List_Olast(X3465,X3464) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).
fof(i_0_986,plain,
! [X4211,X4212] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4212,X4211)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4212,X4211) )
& ( X4212 != X4211
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4212,X4211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_987,plain,
! [X4057,X4058] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4058,X4057)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4058,X4057) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_988,plain,
! [X3467,X3468,X3469] :
( X3469 = c_List_Olist_ONil(X3468)
| c_List_Olast(X3468,hAPP(hAPP(c_List_Oappend(X3468),X3467),X3469)) = c_List_Olast(X3468,X3469) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).
fof(i_0_989,plain,
! [X3458,X3459,X3460] :
( X3460 = c_List_Olist_ONil(X3459)
| c_List_Olast(X3459,hAPP(hAPP(c_List_Olist_OCons(X3459),X3458),X3460)) = c_List_Olast(X3459,X3460) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).
fof(i_0_990,plain,
! [X3455,X3456,X3457] :
( ( X3457 != c_List_Olist_ONil(X3456)
| c_List_Olast(X3456,hAPP(hAPP(c_List_Olist_OCons(X3456),X3455),X3457)) = X3455 )
& ( X3457 = c_List_Olist_ONil(X3456)
| c_List_Olast(X3456,hAPP(hAPP(c_List_Olist_OCons(X3456),X3455),X3457)) = c_List_Olast(X3456,X3457) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).
fof(i_0_991,plain,
! [X3803,X3804,X3805] :
( ~ hBOOL(hAPP(X3805,X3804))
| hBOOL(hAPP(X3805,c_Hilbert__Choice_OEps(X3803,X3805))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).
fof(i_0_992,plain,
! [X3800,X3801,X3802] :
( ~ hBOOL(hAPP(X3801,X3802))
| hBOOL(hAPP(X3801,c_Hilbert__Choice_OEps(X3800,X3801))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).
fof(i_0_993,plain,
! [X3797,X3798,X3799] :
( ~ hBOOL(hAPP(X3798,X3799))
| hBOOL(hAPP(X3798,c_Hilbert__Choice_OEps(X3797,X3798))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).
fof(i_0_994,plain,
! [X2139,X2140] :
( hAPP(X2140,esk1_2(X2139,X2140)) != hAPP(X2139,esk1_2(X2139,X2140))
| X2140 = X2139 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_995,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_996,plain,
! [X4287,X4288] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4288),X4287))
| hBOOL(X4288) ),
inference(variable_rename,[status(thm)],[i_0_572]) ).
fof(i_0_997,plain,
! [X4289,X4290] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4290),X4289))
| hBOOL(X4289) ),
inference(variable_rename,[status(thm)],[i_0_573]) ).
fof(i_0_998,plain,
! [X4279,X4280] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4280),X4279))
| X4280 = X4279 ),
inference(variable_rename,[status(thm)],[i_0_574]) ).
fof(i_0_999,plain,
! [X4257,X4258,X4259,X4260] : hAPP(c_COMBK(X4260,X4259,X4258),X4257) = X4258,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1000,plain,
! [X4197,X4198,X4199] :
( ( X4198 = X4197
| c_Orderings_Oord__class_Oless(X4199,X4198,X4197)
| c_Orderings_Oord__class_Oless(X4199,X4197,X4198)
| ~ class_Orderings_Olinorder(X4199) )
& ( ~ c_Orderings_Oord__class_Oless(X4199,X4198,X4197)
| X4198 != X4197
| ~ class_Orderings_Olinorder(X4199) )
& ( ~ c_Orderings_Oord__class_Oless(X4199,X4197,X4198)
| X4198 != X4197
| ~ class_Orderings_Olinorder(X4199) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_1001,plain,
! [X4191,X4192,X4193] :
( ~ class_Orderings_Olinorder(X4193)
| c_Orderings_Oord__class_Oless(X4193,X4192,X4191)
| X4192 = X4191
| c_Orderings_Oord__class_Oless(X4193,X4191,X4192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_1002,plain,
! [X4188,X4189,X4190] :
( ( c_Orderings_Oord__class_Oless(X4190,X4188,X4189)
| X4188 = X4189
| c_Orderings_Oord__class_Oless(X4190,X4189,X4188)
| ~ class_Orderings_Olinorder(X4190) )
& ( X4188 != X4189
| ~ c_Orderings_Oord__class_Oless(X4190,X4188,X4189)
| c_Orderings_Oord__class_Oless(X4190,X4189,X4188)
| ~ class_Orderings_Olinorder(X4190) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])])]) ).
fof(i_0_1003,plain,
! [X4185,X4186,X4187] :
( ~ class_Orderings_Olinorder(X4187)
| X4186 = X4185
| c_Orderings_Oord__class_Oless(X4187,X4186,X4185)
| c_Orderings_Oord__class_Oless(X4187,X4185,X4186) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])]) ).
fof(i_0_1004,plain,
! [X4134,X4135,X4136] :
( ~ class_Orderings_Olinorder(X4136)
| c_Orderings_Oord__class_Oless(X4136,X4135,X4134)
| X4135 = X4134
| c_Orderings_Oord__class_Oless(X4136,X4134,X4135) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_577])]) ).
fof(i_0_1005,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_1006,plain,
! [X4117,X4118,X4119] :
( ~ class_Orderings_Olinorder(X4119)
| c_Orderings_Oord__class_Oless__eq(X4119,X4118,X4117)
| c_Orderings_Oord__class_Oless(X4119,X4117,X4118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_1007,plain,
! [X4102,X4103,X4104] :
( ~ class_Orderings_Olinorder(X4104)
| c_Orderings_Oord__class_Oless__eq(X4104,X4103,X4102)
| c_Orderings_Oord__class_Oless(X4104,X4102,X4103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_578])]) ).
fof(i_0_1008,plain,
! [X4105,X4106,X4107] :
( ~ class_Orderings_Olinorder(X4107)
| c_Orderings_Oord__class_Oless(X4107,X4106,X4105)
| c_Orderings_Oord__class_Oless__eq(X4107,X4105,X4106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])]) ).
fof(i_0_1009,plain,
! [X4006,X4007,X4008] :
( ~ class_Orderings_Olinorder(X4008)
| c_Orderings_Oord__class_Oless__eq(X4008,X4007,X4006)
| c_Orderings_Oord__class_Oless__eq(X4008,X4006,X4007) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])]) ).
fof(i_0_1010,plain,
! [X3964,X3965,X3966] :
( ~ class_Orderings_Olinorder(X3966)
| c_Orderings_Oord__class_Oless__eq(X3966,X3965,X3964)
| c_Orderings_Oord__class_Oless__eq(X3966,X3964,X3965) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_1011,plain,
! [X3270,X3271,X3272] :
( ~ class_Lattices_Osemilattice__inf(X3272)
| c_Lattices_Osemilattice__inf__class_Oinf(X3272,X3271,X3270) = c_Lattices_Osemilattice__inf__class_Oinf(X3272,X3270,X3271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).
fof(i_0_1012,plain,
! [X3264,X3265,X3266] :
( ~ class_Lattices_Osemilattice__inf(X3266)
| c_Lattices_Osemilattice__inf__class_Oinf(X3266,X3265,X3264) = c_Lattices_Osemilattice__inf__class_Oinf(X3266,X3264,X3265) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).
fof(i_0_1013,plain,
! [X3267,X3268,X3269] :
( ~ class_Lattices_Olattice(X3269)
| c_Lattices_Osemilattice__inf__class_Oinf(X3269,X3268,X3267) = c_Lattices_Osemilattice__inf__class_Oinf(X3269,X3267,X3268) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).
fof(i_0_1014,plain,
! [X4182,X4183,X4184] :
( ~ class_Orderings_Oorder(X4184)
| ~ c_Orderings_Oord__class_Oless(X4184,X4183,X4182)
| X4183 != X4182 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_1015,plain,
! [X4173,X4174,X4175] :
( ~ class_Orderings_Oorder(X4175)
| ~ c_Orderings_Oord__class_Oless(X4175,X4174,X4173)
| X4174 != X4173 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_1016,plain,
! [X4170,X4171,X4172] :
( ~ class_Orderings_Oorder(X4172)
| ~ c_Orderings_Oord__class_Oless(X4172,X4171,X4170)
| X4170 != X4171 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_1017,plain,
! [X3042,X3043] : hBOOL(hAPP(c_List_Olistsp(X3043,X3042),c_List_Olist_ONil(X3043))),
inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J]) ).
fof(i_0_1018,plain,
! [X3032,X3033] : hBOOL(hAPP(c_List_Olistsp(X3033,X3032),c_List_Olist_ONil(X3033))),
inference(variable_rename,[status(thm)],[fact_listsp_ONil]) ).
fof(i_0_1019,plain,
! [X2523,X2524,X2525] :
( ( X2524 = c_List_Olist_ONil(X2525)
| hAPP(hAPP(c_List_Oappend(X2525),X2524),X2523) != c_List_Olist_ONil(X2525) )
& ( X2523 = c_List_Olist_ONil(X2525)
| hAPP(hAPP(c_List_Oappend(X2525),X2524),X2523) != c_List_Olist_ONil(X2525) )
& ( X2524 != c_List_Olist_ONil(X2525)
| X2523 != c_List_Olist_ONil(X2525)
| hAPP(hAPP(c_List_Oappend(X2525),X2524),X2523) = c_List_Olist_ONil(X2525) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).
