%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT141+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 05:06:05 PM UTC 2026
% Result : Theorem 108.13s 96.37s
% Output : CNFRefutation 166.33s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_599)
% Comments :
%------------------------------------------------------------------------------
fof(fact_mem__splitE,axiom,
! [X75,X5,X33,X14,X9,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X33,tc_fun(X6,tc_HOL_Obool)),X5),X75)))
=> ~ ! [X3,X62] :
( X75 = hAPP(hAPP(c_Product__Type_OPair(X14,X33),X3),X62)
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(X5,X3),X62))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitE) ).
fof(fact_converse__rtranclE2,axiom,
! [X17,X83,X84,X85,X61,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),X61),X85)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X83))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X61),X85) != hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X83)
=> ~ ! [X19,X20] :
( 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),X61),X85)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X20))),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),X19),X20)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X83))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [X48,X12,X16,X6] : c_List_Opartition(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = 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,X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(fact_internal__split__def,axiom,
! [X33,X14,X6] : c_Product__Type_Ointernal__split(X6,X14,X33) = c_Product__Type_Oprod_Oprod__case(X6,X14,X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(fact_mem__splitI2,axiom,
! [X5,X9,X33,X14,X6,X75] :
( ! [X19,X20] :
( X75 = hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X20)
=> hBOOL(hAPP(hAPP(c_member(X33),X9),hAPP(hAPP(X5,X19),X20))) )
=> hBOOL(hAPP(hAPP(c_member(X33),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_fun(X33,tc_HOL_Obool)),X5),X75))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI2) ).
fof(fact_Cons__listrel1E2,axiom,
! [X17,X49,X11,X48,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)),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),c_List_Olistrel1(X6,X17)))
=> ( ! [X3] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X49)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X11)),X17)) )
=> ~ ! [X72] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X72)
=> ~ 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)),X72),X49)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1E2) ).
fof(fact_lexord__append__leftD,axiom,
! [X17,X60,X50,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),X50)),hAPP(hAPP(c_List_Oappend(X6),X12),X60))),c_List_Olexord(X6,X17)))
=> ( ! [X19] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X19)),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)),X50),X60)),c_List_Olexord(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_Cons__listrel1E1,axiom,
! [X17,X49,X48,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),X48)),X49)),c_List_Olistrel1(X6,X17)))
=> ( ! [X62] :
( X49 = hAPP(hAPP(c_List_Olist_OCons(X6),X62),X48)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X62)),X17)) )
=> ~ ! [X72] :
( X49 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X72)
=> ~ 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)),X48),X72)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1E1) ).
fof(fact_listrel__Cons2,axiom,
! [X17,X49,X11,X48,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)),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),c_List_Olistrel(X6,X17)))
=> ~ ! [X3,X64] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X64)
=> ( 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)),X64),X49)),c_List_Olistrel(X6,X17))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
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/sandbox/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_listrel__Cons1,axiom,
! [X17,X48,X49,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),X49)),X48)),c_List_Olistrel(X6,X17)))
=> ~ ! [X62,X63] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X62),X63)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X62)),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)),X49),X63)),c_List_Olistrel(X6,X17))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
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_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/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_split__twice,axiom,
! [X75,X1,X87,X88,X2,X6,X33,X14] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X33,X6),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X88,X87,tc_prod(X14,X33)),X1),X75)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X88,X87,X6),hAPP(hAPP(c_COMBB(tc_fun(X87,tc_prod(X14,X33)),tc_fun(X87,X6),X88),hAPP(c_COMBB(tc_prod(X14,X33),X6,X87),hAPP(c_Product__Type_Oprod_Oprod__case(X14,X33,X6),X2))),X1)),X75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__twice) ).
fof(fact_RangeE,axiom,
! [X17,X14,X23,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X23),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),X23)),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
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/sandbox/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_override__on__def,axiom,
! [X1,X2,X14,X8,X24,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X24) = hAPP(X1,X24) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X24) = hAPP(X2,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__def) ).
fof(fact_override__on__apply__notin,axiom,
! [X1,X2,X14,X8,X24,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X24) = hAPP(X2,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).
fof(fact_DomainE,axiom,
! [X17,X14,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),c_Relation_ODomain(X6,X14,X17)))
=> ~ ! [X62] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X62)),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
fof(fact_inf2E,axiom,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
fof(fact_pair__imageI,axiom,
! [X2,X33,X8,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),X8))
=> hBOOL(hAPP(hAPP(c_member(X33),hAPP(hAPP(X2,X24),X23)),c_Set_Oimage(tc_prod(X6,X14),X33,hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X33),X2),X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__imageI) ).