fof(i_0_1020,plain,
! [X2512,X2513,X2514] :
( ( X2513 = c_List_Olist_ONil(X2514)
| c_List_Olist_ONil(X2514) != hAPP(hAPP(c_List_Oappend(X2514),X2513),X2512) )
& ( X2512 = c_List_Olist_ONil(X2514)
| c_List_Olist_ONil(X2514) != hAPP(hAPP(c_List_Oappend(X2514),X2513),X2512) )
& ( X2513 != c_List_Olist_ONil(X2514)
| X2512 != c_List_Olist_ONil(X2514)
| c_List_Olist_ONil(X2514) = hAPP(hAPP(c_List_Oappend(X2514),X2513),X2512) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).
fof(i_0_1021,plain,
! [X4200,X4201] :
( ~ class_Orderings_Opreorder(X4201)
| ~ c_Orderings_Oord__class_Oless(X4201,X4200,X4200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_581])]) ).
fof(i_0_1022,plain,
! [X4285,X4286] :
( ~ hBOOL(X4286)
| ~ hBOOL(X4285)
| hBOOL(hAPP(hAPP(c_fconj,X4286),X4285)) ),
inference(variable_rename,[status(thm)],[i_0_582]) ).
fof(i_0_1023,plain,
! [X2529,X2530,X2531] :
( ( hAPP(hAPP(c_List_Oappend(X2531),X2530),X2529) != X2529
| X2530 = c_List_Olist_ONil(X2531) )
& ( X2530 != c_List_Olist_ONil(X2531)
| hAPP(hAPP(c_List_Oappend(X2531),X2530),X2529) = X2529 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).
fof(i_0_1024,plain,
! [X2526,X2527,X2528] :
( ( hAPP(hAPP(c_List_Oappend(X2528),X2527),X2526) != X2527
| X2526 = c_List_Olist_ONil(X2528) )
& ( X2526 != c_List_Olist_ONil(X2528)
| hAPP(hAPP(c_List_Oappend(X2528),X2527),X2526) = X2527 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).
fof(i_0_1025,plain,
! [X2517,X2518,X2519] :
( ( X2519 != hAPP(hAPP(c_List_Oappend(X2518),X2519),X2517)
| X2517 = c_List_Olist_ONil(X2518) )
& ( X2517 != c_List_Olist_ONil(X2518)
| X2519 = hAPP(hAPP(c_List_Oappend(X2518),X2519),X2517) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).
fof(i_0_1026,plain,
! [X2520,X2521,X2522] :
( ( X2522 != hAPP(hAPP(c_List_Oappend(X2521),X2520),X2522)
| X2520 = c_List_Olist_ONil(X2521) )
& ( X2520 != c_List_Olist_ONil(X2521)
| X2522 = hAPP(hAPP(c_List_Oappend(X2521),X2520),X2522) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).
fof(i_0_1027,plain,
! [X2213,X2214,X2215] : hAPP(hAPP(c_List_Olist_OCons(X2215),X2214),X2213) != c_List_Olist_ONil(X2215),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).
fof(i_0_1028,plain,
! [X2210,X2211,X2212] : c_List_Olist_ONil(X2212) != hAPP(hAPP(c_List_Olist_OCons(X2212),X2211),X2210),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
fof(i_0_1029,plain,
! [X4243,X4244] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4244,X4243)
| X4243 != X4244 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_1030,plain,
! [X4241,X4242] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4242,X4241)
| X4242 != X4241 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_1031,plain,
! [X2738,X2739] : c_List_Olistrel(X2739,c_Transitive__Closure_Ortrancl(X2739,X2738)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X2739),c_List_Olistrel1(X2739,X2738)),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).
fof(i_0_1032,plain,
! [X2262,X2263,X2264] : hAPP(hAPP(c_List_Olist_OCons(X2264),X2263),X2262) != X2262,
inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).
fof(i_0_1033,plain,
! [X2265,X2266,X2267] : X2267 != hAPP(hAPP(c_List_Olist_OCons(X2266),X2265),X2267),
inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).
fof(i_0_1034,plain,
! [X2975,X2976] : c_Relation_ORange(X2976,X2976,c_Relation_OId__on(X2976,X2975)) = X2975,
inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).
fof(i_0_1035,plain,
! [X2971,X2972] : c_Relation_ODomain(X2972,X2972,c_Relation_OId__on(X2972,X2971)) = X2971,
inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).
fof(i_0_1036,plain,
! [X3867,X3868,X3869] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3867,tc_HOL_Obool),X3869,X3868)
| X3869 != X3868 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3867,tc_HOL_Obool),X3868,X3869)
| X3869 != X3868 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_583])])]) ).
fof(i_0_1037,plain,
! [X3857,X3858,X3859] :
( X3859 != X3858
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3857,tc_HOL_Obool),X3859,X3858) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_1038,plain,
! [X3860,X3861,X3862] :
( X3862 != X3861
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3860,tc_HOL_Obool),X3861,X3862) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_1039,plain,
! [X2977,X2978] : c_Relation_Osingle__valued(X2978,X2978,c_Relation_OId__on(X2978,X2977)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).
fof(i_0_1040,plain,
! [X4281,X4282] :
( X4282 != X4281
| hBOOL(hAPP(hAPP(c_fequal,X4282),X4281)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1041,plain,
! [X3131,X3132] : c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3132,tc_HOL_Obool),X3131,X3131) = X3131,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
fof(i_0_1042,plain,
! [X2661,X2662] :
( ( ~ c_List_Odistinct(X2662,c_List_Orotate1(X2662,X2661))
| c_List_Odistinct(X2662,X2661) )
& ( ~ c_List_Odistinct(X2662,X2661)
| c_List_Odistinct(X2662,c_List_Orotate1(X2662,X2661)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).
fof(i_0_1043,plain,
! [X3852,X3853] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3853,tc_HOL_Obool),X3852,X3852),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_1044,plain,
! [X2734,X2735] :
( ~ c_Relation_Otrans(X2735,X2734)
| c_Relation_Otrans(tc_List_Olist(X2735),c_List_Olistrel(X2735,X2734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__trans])]) ).
fof(i_0_1045,plain,
! [X2736,X2737] :
( ~ c_Relation_Otrans(X2737,X2736)
| c_Relation_Otrans(tc_List_Olist(X2737),c_List_Olexord(X2737,X2736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__transI])]) ).
fof(i_0_1046,plain,
! [X2532,X2533,X2534] :
( X2534 != X2533
| X2534 = hAPP(hAPP(c_List_Oappend(X2532),c_List_Olist_ONil(X2532)),X2533) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).
fof(i_0_1047,plain,
! [X3504,X3505] :
( X3505 = c_List_Olist_ONil(X3504)
| ~ c_List_Odistinct(X3504,X3505)
| c_List_Odistinct(X3504,c_List_Obutlast(X3504,X3505)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).
fof(i_0_1048,plain,
! [X2654,X2655] : c_Nat_Osize__class_Osize(tc_List_Olist(X2655),c_List_Orotate1(X2655,X2654)) = c_Nat_Osize__class_Osize(tc_List_Olist(X2655),X2654),
inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).
fof(i_0_1049,plain,
! [X3970,X3971,X3972] :
( ~ class_Orderings_Opreorder(X3972)
| X3971 != X3970
| c_Orderings_Oord__class_Oless__eq(X3972,X3971,X3970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1050,plain,
! [X2510,X2511] : hAPP(hAPP(c_List_Oappend(X2511),c_List_Olist_ONil(X2511)),X2510) = X2510,
inference(variable_rename,[status(thm)],[fact_append__Nil]) ).
fof(i_0_1051,plain,
! [X3566,X3567] : c_List_OdropWhile(X3567,X3566,c_List_Olist_ONil(X3567)) = c_List_Olist_ONil(X3567),
inference(variable_rename,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).
fof(i_0_1052,plain,
! [X3533,X3534] : c_List_OtakeWhile(X3534,X3533,c_List_Olist_ONil(X3534)) = c_List_Olist_ONil(X3534),
inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).
fof(i_0_1053,plain,
! [X3275,X3276] :
( ~ class_Lattices_Osemilattice__inf(X3276)
| c_Lattices_Osemilattice__inf__class_Oinf(X3276,X3275,X3275) = X3275 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).
fof(i_0_1054,plain,
! [X3273,X3274] :
( ~ class_Lattices_Osemilattice__inf(X3274)
| c_Lattices_Osemilattice__inf__class_Oinf(X3274,X3273,X3273) = X3273 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).
fof(i_0_1055,plain,
! [X3939,X3940] :
( ~ class_Orderings_Opreorder(X3940)
| c_Orderings_Oord__class_Oless__eq(X3940,X3939,X3939) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1056,plain,
! [X2334,X2335] : c_List_Osplice(X2335,c_List_Olist_ONil(X2335),X2334) = X2334,
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).
fof(i_0_1057,plain,
! [X2336,X2337] : c_List_Osplice(X2337,X2336,c_List_Olist_ONil(X2337)) = X2336,
inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).
fof(i_0_1058,plain,
! [X2515,X2516] : hAPP(hAPP(c_List_Oappend(X2516),X2515),c_List_Olist_ONil(X2516)) = X2515,
inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).
fof(i_0_1059,plain,
! [X2794,X2795] : c_Transitive__Closure_Ortrancl(X2795,c_Transitive__Closure_Ortrancl(X2795,X2794)) = c_Transitive__Closure_Ortrancl(X2795,X2794),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).
fof(i_0_1060,plain,
! [X4283] :
( ~ hBOOL(hAPP(c_fNot,X4283))
| ~ hBOOL(X4283) ),
inference(variable_rename,[status(thm)],[i_0_584]) ).
fof(i_0_1061,plain,
! [X2973,X2974] : c_Relation_Otrans(X2974,c_Relation_OId__on(X2974,X2973)),
inference(variable_rename,[status(thm)],[fact_trans__Id__on]) ).
fof(i_0_1062,plain,
! [X2796,X2797] : c_Relation_Otrans(X2797,c_Transitive__Closure_Ortrancl(X2797,X2796)),
inference(variable_rename,[status(thm)],[fact_trans__rtrancl]) ).
fof(i_0_1063,plain,
! [X3787,X3788] : c_Hilbert__Choice_OEps(X3788,hAPP(c_fequal,X3787)) = X3787,
inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).
fof(i_0_1064,plain,
! [X4251,X4252] :
( ~ class_Orderings_Oorder(X4252)
| class_Orderings_Oorder(tc_fun(X4251,X4252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1065,plain,
! [X4253,X4254] :
( ~ class_Orderings_Oord(X4254)
| class_Orderings_Oord(tc_fun(X4253,X4254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1066,plain,
! [X4247,X4248] :
( ~ class_Orderings_Opreorder(X4248)
| class_Orderings_Opreorder(tc_fun(X4247,X4248)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1067,plain,
! [X4245,X4246] :
( ~ class_Lattices_Olattice(X4246)
| class_Lattices_Osemilattice__inf(tc_fun(X4245,X4246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).
fof(i_0_1068,plain,
! [X4249,X4250] :
( ~ class_Lattices_Olattice(X4250)
| class_Lattices_Olattice(tc_fun(X4249,X4250)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).
fof(i_0_1069,plain,
! [X2659,X2660] :
( ( c_List_Orotate1(X2660,X2659) != c_List_Olist_ONil(X2660)
| X2659 = c_List_Olist_ONil(X2660) )
& ( X2659 != c_List_Olist_ONil(X2660)
| c_List_Orotate1(X2660,X2659) = c_List_Olist_ONil(X2660) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).
fof(i_0_1070,plain,
! [X4284] :
( hBOOL(X4284)
| hBOOL(hAPP(c_fNot,X4284)) ),
inference(variable_rename,[status(thm)],[i_0_585]) ).
fof(i_0_1071,plain,
! [X3487] : c_List_Obutlast(X3487,c_List_Olist_ONil(X3487)) = c_List_Olist_ONil(X3487),
inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).
fof(i_0_1072,plain,
! [X4255,X4256] : hAPP(c_COMBI(X4256),X4255) = X4255,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1073,plain,
! [X2209] : c_List_Odistinct(X2209,c_List_Olist_ONil(X2209)),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
cnf(i_0_1074,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))),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),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),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____))),v_b____)),v_a____))),v_a____)),v_c____)),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096]),
[final] ).
cnf(i_0_1075,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_586]),
[final] ).
cnf(i_0_1076,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_587]),
[final] ).
cnf(i_0_1077,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_587]),
[final] ).
cnf(i_0_1078,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_586]),
[final] ).
cnf(i_0_1079,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_c____)),hAPP(v_F,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____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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),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____))),v_b____)),v_a____)))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1080,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_c____)),hAPP(v_F,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),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____))),v_b____)),v_a____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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____)))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1081,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))),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),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____))),v_b____)),v_a____)),c_Arrow__Order__Mirabelle_OProf)),
inference(split_conjunct,[status(thm)],[fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096]),
[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),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_589]),
[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),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_589]),
[final] ).
cnf(i_0_1084,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_586]),
[final] ).
cnf(i_0_1085,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_587]),
[final] ).
cnf(i_0_1086,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_590]),
[final] ).
cnf(i_0_1087,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_586]),
[final] ).
cnf(i_0_1088,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_587]),
[final] ).
cnf(i_0_1089,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_590]),
[final] ).
cnf(i_0_1090,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_591]),
[final] ).
cnf(i_0_1091,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_592]),
[final] ).
cnf(i_0_1092,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_593]),
[final] ).
cnf(i_0_1093,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_F,v_P____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(v_F,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____)))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1094,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_592]),
[final] ).
cnf(i_0_1095,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_595]),
[final] ).
cnf(i_0_1096,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_c____)),hAPP(v_F,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____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_F,v_P____))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1097,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))),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)],[fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096]),
[final] ).
cnf(i_0_1098,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,esk84_6(X3,X2,X1,X4,X5,X6)),esk85_6(X3,X2,X1,X4,X5,X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1099,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_595]),
[final] ).
cnf(i_0_1100,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_597]),
[final] ).
cnf(i_0_1101,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_591]),
[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)))
| 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,esk5_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,esk5_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_598]),
[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),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,esk5_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,esk5_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_598]),
[final] ).
cnf(i_0_1104,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,esk4_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,esk4_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_599]),
[final] ).
cnf(i_0_1105,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_600]),
[final] ).
cnf(i_0_1106,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_601]),
[final] ).
cnf(i_0_1107,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_602]),
[final] ).
cnf(i_0_1108,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_603]),
[final] ).
cnf(i_0_1109,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk86_6(X4,X3,X5,X6,X2,X1)),esk87_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_604]),
[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),X4),X5)),hAPP(X6,esk5_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,esk5_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_598]),
[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),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,esk5_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,esk5_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_598]),
[final] ).
cnf(i_0_1112,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,esk4_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,esk4_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_599]),
[final] ).
cnf(i_0_1113,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_600]),
[final] ).
cnf(i_0_1114,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_601]),
[final] ).
cnf(i_0_1115,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_602]),
[final] ).
cnf(i_0_1116,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_605]),
[final] ).
cnf(i_0_1117,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1118,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_1119,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_1120,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_1121,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_1122,negated_conjecture,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk105_0)),v_c____),v_b____)),v_b____),v_a____)),v_a____),v_c____))) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1123,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_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)),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_605]),
[final] ).
cnf(i_0_1125,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_1126,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,esk20_5(X3,X2,X1,X4,X5))),hAPP(X3,esk20_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1127,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_1128,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_605]),
[final] ).
cnf(i_0_1129,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)),esk37_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_1130,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk36_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_1131,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_1132,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_1133,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,esk6_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,esk6_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_1134,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,esk6_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,esk6_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_1135,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk86_6(X1,X4,X3,X2,X5,X6)),esk87_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_604]),
[final] ).
cnf(i_0_1136,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_597]),
[final] ).
cnf(i_0_1137,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk84_6(X4,X5,X6,X3,X2,X1)),esk85_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_596]),
[final] ).
cnf(i_0_1138,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_1139,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,esk22_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_617]),
[final] ).
cnf(i_0_1140,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_1141,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_1142,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_1143,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_1144,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,esk6_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,esk6_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_1145,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,esk6_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,esk6_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_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)),X2),esk35_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_1147,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk34_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_1148,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)),esk27_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1149,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),esk27_4(X2,X3,X4,X1)),esk28_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1150,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_1151,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_1152,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_1153,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_1154,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_1155,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_1156,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_1157,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_1158,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),esk16_2(X1,X2)),esk17_2(X1,X2))),hAPP(X2,esk15_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_1159,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_1160,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_1161,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_1162,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_1163,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),esk16_2(X1,X2)),esk17_2(X1,X2))),hAPP(esk15_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_1164,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_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_1165,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_1166,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_1167,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk16_2(X1,X2) != esk17_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_1168,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_1169,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_1170,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_1171,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_1172,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk34_5(X3,X1,X4,X5,X2)),esk35_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_1173,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_1174,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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X1)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X1)),v_c____),v_b____)),v_b____),v_a____))) ),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1175,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk22_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_1176,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_634]),
[final] ).
cnf(i_0_1177,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_1178,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_605]),
[final] ).
cnf(i_0_1179,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk36_5(X3,X4,X5,X1,X2)),esk37_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_1180,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_1181,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk20_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_1182,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_1183,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_635]),
[final] ).
cnf(i_0_1184,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_636]),
[final] ).
cnf(i_0_1185,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_1186,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_1187,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_637]),
[final] ).
cnf(i_0_1188,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_638]),
[final] ).
cnf(i_0_1189,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_639]),
[final] ).
cnf(i_0_1190,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_640]),
[final] ).
cnf(i_0_1191,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_641]),
[final] ).
cnf(i_0_1192,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_634]),
[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)),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_642]),
[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)),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_643]),
[final] ).
cnf(i_0_1195,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_644]),
[final] ).
cnf(i_0_1196,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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X1)),v_c____),v_b____)),v_b____),v_a____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X1)),v_c____),v_b____))) ),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1197,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_591]),
[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)),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_645]),
[final] ).
cnf(i_0_1199,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_646]),
[final] ).
cnf(i_0_1200,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_1201,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_647]),
[final] ).
cnf(i_0_1202,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_643]),
[final] ).
cnf(i_0_1203,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_642]),
[final] ).
cnf(i_0_1204,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,esk11_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1205,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_642]),
[final] ).