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/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X23,X24,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),X24),X23)),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),X23),X24)),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_splitD_H,axiom,
! [X5,X23,X24,X13,X33,X14,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_fun(X33,tc_HOL_Obool)),X13),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),X5))
=> hBOOL(hAPP(hAPP(hAPP(X13,X24),X23),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD_H) ).
fof(fact_SigmaE2,axiom,
! [X7,X8,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),c_Product__Type_OSigma(X6,X14,X8,X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X14),X23),hAPP(X7,X24))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
fof(fact_not__acc__down,axiom,
! [X13,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X13)))
=> ~ ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X66),X12)),X13))
=> hBOOL(hAPP(hAPP(c_member(X6),X66),c_Wellfounded_Oacc(X6,X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(fact_split__eta,axiom,
! [X2,X33,X14,X6] : hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X33),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_prod(X6,X14)),tc_fun(X14,X33),X6),hAPP(c_COMBB(tc_prod(X6,X14),X33,X14),X2)),c_Product__Type_OPair(X6,X14))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__eta) ).
fof(fact_not__Nil__listrel1,axiom,
! [X17,X48,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)),X48)),c_List_Olistrel1(X6,X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_Nil__notin__lex,axiom,
! [X17,X49,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)),X49)),c_List_Olex(X6,X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_not__listrel1__Nil,axiom,
! [X17,X48,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)),X48),c_List_Olist_ONil(X6))),c_List_Olistrel1(X6,X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_Nil2__notin__lex,axiom,
! [X17,X48,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)),X48),c_List_Olist_ONil(X6))),c_List_Olex(X6,X17))),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_swap__product,axiom,
! [X7,X8,X6,X14] : c_Set_Oimage(tc_prod(X14,X6),tc_prod(X6,X14),hAPP(c_Product__Type_Oprod_Oprod__case(X14,X6,tc_prod(X6,X14)),hAPP(c_COMBC(X6,X14,tc_prod(X6,X14)),c_Product__Type_OPair(X6,X14))),c_Product__Type_OSigma(X14,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X14,X7))) = c_Product__Type_OSigma(X6,X14,X7,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__product) ).
fof(fact_mem__splitI,axiom,
! [X33,X14,X23,X24,X5,X9,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(X5,X24),X23)))
=> hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X33,tc_fun(X6,tc_HOL_Obool)),X5),hAPP(hAPP(c_Product__Type_OPair(X14,X33),X24),X23)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI) ).
fof(fact_nth__length__takeWhile,axiom,
! [X48,X16,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X48)),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> ~ hBOOL(hAPP(X16,c_List_Onth(X6,X48,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X48))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).
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/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
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/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_splitD,axiom,
! [X23,X24,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),X24),X23)))
=> hBOOL(hAPP(hAPP(X2,X24),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD) ).
fof(fact_IntE,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
fof(fact_prod__caseI,axiom,
! [X14,X6,X23,X24,X32] :
( hBOOL(hAPP(hAPP(X32,X24),X23))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_HOL_Obool),X32),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__caseI) ).
fof(fact_splitI,axiom,
! [X14,X6,X23,X24,X2] :
( hBOOL(hAPP(hAPP(X2,X24),X23))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitI) ).
fof(fact_inf1E,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
fof(fact_dropWhile__eq__Cons__conv,axiom,
! [X49,X11,X48,X16,X6] :
( c_List_OdropWhile(X6,X16,X48) = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49)
<=> ( X48 = hAPP(hAPP(c_List_Oappend(X6),c_List_OtakeWhile(X6,X16,X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))
& ~ hBOOL(hAPP(X16,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
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,
~ ! [X29] : ~ 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),X29),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
file('/export/starexec/sandbox/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_split__curry,axiom,
! [X2,X33,X14,X6] : hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X33),c_Product__Type_Ocurry(X6,X14,X33,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__curry) ).
fof(fact_curry__split,axiom,
! [X2,X33,X14,X6] : c_Product__Type_Ocurry(X6,X14,X33,hAPP(c_Product__Type_Oprod_Oprod__case(X6,X14,X33),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__split) ).
fof(fact_split__conv,axiom,
! [X23,X24,X2,X6,X33,X14] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X33,X6),X2),hAPP(hAPP(c_Product__Type_OPair(X14,X33),X24),X23)) = hAPP(hAPP(X2,X24),X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__conv) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [X23,X24,X32,X6,X33,X14] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X33,X6),X32),hAPP(hAPP(c_Product__Type_OPair(X14,X33),X24),X23)) = hAPP(hAPP(X32,X24),X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_takeWhile__tail,axiom,
! [X86,X48,X6,X12,X16] :
( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Oappend(X6),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X86))) = c_List_OtakeWhile(X6,X16,X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__tail) ).
fof(fact_takeWhile_Osimps_I2_J,axiom,
! [X48,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_OtakeWhile(X6,X16,X48)) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = c_List_Olist_ONil(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
fof(fact_le__infE,axiom,
! [X27,X28,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X40,X28)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X40,X27) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_dropWhile_Osimps_I2_J,axiom,
! [X48,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = c_List_OdropWhile(X6,X16,X48) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X28,X27,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X27,X28)
=> ~ c_Orderings_Oord__class_Oless(X6,X28,X27) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_leD,axiom,
! [X40,X46,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> ~ c_Orderings_Oord__class_Oless(X6,X40,X46) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
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/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
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/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_order__less__asym,axiom,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ~ c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X27,X28,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X28,X27)
=> ~ c_Orderings_Oord__class_Oless(X6,X27,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ~ c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ~ c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(help_c__fconj__2,axiom,
! [X97,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X97))
| hBOOL(X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [X97,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X97))
| hBOOL(X97) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_linorder__cases,axiom,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ( X40 != X46
=> c_Orderings_Oord__class_Oless(X6,X46,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( X40 != X46
=> ( ~ c_Orderings_Oord__class_Oless(X6,X40,X46)
=> c_Orderings_Oord__class_Oless(X6,X46,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
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/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X40,X46,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> c_Orderings_Oord__class_Oless(X6,X40,X46) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X40,X46)
=> c_Orderings_Oord__class_Oless__eq(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> c_Orderings_Oord__class_Oless__eq(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_linorder__neqE__nat,axiom,
! [X46,X40] :
( X40 != X46
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X46)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X40,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X40,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(help_c__fconj__1,axiom,
! [X97,X16] :
( ~ hBOOL(X16)
| ~ hBOOL(X97)
| hBOOL(hAPP(hAPP(c_fconj,X16),X97)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(fact_less__irrefl__nat,axiom,
! [X103] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X103,X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X103] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X103,X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
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/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(help_c__fNot__1,axiom,
! [X16] :
( ~ hBOOL(hAPP(c_fNot,X16))
| ~ hBOOL(X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [X16] :
( ~ ~ hBOOL(X16)
| hBOOL(hAPP(c_fNot,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_rtrancl__induct2,axiom,
! [X16,X17,X77,X78,X79,X80,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),X80),X79)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X78),X77))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hBOOL(hAPP(hAPP(X16,X80),X79))
=> ( ! [X19,X20] :
( 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),X80),X79)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X20))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ! [X81,X82] :
( 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),X20)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X81),X82))),X17))
=> ( hBOOL(hAPP(hAPP(X16,X19),X20))
=> hBOOL(hAPP(hAPP(X16,X81),X82)) ) ) )
=> hBOOL(hAPP(hAPP(X16,X78),X77)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
fof(fact_converse__rtrancl__induct2,axiom,
! [X16,X17,X77,X78,X79,X80,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),X80),X79)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X78),X77))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hBOOL(hAPP(hAPP(X16,X78),X77))
=> ( ! [X19,X20,X81,X82] :
( 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),X20)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X81),X82))),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),X81),X82)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X78),X77))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hBOOL(hAPP(hAPP(X16,X81),X82))
=> hBOOL(hAPP(hAPP(X16,X19),X20)) ) ) )
=> hBOOL(hAPP(hAPP(X16,X80),X79)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
fof(fact_inf__Int__eq2,axiom,
! [X11,X12,X31,X13,X14,X6] :
( hBOOL(hAPP(hAPP(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)))),X31)),X12),X11))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X12),X11)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X14),tc_HOL_Obool)),X13),X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
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/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
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/sandbox/benchmark/theBenchmark.p',fact_ab) ).