cnf(i_0_1206,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_643]),
[final] ).
cnf(i_0_1207,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_644]),
[final] ).
cnf(i_0_1208,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_638]),
[final] ).
cnf(i_0_1209,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_638]),
[final] ).
cnf(i_0_1210,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_649]),
[final] ).
cnf(i_0_1211,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_650]),
[final] ).
cnf(i_0_1212,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_651]),
[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),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_652]),
[final] ).
cnf(i_0_1214,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_652]),
[final] ).
cnf(i_0_1215,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_642]),
[final] ).
cnf(i_0_1216,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_643]),
[final] ).
cnf(i_0_1217,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_644]),
[final] ).
cnf(i_0_1218,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_653]),
[final] ).
cnf(i_0_1219,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_654]),
[final] ).
cnf(i_0_1220,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_1221,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_1222,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_655,c_0_623]),
[final] ).
cnf(i_0_1223,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_639]),
[final] ).
cnf(i_0_1224,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_656,c_0_623]),
[final] ).
cnf(i_0_1225,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_643]),
[final] ).
cnf(i_0_1226,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_642]),
[final] ).
cnf(i_0_1227,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_657]),
[final] ).
cnf(i_0_1228,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_658]),
[final] ).
cnf(i_0_1229,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk29_3(X2,X3,X1)),esk29_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_659]),
[final] ).
cnf(i_0_1230,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_1231,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_661]),
[final] ).
cnf(i_0_1232,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_662]),
[final] ).
cnf(i_0_1233,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_1234,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_663]),
[final] ).
cnf(i_0_1235,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_643]),
[final] ).
cnf(i_0_1236,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_642]),
[final] ).
cnf(i_0_1237,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_664]),
[final] ).
cnf(i_0_1238,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_644]),
[final] ).
cnf(i_0_1239,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_665]),
[final] ).
cnf(i_0_1240,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_666]),
[final] ).
cnf(i_0_1241,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_667,c_0_623]),
[final] ).
cnf(i_0_1242,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_668]),
[final] ).
cnf(i_0_1243,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_669]),
[final] ).
cnf(i_0_1244,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_638]),
[final] ).
cnf(i_0_1245,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk33_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_670]),
[final] ).
cnf(i_0_1246,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk32_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_671]),
[final] ).
cnf(i_0_1247,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk32_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_671]),
[final] ).
cnf(i_0_1248,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk33_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_670]),
[final] ).
cnf(i_0_1249,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_672]),
[final] ).
cnf(i_0_1250,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_591]),
[final] ).
cnf(i_0_1251,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_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)),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_657]),
[final] ).
cnf(i_0_1253,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_657]),
[final] ).
cnf(i_0_1254,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_657]),
[final] ).
cnf(i_0_1255,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_673]),
[final] ).
cnf(i_0_1256,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_658]),
[final] ).
cnf(i_0_1257,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_658]),
[final] ).
cnf(i_0_1258,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_658]),
[final] ).
cnf(i_0_1259,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_658]),
[final] ).
cnf(i_0_1260,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_674]),
[final] ).
cnf(i_0_1261,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_675]),
[final] ).
cnf(i_0_1262,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_676]),
[final] ).
cnf(i_0_1263,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_677]),
[final] ).
cnf(i_0_1264,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_678]),
[final] ).
cnf(i_0_1265,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_679]),
[final] ).
cnf(i_0_1266,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_680]),
[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_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_681]),
[final] ).
cnf(i_0_1268,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_682]),
[final] ).
cnf(i_0_1269,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_683,c_0_623]),
[final] ).
cnf(i_0_1270,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_1271,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_685]),
[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)),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_682]),
[final] ).
cnf(i_0_1273,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)))
| esk27_4(X1,X2,X3,X4) != esk28_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1274,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_686]),
[final] ).
cnf(i_0_1275,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_687]),
[final] ).
cnf(i_0_1276,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_676]),
[final] ).
cnf(i_0_1277,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_688]),
[final] ).
cnf(i_0_1278,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_689]),
[final] ).
cnf(i_0_1279,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_657]),
[final] ).
cnf(i_0_1280,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_657]),
[final] ).
cnf(i_0_1281,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_657]),
[final] ).
cnf(i_0_1282,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_690]),
[final] ).
cnf(i_0_1283,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_691]),
[final] ).
cnf(i_0_1284,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_692]),
[final] ).
cnf(i_0_1285,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_692]),
[final] ).
cnf(i_0_1286,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_693]),
[final] ).
cnf(i_0_1287,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_693]),
[final] ).
cnf(i_0_1288,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_676]),
[final] ).
cnf(i_0_1289,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_1290,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_695]),
[final] ).
cnf(i_0_1291,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_657]),
[final] ).
cnf(i_0_1292,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_657]),
[final] ).
cnf(i_0_1293,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_657]),
[final] ).
cnf(i_0_1294,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_657]),
[final] ).
cnf(i_0_1295,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_657]),
[final] ).
cnf(i_0_1296,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_658]),
[final] ).
cnf(i_0_1297,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_658]),
[final] ).
cnf(i_0_1298,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_658]),
[final] ).
cnf(i_0_1299,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_696]),
[final] ).
cnf(i_0_1300,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_697]),
[final] ).
cnf(i_0_1301,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_698]),
[final] ).
cnf(i_0_1302,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),esk9_1(X1)),esk10_1(X1))),hAPP(X1,esk7_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),esk9_1(X1)),esk10_1(X1))),hAPP(X1,esk8_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1303,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_658]),
[final] ).
cnf(i_0_1304,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_658]),
[final] ).
cnf(i_0_1305,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_658]),
[final] ).
cnf(i_0_1306,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_658]),
[final] ).
cnf(i_0_1307,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_658]),
[final] ).
cnf(i_0_1308,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_699]),
[final] ).
cnf(i_0_1309,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_697]),
[final] ).
cnf(i_0_1310,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_693]),
[final] ).
cnf(i_0_1311,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_700]),
[final] ).
cnf(i_0_1312,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_701]),
[final] ).
cnf(i_0_1313,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_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X1)),v_c____),v_b____))) ),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_1314,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_675]),
[final] ).
cnf(i_0_1315,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_703]),
[final] ).
cnf(i_0_1316,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_704]),
[final] ).
cnf(i_0_1317,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_705]),
[final] ).
cnf(i_0_1318,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_706]),
[final] ).
cnf(i_0_1319,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_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,X1)),v_c____),v_b____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_702]),
[final] ).
cnf(i_0_1320,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_707]),
[final] ).
cnf(i_0_1321,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_708]),
[final] ).
cnf(i_0_1322,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_708]),
[final] ).
cnf(i_0_1323,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_709]),
[final] ).
cnf(i_0_1324,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk60_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_710]),
[final] ).
cnf(i_0_1325,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_711]),
[final] ).
cnf(i_0_1326,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_657]),
[final] ).
cnf(i_0_1327,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_712]),
[final] ).
cnf(i_0_1328,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_713]),
[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),esk9_1(X1)),esk10_1(X1))),hAPP(esk8_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),esk9_1(X1)),esk10_1(X1))),hAPP(esk7_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1330,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),esk9_1(X1)),esk10_1(X1))),hAPP(esk7_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),esk9_1(X1)),esk10_1(X1))),hAPP(esk8_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1331,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_707]),
[final] ).
cnf(i_0_1332,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_714]),
[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)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1334,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_716]),
[final] ).
cnf(i_0_1335,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_717]),
[final] ).
cnf(i_0_1336,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_690]),
[final] ).
cnf(i_0_1337,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_718]),
[final] ).
cnf(i_0_1338,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_719]),
[final] ).
cnf(i_0_1339,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_720]),
[final] ).
cnf(i_0_1340,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_721]),
[final] ).
cnf(i_0_1341,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_658]),
[final] ).
cnf(i_0_1342,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_722]),
[final] ).
cnf(i_0_1343,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_723]),
[final] ).
cnf(i_0_1344,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_682]),
[final] ).
cnf(i_0_1345,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk33_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_670]),
[final] ).
cnf(i_0_1346,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk32_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_671]),
[final] ).
cnf(i_0_1347,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_724]),
[final] ).
cnf(i_0_1348,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_725]),
[final] ).
cnf(i_0_1349,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_726]),
[final] ).
cnf(i_0_1350,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_1351,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk2_2(X2,X1)),esk2_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_1352,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk33_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_670]),
[final] ).
cnf(i_0_1353,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk32_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_671]),
[final] ).
cnf(i_0_1354,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_728]),
[final] ).
cnf(i_0_1355,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_729]),
[final] ).
cnf(i_0_1356,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_730,c_0_623]),
[final] ).
cnf(i_0_1357,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_731]),
[final] ).
cnf(i_0_1358,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_732]),
[final] ).
cnf(i_0_1359,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_733]),
[final] ).
cnf(i_0_1360,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_734]),
[final] ).
cnf(i_0_1361,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_735]),
[final] ).
cnf(i_0_1362,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_736]),
[final] ).
cnf(i_0_1363,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_676]),
[final] ).
cnf(i_0_1364,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_737]),
[final] ).
cnf(i_0_1365,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_738]),
[final] ).
cnf(i_0_1366,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_738]),
[final] ).
cnf(i_0_1367,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_737]),
[final] ).