fof(fact_pred__subset__eq2,axiom,
! [X31,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)))),X31))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X13,X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact__C2_C,axiom,
! [X30,X16,X21,X22,X23,X24] :
( X24 != X23
=> ( X22 != X21
=> ( X24 != X21
=> ( X23 != X22
=> ( 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))),X30),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),X24),X23)),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),X22),X21)),hAPP(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),X24),X23)),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),X22),X21)),hAPP(v_F,X30))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__C1_C,axiom,
! [X30,X16,X21,X22,X23,X24] :
( X24 != X23
=> ( X22 != X21
=> ( X24 != X21
=> ( X23 != X22
=> ( 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))),X30),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),X24),X23)),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),X22),X21)),hAPP(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),X24),X23)),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),X22),X21)),hAPP(v_F,X30))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_listrelp__listrel__eq,axiom,
! [X61,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,X61)
<=> 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),X61)),c_List_Olistrel(X6,X17))) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X31,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)))),X31)
<=> X13 = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_funcset__compose,axiom,
! [X90,X1,X33,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,X33)),X1),c_FuncSet_OPi(X14,X33,X7,c_COMBK(tc_fun(X33,tc_HOL_Obool),X14,X90))))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X33)),c_FuncSet_Ocompose(X6,X14,X33,X8,X1,X2)),c_FuncSet_OPi(X6,X33,X8,c_COMBK(tc_fun(X33,tc_HOL_Obool),X6,X90)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__compose) ).
fof(fact_Pi__cong,axiom,
! [X7,X14,X1,X2,X8,X6] :
( ! [X94] :
( hBOOL(hAPP(hAPP(c_member(X6),X94),X8))
=> hAPP(X2,X94) = hAPP(X1,X94) )
=> ( 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/sandbox/benchmark/theBenchmark.p',fact_Pi__cong) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_compose__assoc,axiom,
! [X95,X96,X88,X90,X1,X33,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,X33)),X1),c_FuncSet_OPi(X14,X33,X7,c_COMBK(tc_fun(X33,tc_HOL_Obool),X14,X90))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33,X88)),X96),c_FuncSet_OPi(X33,X88,X90,c_COMBK(tc_fun(X88,tc_HOL_Obool),X33,X95))))
=> c_FuncSet_Ocompose(X6,X33,X88,X8,X96,c_FuncSet_Ocompose(X6,X14,X33,X8,X1,X2)) = c_FuncSet_Ocompose(X6,X14,X88,X8,c_FuncSet_Ocompose(X14,X33,X88,X7,X96,X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__assoc) ).
fof(fact_listrel__iff__nth,axiom,
! [X17,X49,X48,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)),X48),X49)),c_List_Olistrel(X6,X17)))
<=> ( c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X49)
& ! [X110] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X110,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),c_List_Onth(X6,X48,X110)),c_List_Onth(X6,X49,X110))),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).
fof(fact_IIA__def,axiom,
! [X35] :
( c_Arrow__Order__Mirabelle_OIIA(X35)
<=> ! [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))
=> ! [X36] :
( 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))),X36),c_Arrow__Order__Mirabelle_OProf))
=> ! [X19,X20] :
( ! [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),X20)),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),X19),X20)),hAPP(X36,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),X20)),hAPP(X35,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),X19),X20)),hAPP(X35,X36))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
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/sandbox/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(fact_lexord__linear,axiom,
! [X11,X12,X17,X6] :
( ! [X19,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X20)),X17))
| X19 = X20
| hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X20),X19)),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/sandbox/benchmark/theBenchmark.p',fact_lexord__linear) ).
fof(fact_SigmaE,axiom,
! [X7,X8,X5,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),X5),c_Product__Type_OSigma(X6,X14,X8,X7)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> ! [X62] :
( hBOOL(hAPP(hAPP(c_member(X14),X62),hAPP(X7,X3)))
=> X5 != hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X62) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
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/sandbox/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).