cnf(i_0_1368,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_738]),
[final] ).
cnf(i_0_1369,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_737]),
[final] ).
cnf(i_0_1370,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_739]),
[final] ).
cnf(i_0_1371,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_739]),
[final] ).
cnf(i_0_1372,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_597]),
[final] ).
cnf(i_0_1373,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_740]),
[final] ).
cnf(i_0_1374,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),esk9_1(X1)),esk10_1(X1))),hAPP(X1,esk7_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),esk9_1(X1)),esk10_1(X1))),hAPP(X1,esk8_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1375,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_741]),
[final] ).
cnf(i_0_1376,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_689]),
[final] ).
cnf(i_0_1377,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_657]),
[final] ).
cnf(i_0_1378,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_742]),
[final] ).
cnf(i_0_1379,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_743]),
[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)),c_Transitive__Closure_Ortrancl(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_744]),
[final] ).
cnf(i_0_1381,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_745]),
[final] ).
cnf(i_0_1382,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_658]),
[final] ).
cnf(i_0_1383,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_1384,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_747]),
[final] ).
cnf(i_0_1385,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_748]),
[final] ).
cnf(i_0_1386,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_711]),
[final] ).
cnf(i_0_1387,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_749]),
[final] ).
cnf(i_0_1388,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_750]),
[final] ).
cnf(i_0_1389,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_751]),
[final] ).
cnf(i_0_1390,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_752]),
[final] ).
cnf(i_0_1391,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_669]),
[final] ).
cnf(i_0_1392,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_753]),
[final] ).
cnf(i_0_1393,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_641]),
[final] ).
cnf(i_0_1394,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_754]),
[final] ).
cnf(i_0_1395,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_755]),
[final] ).
cnf(i_0_1396,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_703]),
[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)),c_List_Olist_ONil(X1)),c_List_Olist_ONil(X1))),c_List_Olistrel(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_756]),
[final] ).
cnf(i_0_1398,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_757]),
[final] ).
cnf(i_0_1399,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_758]),
[final] ).
cnf(i_0_1400,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_759]),
[final] ).
cnf(i_0_1401,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_759]),
[final] ).
cnf(i_0_1402,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_760]),
[final] ).
cnf(i_0_1403,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_761]),
[final] ).
cnf(i_0_1404,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_762]),
[final] ).
cnf(i_0_1405,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),esk13_1(X1)),esk14_1(X1))),hAPP(X1,esk12_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1406,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_763,c_0_623]),
[final] ).
cnf(i_0_1407,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_757]),
[final] ).
cnf(i_0_1408,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_764]),
[final] ).
cnf(i_0_1409,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_726]),
[final] ).
cnf(i_0_1410,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_726]),
[final] ).
cnf(i_0_1411,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_1412,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_1413,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_764]),
[final] ).
cnf(i_0_1414,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_765]),
[final] ).
cnf(i_0_1415,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_766]),
[final] ).
cnf(i_0_1416,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_767]),
[final] ).
cnf(i_0_1417,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_735]),
[final] ).
cnf(i_0_1418,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_768]),
[final] ).
cnf(i_0_1419,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_737]),
[final] ).
cnf(i_0_1420,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_738]),
[final] ).
cnf(i_0_1421,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_769]),
[final] ).
cnf(i_0_1422,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_738]),
[final] ).
cnf(i_0_1423,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_737]),
[final] ).
cnf(i_0_1424,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_770]),
[final] ).
cnf(i_0_1425,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_748]),
[final] ).
cnf(i_0_1426,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_771]),
[final] ).
cnf(i_0_1427,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_772]),
[final] ).
cnf(i_0_1428,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_773]),
[final] ).
cnf(i_0_1429,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_751]),
[final] ).
cnf(i_0_1430,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))),esk19_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_1431,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_774]),
[final] ).
cnf(i_0_1432,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_775]),
[final] ).
cnf(i_0_1433,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_776]),
[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))),esk12_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[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))),esk8_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_1436,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_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_1437,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_777]),
[final] ).
cnf(i_0_1438,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_689]),
[final] ).
cnf(i_0_1439,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_778]),
[final] ).
cnf(i_0_1440,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_779]),
[final] ).
cnf(i_0_1441,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_1442,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_1443,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_780]),
[final] ).
cnf(i_0_1444,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_781]),
[final] ).
cnf(i_0_1445,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_782]),
[final] ).
cnf(i_0_1446,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_757]),
[final] ).
cnf(i_0_1447,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_783]),
[final] ).
cnf(i_0_1448,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_758]),
[final] ).
cnf(i_0_1449,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_784]),
[final] ).
cnf(i_0_1450,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_785]),
[final] ).
cnf(i_0_1451,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_786]),
[final] ).
cnf(i_0_1452,plain,
c_List_Olist_Olist__case(X1,X2,X3,X4,c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1453,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_788]),
[final] ).
cnf(i_0_1454,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_782]),
[final] ).
cnf(i_0_1455,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_782]),
[final] ).
cnf(i_0_1456,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_789]),
[final] ).
cnf(i_0_1457,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),esk13_1(X1)),esk14_1(X1))),hAPP(esk12_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1458,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_789]),
[final] ).
cnf(i_0_1459,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_790]),
[final] ).
cnf(i_0_1460,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_791]),
[final] ).
cnf(i_0_1461,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_792]),
[final] ).
cnf(i_0_1462,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),esk18_2(X2,X1)),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1463,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_697]),
[final] ).
cnf(i_0_1464,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_709]),
[final] ).
cnf(i_0_1465,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk60_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_710]),
[final] ).
cnf(i_0_1466,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_711]),
[final] ).
cnf(i_0_1467,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_794]),
[final] ).
cnf(i_0_1468,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_789]),
[final] ).
cnf(i_0_1469,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_727]),
[final] ).
cnf(i_0_1470,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_795]),
[final] ).
cnf(i_0_1471,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_796]),
[final] ).
cnf(i_0_1472,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_790]),
[final] ).
cnf(i_0_1473,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_797]),
[final] ).
cnf(i_0_1474,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_798]),
[final] ).
cnf(i_0_1475,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_799]),
[final] ).
cnf(i_0_1476,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_800]),
[final] ).
cnf(i_0_1477,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_798]),
[final] ).
cnf(i_0_1478,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_801]),
[final] ).
cnf(i_0_1479,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_737]),
[final] ).
cnf(i_0_1480,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_738]),
[final] ).
cnf(i_0_1481,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_802]),
[final] ).
cnf(i_0_1482,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)),esk21_2(X2,X1)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1483,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_804]),
[final] ).
cnf(i_0_1484,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_800]),
[final] ).
cnf(i_0_1485,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_805]),
[final] ).
cnf(i_0_1486,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_806]),
[final] ).
cnf(i_0_1487,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_807]),
[final] ).
cnf(i_0_1488,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_798]),
[final] ).
cnf(i_0_1489,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_800]),
[final] ).
cnf(i_0_1490,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_724]),
[final] ).
cnf(i_0_1491,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_1492,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_809]),
[final] ).
cnf(i_0_1493,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_810]),
[final] ).
cnf(i_0_1494,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_809]),
[final] ).
cnf(i_0_1495,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_810]),
[final] ).
cnf(i_0_1496,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_811]),
[final] ).
cnf(i_0_1497,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_809]),
[final] ).
cnf(i_0_1498,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_812]),
[final] ).
cnf(i_0_1499,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_813]),
[final] ).
cnf(i_0_1500,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk21_2(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1501,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_800]),
[final] ).
cnf(i_0_1502,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_814]),
[final] ).
cnf(i_0_1503,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_815]),
[final] ).
cnf(i_0_1504,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_816]),
[final] ).
cnf(i_0_1505,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_817]),
[final] ).
cnf(i_0_1506,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_818]),
[final] ).
cnf(i_0_1507,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_1508,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_814]),
[final] ).
cnf(i_0_1509,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_815]),
[final] ).
cnf(i_0_1510,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_819]),
[final] ).
cnf(i_0_1511,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_820]),
[final] ).
cnf(i_0_1512,plain,
( hBOOL(hAPP(hAPP(X1,esk58_3(X2,X1,X3)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_821]),
[final] ).
cnf(i_0_1513,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_822]),
[final] ).
cnf(i_0_1514,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_823]),
[final] ).
cnf(i_0_1515,plain,
( hBOOL(hAPP(hAPP(X3,esk57_2(X4,X3)),X4))
| ~ c_Predicate_ORangeP(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1516,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_825]),
[final] ).
cnf(i_0_1517,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_826]),
[final] ).
cnf(i_0_1518,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_827]),
[final] ).
cnf(i_0_1519,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_827]),
[final] ).
cnf(i_0_1520,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_828]),
[final] ).
cnf(i_0_1521,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_829]),
[final] ).
cnf(i_0_1522,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_820]),
[final] ).
cnf(i_0_1523,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk58_3(X3,X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_821]),
[final] ).
cnf(i_0_1524,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_830]),
[final] ).
cnf(i_0_1525,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_813]),
[final] ).
cnf(i_0_1526,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_830]),
[final] ).
cnf(i_0_1527,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_830]),
[final] ).
cnf(i_0_1528,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_831]),
[final] ).
cnf(i_0_1529,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_832]),
[final] ).
cnf(i_0_1530,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_832]),
[final] ).
cnf(i_0_1531,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_833]),
[final] ).
cnf(i_0_1532,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_834]),
[final] ).
cnf(i_0_1533,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_835]),
[final] ).
cnf(i_0_1534,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_836]),
[final] ).
cnf(i_0_1535,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_831]),
[final] ).
cnf(i_0_1536,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_837]),
[final] ).
cnf(i_0_1537,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_838,c_0_839]),
[final] ).
cnf(i_0_1538,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_840]),
[final] ).
cnf(i_0_1539,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_841]),
[final] ).
cnf(i_0_1540,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_842]),
[final] ).
cnf(i_0_1541,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_831]),
[final] ).
cnf(i_0_1542,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_843]),
[final] ).
cnf(i_0_1543,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_844]),
[final] ).
cnf(i_0_1544,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_845]),
[final] ).
cnf(i_0_1545,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_846]),
[final] ).
cnf(i_0_1546,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_847]),
[final] ).
cnf(i_0_1547,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_848]),
[final] ).
cnf(i_0_1548,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_849]),
[final] ).
cnf(i_0_1549,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_833]),
[final] ).
cnf(i_0_1550,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_850]),
[final] ).
cnf(i_0_1551,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_851]),
[final] ).
cnf(i_0_1552,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_852]),
[final] ).
cnf(i_0_1553,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_853]),
[final] ).
cnf(i_0_1554,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_854]),
[final] ).
cnf(i_0_1555,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_855]),
[final] ).
cnf(i_0_1556,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_856]),
[final] ).
cnf(i_0_1557,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_1558,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_858]),
[final] ).
cnf(i_0_1559,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_859]),
[final] ).
cnf(i_0_1560,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_860]),
[final] ).
cnf(i_0_1561,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_833]),
[final] ).
cnf(i_0_1562,plain,
( c_Predicate_ODomainP(X4,X5,X1,X2)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1563,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1564,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1565,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_863]),
[final] ).
cnf(i_0_1566,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_864]),
[final] ).
cnf(i_0_1567,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_865]),
[final] ).
cnf(i_0_1568,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_866]),
[final] ).
cnf(i_0_1569,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_867]),
[final] ).
cnf(i_0_1570,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_868]),
[final] ).
cnf(i_0_1571,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_833]),
[final] ).
cnf(i_0_1572,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_869]),
[final] ).
cnf(i_0_1573,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_870]),
[final] ).
cnf(i_0_1574,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_1575,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_872]),
[final] ).
cnf(i_0_1576,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_873]),
[final] ).
cnf(i_0_1577,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_874]),
[final] ).
cnf(i_0_1578,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_820]),
[final] ).
cnf(i_0_1579,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_821]),
[final] ).
cnf(i_0_1580,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_875]),
[final] ).
cnf(i_0_1581,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_876]),
[final] ).
cnf(i_0_1582,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_877]),
[final] ).
cnf(i_0_1583,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_878]),
[final] ).
cnf(i_0_1584,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_879]),
[final] ).
cnf(i_0_1585,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_880]),
[final] ).
cnf(i_0_1586,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_881]),
[final] ).
cnf(i_0_1587,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_882]),
[final] ).
cnf(i_0_1588,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_883]),
[final] ).
cnf(i_0_1589,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_884]),
[final] ).
cnf(i_0_1590,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_885]),
[final] ).
cnf(i_0_1591,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_886]),
[final] ).
cnf(i_0_1592,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_887]),
[final] ).
cnf(i_0_1593,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_1594,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_888]),
[final] ).
cnf(i_0_1595,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_1596,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_888]),
[final] ).
cnf(i_0_1597,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_889]),
[final] ).
cnf(i_0_1598,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_890]),
[final] ).
cnf(i_0_1599,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_891]),
[final] ).
cnf(i_0_1600,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_892]),
[final] ).
cnf(i_0_1601,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_893]),
[final] ).
cnf(i_0_1602,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_894]),
[final] ).
cnf(i_0_1603,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_893]),
[final] ).
cnf(i_0_1604,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_894]),
[final] ).
cnf(i_0_1605,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_895]),
[final] ).
cnf(i_0_1606,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_896]),
[final] ).
cnf(i_0_1607,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_897]),
[final] ).
cnf(i_0_1608,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_898]),
[final] ).
cnf(i_0_1609,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_899]),
[final] ).
cnf(i_0_1610,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_899]),
[final] ).
cnf(i_0_1611,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_638]),
[final] ).
cnf(i_0_1612,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_900]),
[final] ).
cnf(i_0_1613,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_670]),
[final] ).
cnf(i_0_1614,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_901]),
[final] ).
cnf(i_0_1615,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_638]),
[final] ).
cnf(i_0_1616,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_671]),
[final] ).
cnf(i_0_1617,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_899]),
[final] ).
cnf(i_0_1618,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_902]),
[final] ).
cnf(i_0_1619,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_903]),
[final] ).
cnf(i_0_1620,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_891]),
[final] ).
cnf(i_0_1621,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_904]),
[final] ).
cnf(i_0_1622,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_905]),
[final] ).
cnf(i_0_1623,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_906]),
[final] ).
cnf(i_0_1624,plain,
c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
inference(split_conjunct,[status(thm)],[i_0_907]),
[final] ).
cnf(i_0_1625,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_908]),
[final] ).
cnf(i_0_1626,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_909]),
[final] ).
cnf(i_0_1627,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_910]),
[final] ).
cnf(i_0_1628,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_911]),
[final] ).
cnf(i_0_1629,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_912]),
[final] ).
cnf(i_0_1630,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_913]),
[final] ).
cnf(i_0_1631,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_914]),
[final] ).
cnf(i_0_1632,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1633,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_916]),
[final] ).
cnf(i_0_1634,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_917]),
[final] ).
cnf(i_0_1635,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_701]),
[final] ).
cnf(i_0_1636,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_906]),
[final] ).
cnf(i_0_1637,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_918]),
[final] ).
cnf(i_0_1638,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_919]),
[final] ).
cnf(i_0_1639,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_920]),
[final] ).
cnf(i_0_1640,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_921]),
[final] ).
cnf(i_0_1641,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_922]),
[final] ).
cnf(i_0_1642,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_923]),
[final] ).
cnf(i_0_1643,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_924]),
[final] ).
cnf(i_0_1644,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_925]),
[final] ).
cnf(i_0_1645,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_926]),
[final] ).
cnf(i_0_1646,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_927]),
[final] ).
cnf(i_0_1647,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_928]),
[final] ).
cnf(i_0_1648,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_692]),
[final] ).
cnf(i_0_1649,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_693]),
[final] ).
cnf(i_0_1650,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_929]),
[final] ).
cnf(i_0_1651,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_930]),
[final] ).
cnf(i_0_1652,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_931]),
[final] ).
cnf(i_0_1653,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_899]),
[final] ).
cnf(i_0_1654,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_932]),
[final] ).
cnf(i_0_1655,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_800]),
[final] ).
cnf(i_0_1656,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_813]),
[final] ).
cnf(i_0_1657,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_891]),
[final] ).
cnf(i_0_1658,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_933]),
[final] ).
cnf(i_0_1659,plain,
( hBOOL(hAPP(X1,esk101_2(X2,X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1660,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_935]),
[final] ).
cnf(i_0_1661,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_936]),
[final] ).
cnf(i_0_1662,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_937]),
[final] ).
cnf(i_0_1663,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_938]),
[final] ).
cnf(i_0_1664,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_939]),
[final] ).
cnf(i_0_1665,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_940]),
[final] ).
cnf(i_0_1666,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_941]),
[final] ).
cnf(i_0_1667,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_942]),
[final] ).
cnf(i_0_1668,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_936]),
[final] ).
cnf(i_0_1669,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_937]),
[final] ).
cnf(i_0_1670,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_943]),
[final] ).
cnf(i_0_1671,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_944]),
[final] ).
cnf(i_0_1672,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1673,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_670]),
[final] ).
cnf(i_0_1674,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_671]),
[final] ).
cnf(i_0_1675,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_946]),
[final] ).
cnf(i_0_1676,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_864]),
[final] ).
cnf(i_0_1677,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_947]),
[final] ).
cnf(i_0_1678,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_948]),
[final] ).
cnf(i_0_1679,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_949]),
[final] ).
cnf(i_0_1680,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_950]),
[final] ).
cnf(i_0_1681,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_951]),
[final] ).
cnf(i_0_1682,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_952]),
[final] ).
cnf(i_0_1683,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_953]),
[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_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1685,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_955]),
[final] ).
cnf(i_0_1686,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_956]),
[final] ).
cnf(i_0_1687,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_1688,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_1689,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_959]),
[final] ).
cnf(i_0_1690,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_960]),
[final] ).
cnf(i_0_1691,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_935]),
[final] ).
cnf(i_0_1692,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_961]),
[final] ).
cnf(i_0_1693,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_962]),
[final] ).
cnf(i_0_1694,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_963]),
[final] ).
cnf(i_0_1695,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_964]),
[final] ).
cnf(i_0_1696,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_965]),
[final] ).
cnf(i_0_1697,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_965]),
[final] ).
cnf(i_0_1698,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_966]),
[final] ).
cnf(i_0_1699,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_967]),
[final] ).
cnf(i_0_1700,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1701,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_968]),
[final] ).
cnf(i_0_1702,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
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_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1704,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_970]),
[final] ).
cnf(i_0_1705,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_971]),
[final] ).
cnf(i_0_1706,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_972]),
[final] ).
cnf(i_0_1707,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_973]),
[final] ).
cnf(i_0_1708,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_974]),
[final] ).
cnf(i_0_1709,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_975]),
[final] ).
cnf(i_0_1710,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_947]),
[final] ).
cnf(i_0_1711,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_976]),
[final] ).
cnf(i_0_1712,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_977]),
[final] ).
cnf(i_0_1713,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_977]),
[final] ).
cnf(i_0_1714,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_978]),
[final] ).
cnf(i_0_1715,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_979]),
[final] ).
cnf(i_0_1716,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_969]),
[final] ).
cnf(i_0_1717,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_970]),
[final] ).
cnf(i_0_1718,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_935]),
[final] ).
cnf(i_0_1719,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_980]),
[final] ).
cnf(i_0_1720,plain,
( c_List_Odistinct(X1,c_List_OdropWhile(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1721,plain,
( c_List_Odistinct(X1,c_List_OtakeWhile(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1722,plain,
( c_List_Odistinct(X1,c_List_Oinsert(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1723,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk19_2(X2,X1)) != hAPP(esk19_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_1724,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_943]),
[final] ).
cnf(i_0_1725,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_1726,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_985]),
[final] ).
cnf(i_0_1727,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_986]),
[final] ).
cnf(i_0_1728,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_987]),
[final] ).
cnf(i_0_1729,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_1730,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_988]),
[final] ).
cnf(i_0_1731,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_989]),
[final] ).
cnf(i_0_1732,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_990]),
[final] ).
cnf(i_0_1733,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_1734,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1735,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1736,plain,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1737,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_944]),
[final] ).
cnf(i_0_1738,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1739,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1740,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_995]),
[final] ).
cnf(i_0_1741,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_990]),
[final] ).
cnf(i_0_1742,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_996]),
[final] ).
cnf(i_0_1743,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1744,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1745,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1746,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_975]),
[final] ).
cnf(i_0_1747,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_1000]),
[final] ).
cnf(i_0_1748,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_953]),
[final] ).
cnf(i_0_1749,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_1750,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_1751,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_1003]),
[final] ).
cnf(i_0_1752,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_1004]),
[final] ).
cnf(i_0_1753,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_1005]),
[final] ).
cnf(i_0_1754,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_956]),
[final] ).
cnf(i_0_1755,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_1006]),
[final] ).
cnf(i_0_1756,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_1007]),
[final] ).
cnf(i_0_1757,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_1758,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_1008]),
[final] ).
cnf(i_0_1759,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_1009]),
[final] ).
cnf(i_0_1760,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_1010]),
[final] ).
cnf(i_0_1761,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_1011]),
[final] ).
cnf(i_0_1762,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_1012]),
[final] ).
cnf(i_0_1763,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_1013]),
[final] ).
cnf(i_0_1764,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1765,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1766,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1767,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1768,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1769,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1770,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1771,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1772,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_1773,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_1019]),
[final] ).
cnf(i_0_1774,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_1019]),
[final] ).
cnf(i_0_1775,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_1020]),
[final] ).
cnf(i_0_1776,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_1020]),
[final] ).
cnf(i_0_1777,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1778,plain,
( hBOOL(hAPP(c_List_Olistsp(X2,X3),X1))
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1779,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1022]),
[final] ).
cnf(i_0_1780,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1781,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1782,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1783,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1784,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1785,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[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_1029]),
[final] ).
cnf(i_0_1787,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_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_1031]),
[final] ).
cnf(i_0_1789,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1790,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1791,plain,
c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1792,plain,
c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1793,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1794,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[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_913]),
[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_913]),
[final] ).
cnf(i_0_1797,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_936]),
[final] ).
cnf(i_0_1798,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1799,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1800,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1801,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1802,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool),X2,X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1803,plain,
( c_List_Odistinct(X1,X2)
| ~ c_List_Odistinct(X1,c_List_Orotate1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1804,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1805,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_1019]),
[final] ).
cnf(i_0_1806,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_1020]),
[final] ).
cnf(i_0_1807,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_1044]),
[final] ).
cnf(i_0_1808,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_1045]),
[final] ).
cnf(i_0_1809,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1810,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_1047]),
[final] ).
cnf(i_0_1811,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_1048]),
[final] ).
cnf(i_0_1812,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1813,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_951]),
[final] ).
cnf(i_0_1814,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1815,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_970]),
[final] ).
cnf(i_0_1816,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1817,plain,
c_List_OdropWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1818,plain,
c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1819,plain,
( c_List_Odistinct(X1,c_List_Orotate1(X1,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1820,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1053]),
[final] ).
cnf(i_0_1821,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(X1,X2,X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1822,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1823,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1824,plain,
( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1825,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1826,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1827,plain,
c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1828,plain,
c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1829,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1830,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1831,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_1059]),
[final] ).
cnf(i_0_1832,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1060]),
[final] ).
cnf(i_0_1833,plain,
c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1061]),
[final] ).
cnf(i_0_1834,plain,
c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1062]),
[final] ).
cnf(i_0_1835,plain,
c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1063]),
[final] ).
cnf(i_0_1836,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1064]),
[final] ).
cnf(i_0_1837,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1065]),
[final] ).
cnf(i_0_1838,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1066]),
[final] ).
cnf(i_0_1839,plain,
( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1067]),
[final] ).
cnf(i_0_1840,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1068]),
[final] ).
cnf(i_0_1841,plain,
( X2 = c_List_Olist_ONil(X1)
| c_List_Orotate1(X1,X2) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1069]),
[final] ).
cnf(i_0_1842,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1070]),
[final] ).
cnf(i_0_1843,plain,
( c_List_Orotate1(X2,X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1069]),
[final] ).
cnf(i_0_1844,plain,
c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1071]),
[final] ).
cnf(i_0_1845,plain,
c_List_Orotate1(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1846,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1072]),
[final] ).
cnf(i_0_1847,plain,
c_List_Odistinct(X1,c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_1073]),
[final] ).
cnf(i_0_1848,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1849,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1850,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1851,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1852,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1853,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1854,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1855,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1856,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1857,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
[final] ).
cnf(i_0_1858,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
[final] ).
cnf(i_0_1859,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1860,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1861,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1862,axiom,
X1 = X1 ).
cnf(i_0_1863,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1864,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1865,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1866,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1867,axiom,
( X1 != X2
| c_List_Orotate1(X1,X3) = c_List_Orotate1(X2,X3) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| c_List_Orotate1(X3,X1) = c_List_Orotate1(X3,X2) ) ).
cnf(i_0_1869,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_1870,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_1871,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_1872,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_1873,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_1874,axiom,
( X1 != X2
| esk79_3(X1,X3,X4) = esk79_3(X2,X3,X4) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| esk79_3(X3,X1,X4) = esk79_3(X3,X2,X4) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| esk79_3(X3,X4,X1) = esk79_3(X3,X4,X2) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| esk78_3(X1,X3,X4) = esk78_3(X2,X3,X4) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| esk78_3(X3,X1,X4) = esk78_3(X3,X2,X4) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| esk78_3(X3,X4,X1) = esk78_3(X3,X4,X2) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| esk51_3(X1,X3,X4) = esk51_3(X2,X3,X4) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| esk51_3(X3,X1,X4) = esk51_3(X3,X2,X4) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| esk51_3(X3,X4,X1) = esk51_3(X3,X4,X2) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| esk50_3(X1,X3,X4) = esk50_3(X2,X3,X4) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| esk50_3(X3,X1,X4) = esk50_3(X3,X2,X4) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| esk50_3(X3,X4,X1) = esk50_3(X3,X4,X2) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X1,X3,X4,X5) = c_FuncSet_Oextensional__funcset(X2,X3,X4,X5) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X1,X4,X5) = c_FuncSet_Oextensional__funcset(X3,X2,X4,X5) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X1,X5) = c_FuncSet_Oextensional__funcset(X3,X4,X2,X5) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| c_FuncSet_Oextensional__funcset(X3,X4,X5,X1) = c_FuncSet_Oextensional__funcset(X3,X4,X5,X2) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| c_HOL_Oundefined(X1) = c_HOL_Oundefined(X2) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).
cnf(i_0_1904,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_1905,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_1906,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_1907,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_1908,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_1909,axiom,
( X1 != X2
| c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| c_List_OdropWhile(X1,X3,X4) = c_List_OdropWhile(X2,X3,X4) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| c_List_OdropWhile(X3,X1,X4) = c_List_OdropWhile(X3,X2,X4) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| c_List_OdropWhile(X3,X4,X1) = c_List_OdropWhile(X3,X4,X2) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X1,X3,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X1,X4) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X1) = c_Lattices_Osemilattice__inf__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| c_Relation_ORange(X1,X3,X4) = c_Relation_ORange(X2,X3,X4) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| c_Relation_ORange(X3,X1,X4) = c_Relation_ORange(X3,X2,X4) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| c_Relation_ORange(X3,X4,X1) = c_Relation_ORange(X3,X4,X2) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X1,X3,X4,X5) = c_FuncSet_Orestrict(X2,X3,X4,X5) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X1,X4,X5) = c_FuncSet_Orestrict(X3,X2,X4,X5) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X1,X5) = c_FuncSet_Orestrict(X3,X4,X2,X5) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| c_FuncSet_Orestrict(X3,X4,X5,X1) = c_FuncSet_Orestrict(X3,X4,X5,X2) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).
cnf(i_0_1941,axiom,
( X1 != X2
| c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).
cnf(i_0_1942,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| esk28_4(X1,X3,X4,X5) = esk28_4(X2,X3,X4,X5) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| esk28_4(X3,X1,X4,X5) = esk28_4(X3,X2,X4,X5) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| esk28_4(X3,X4,X1,X5) = esk28_4(X3,X4,X2,X5) ) ).
cnf(i_0_1947,axiom,
( X1 != X2
| esk28_4(X3,X4,X5,X1) = esk28_4(X3,X4,X5,X2) ) ).
cnf(i_0_1948,axiom,
( X1 != X2
| esk27_4(X1,X3,X4,X5) = esk27_4(X2,X3,X4,X5) ) ).
cnf(i_0_1949,axiom,
( X1 != X2
| esk27_4(X3,X1,X4,X5) = esk27_4(X3,X2,X4,X5) ) ).
cnf(i_0_1950,axiom,
( X1 != X2
| esk27_4(X3,X4,X1,X5) = esk27_4(X3,X4,X2,X5) ) ).
cnf(i_0_1951,axiom,
( X1 != X2
| esk27_4(X3,X4,X5,X1) = esk27_4(X3,X4,X5,X2) ) ).
cnf(i_0_1952,axiom,
( X1 != X2
| c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).
cnf(i_0_1953,axiom,
( X1 != X2
| c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).
cnf(i_0_1954,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_1955,axiom,
( X1 != X2
| esk16_2(X1,X3) = esk16_2(X2,X3) ) ).
cnf(i_0_1956,axiom,
( X1 != X2
| esk16_2(X3,X1) = esk16_2(X3,X2) ) ).
cnf(i_0_1957,axiom,
( X1 != X2
| esk17_2(X1,X3) = esk17_2(X2,X3) ) ).
cnf(i_0_1958,axiom,
( X1 != X2
| esk17_2(X3,X1) = esk17_2(X3,X2) ) ).
cnf(i_0_1959,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1960,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1961,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1962,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1963,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1964,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1965,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_1966,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_1967,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_1968,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_1969,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_1970,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_1971,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1972,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X1,X3)
| c_Relation_Otrans(X2,X3) ) ).
cnf(i_0_1973,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X3,X1)
| c_Relation_Otrans(X3,X2) ) ).
cnf(i_0_1974,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_1975,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_1976,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_1977,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1978,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1979,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1980,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1981,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1982,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1983,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1984,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1985,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1986,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1987,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1988,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_1989,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_1990,axiom,
( X1 != X2
| ~ c_List_Odistinct(X1,X3)
| c_List_Odistinct(X2,X3) ) ).
cnf(i_0_1991,axiom,
( X1 != X2
| ~ c_List_Odistinct(X3,X1)
| c_List_Odistinct(X3,X2) ) ).
cnf(i_0_1992,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_1993,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_1994,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X1,X3,X4,X5)
| c_Recdef_Oadm__wf(X2,X3,X4,X5) ) ).
cnf(i_0_1995,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X1,X4,X5)
| c_Recdef_Oadm__wf(X3,X2,X4,X5) ) ).
cnf(i_0_1996,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X1,X5)
| c_Recdef_Oadm__wf(X3,X4,X2,X5) ) ).
cnf(i_0_1997,axiom,
( X1 != X2
| ~ c_Recdef_Oadm__wf(X3,X4,X5,X1)
| c_Recdef_Oadm__wf(X3,X4,X5,X2) ) ).
cnf(i_0_1998,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1999,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2000,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2001,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_2002,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_2003,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_2004,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X1,X3,X4,X5)
| c_List_Olistrelp(X2,X3,X4,X5) ) ).
cnf(i_0_2005,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X1,X4,X5)
| c_List_Olistrelp(X3,X2,X4,X5) ) ).
cnf(i_0_2006,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X1,X5)
| c_List_Olistrelp(X3,X4,X2,X5) ) ).
cnf(i_0_2007,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X5,X1)
| c_List_Olistrelp(X3,X4,X5,X2) ) ).
cnf(i_0_2008,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X1,X3,X4,X5)
| c_Predicate_ODomainP(X2,X3,X4,X5) ) ).
cnf(i_0_2009,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X1,X4,X5)
| c_Predicate_ODomainP(X3,X2,X4,X5) ) ).
cnf(i_0_2010,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X1,X5)
| c_Predicate_ODomainP(X3,X4,X2,X5) ) ).
cnf(i_0_2011,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X5,X1)
| c_Predicate_ODomainP(X3,X4,X5,X2) ) ).
cnf(i_0_2012,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X1,X3,X4,X5)
| c_Predicate_ORangeP(X2,X3,X4,X5) ) ).
cnf(i_0_2013,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X1,X4,X5)
| c_Predicate_ORangeP(X3,X2,X4,X5) ) ).
cnf(i_0_2014,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X1,X5)
| c_Predicate_ORangeP(X3,X4,X2,X5) ) ).
cnf(i_0_2015,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X5,X1)
| c_Predicate_ORangeP(X3,X4,X5,X2) ) ).
cnf(i_0_2016,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_2017,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_2018,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_2019,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_2021,plain,
X1 = X1,
inference(equality_inference,[],[1108]) ).
cnf(i_0_2022,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,[],[1136]) ).
cnf(i_0_2068,plain,
X1 = X1,
inference(equality_inference,[],[1460]) ).
cnf(i_0_2073,plain,
X1 = X1,
inference(equality_inference,[],[1529]) ).
cnf(i_0_2074,plain,
X1 = X1,
inference(equality_inference,[],[1530]) ).
cnf(i_0_2076,plain,
X1 = X1,
inference(equality_inference,[],[1602]) ).
cnf(i_0_2077,plain,
X1 = X1,
inference(equality_inference,[],[1604]) ).
cnf(i_0_2081,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(equality_inference,[],[1655]) ).
cnf(i_0_2082,plain,
X1 = X1,
inference(equality_inference,[],[1696]) ).
cnf(i_0_2083,plain,
X1 = X1,
inference(equality_inference,[],[1697]) ).
cnf(i_0_2084,plain,
X1 = X1,
inference(equality_inference,[],[1698]) ).
cnf(i_0_2085,plain,
X1 = X1,
inference(equality_inference,[],[1699]) ).
cnf(i_0_2086,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1700]) ).
cnf(i_0_2087,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,[],[1724]) ).
cnf(i_0_2088,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,[],[1726]) ).
cnf(i_0_2090,plain,
X1 = X1,
inference(equality_inference,[],[1738]) ).
cnf(i_0_2091,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1739]) ).
cnf(i_0_2092,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
inference(equality_inference,[],[1741]) ).
cnf(i_0_2098,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(equality_inference,[],[1778]) ).
cnf(i_0_2099,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1786]) ).
cnf(i_0_2100,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1787]) ).
cnf(i_0_2101,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1798]) ).
cnf(i_0_2102,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1799]) ).
cnf(i_0_2103,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1801]) ).
cnf(i_0_2104,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[1809]) ).
cnf(i_0_2108,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(equality_inference,[],[1823]) ).
cnf(i_0_2109,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(equality_inference,[],[1824]) ).
cnf(i_0_2110,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[1825]) ).
cnf(i_0_2111,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
inference(equality_inference,[],[1826]) ).
cnf(i_0_2112,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1830]) ).
cnf(i_0_2113,plain,
c_List_Orotate1(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[1843]) ).
cnf(i_0_2240,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2249,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1804]) ).
cnf(i_0_2254,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1804]) ).
cnf(i_0_2290,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2300,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_1645]) ).
cnf(i_0_2303,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rename_variables,[],[i_0_1622]) ).
cnf(i_0_2342,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1784]) ).
cnf(i_0_2346,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(rename_variables,[],[i_0_1785]) ).
cnf(i_0_2347,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(rename_variables,[],[i_0_1829]) ).
cnf(i_0_2360,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(rename_variables,[],[i_0_1829]) ).
cnf(i_0_2366,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2377,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1784]) ).
cnf(i_0_2384,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2391,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2397,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2414,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2481,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2484,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_1645]) ).
cnf(i_0_2745,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2753,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1789]) ).
cnf(i_0_2765,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2794,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_1645]) ).
cnf(c_0_1850,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
i_0_1790 ).
cnf(c_0_1851,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
i_0_1513 ).
cnf(c_0_1852,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_1850,c_0_1851]) ).
cnf(c_0_1853,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_1852,c_0_1851]) ).
cnf(c_0_1854,plain,
hAPP(c_COMBI(X1),X2) = X2,
i_0_1846 ).
cnf(c_0_1855,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_1853,c_0_1854]) ).
cnf(c_0_1856,plain,
$false,
inference(er,[status(thm)],[c_0_1855]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT143+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:58:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 252.30/180.89 % Version : CSE_E---1.7
% 252.30/180.89 % Problem : theBenchmark.p
% 252.30/180.89 % SZS status Theorem for theBenchmark.p
% 252.30/180.89 % SZS output start CNFRefutation
% See solution above
% 292.62/221.15 % Total time : 179.225s
%------------------------------------------------------------------------------