fof(fact_lists__IntI,axiom,
! [X7,X8,X86,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X86),c_List_Olists(X6,X8)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X86),c_List_Olists(X6,X7)))
=> hBOOL(hAPP(c_List_Olistsp(X6,hAPP(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)),X8)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X7))),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__IntI) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [X17,X11,X49,X12,X48,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),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_Olist_ONil(X6)))),hAPP(hAPP(c_List_Oappend(X6),X49),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)),X48),X49)),c_List_Olistrel1(X6,X17)))
& X12 = X11 )
| ( X48 = X49
& hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_Pi__mono,axiom,
! [X90,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(X90,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,X90)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_in__lex__prod,axiom,
! [X42,X17,X21,X22,X23,X24,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),X24),X23)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X22),X21))),c_Wellfounded_Olex__prod(X6,X14,X17,X42)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X22)),X17))
| ( X24 = X22
& hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X14)),hAPP(hAPP(c_Product__Type_OPair(X14,X14),X23),X21)),X42)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact_dictatorI,axiom,
! [X41,X35] :
( 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))),X35),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))
=> ! [X19,X20] :
( X19 != X20
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X20)),hAPP(X3,X41)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X20)),hAPP(X35,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X35,X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_listrel1E,axiom,
! [X17,X49,X48,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)),X48),X49)),c_List_Olistrel1(X6,X17)))
=> ~ ! [X3,X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X62)),X17))
=> ! [X56,X65] :
( X48 = hAPP(hAPP(c_List_Oappend(X6),X56),hAPP(hAPP(c_List_Olist_OCons(X6),X3),X65))
=> X49 != hAPP(hAPP(c_List_Oappend(X6),X56),hAPP(hAPP(c_List_Olist_OCons(X6),X62),X65)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1E) ).
fof(fact_inf__Int__eq,axiom,
! [X12,X31,X13,X6] :
( hBOOL(hAPP(hAPP(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)),X31)),X12))
<=> hBOOL(hAPP(hAPP(c_member(X6),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X13),X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_surj__compose,axiom,
! [X90,X1,X33,X7,X8,X2,X6,X14] :
( c_Set_Oimage(X14,X6,X2,X8) = X7
=> ( c_Set_Oimage(X6,X33,X1,X7) = X90
=> c_Set_Oimage(X14,X33,c_FuncSet_Ocompose(X14,X6,X33,X8,X1,X2),X8) = X90 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__compose) ).
fof(fact_compose__eq,axiom,
! [X2,X1,X14,X33,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> hAPP(c_FuncSet_Ocompose(X6,X33,X14,X8,X1,X2),X12) = hAPP(X1,hAPP(X2,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__eq) ).
fof(fact_lexord__append__left__rightI,axiom,
! [X11,X12,X50,X17,X23,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),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),X50),hAPP(hAPP(c_List_Olist_OCons(X6),X24),X12))),hAPP(hAPP(c_List_Oappend(X6),X50),hAPP(hAPP(c_List_Olist_OCons(X6),X23),X11)))),c_List_Olexord(X6,X17))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [X7,X8,X113,X14,X6] : c_Product__Type_OSigma(X6,X14,X113,hAPP(hAPP(c_COMBS(X6,tc_fun(X14,tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X14,tc_HOL_Obool),tc_fun(tc_fun(X14,tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X6),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14,tc_HOL_Obool))),X8)),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X14),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X14,X113,X8)),c_Product__Type_OSigma(X6,X14,X113,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_append__eq__append__conv2,axiom,
! [X55,X54,X49,X48,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X48),X49) = hAPP(hAPP(c_List_Oappend(X6),X54),X55)
<=> ? [X56] :
( ( X48 = hAPP(hAPP(c_List_Oappend(X6),X54),X56)
& hAPP(hAPP(c_List_Oappend(X6),X56),X49) = X55 )
| ( hAPP(hAPP(c_List_Oappend(X6),X48),X56) = X54
& X49 = hAPP(hAPP(c_List_Oappend(X6),X56),X55) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_Range__iff,axiom,
! [X17,X14,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),c_Relation_ORange(X14,X6,X17)))
<=> ? [X62] : hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X6)),hAPP(hAPP(c_Product__Type_OPair(X14,X6),X62),X24)),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [X17,X49,X11,X48,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),X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),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))
& X48 = X49 )
| ( 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)),X48),X49)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_Cons__in__lex,axiom,
! [X17,X49,X11,X48,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),X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),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),X48) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X49) )
| ( 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)),X48),X49)),c_List_Olex(X6,X17))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_lexord__cons__cons,axiom,
! [X17,X11,X23,X12,X24,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),X24),X12)),hAPP(hAPP(c_List_Olist_OCons(X6),X23),X11))),c_List_Olexord(X6,X17)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),X17))
| ( X24 = X23
& 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/sandbox/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [X49,X48,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)),X48),X49)),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),X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_listrel_OCons,axiom,
! [X49,X48,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)),X48),X49)),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),X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),c_List_Olistrel(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_OCons) ).
fof(fact_unanimity__def,axiom,
! [X35] :
( c_Arrow__Order__Mirabelle_Ounanimity(X35)
<=> ! [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))
=> ! [X19,X20] :
( ! [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),X20)),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),X19),X20)),hAPP(X35,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_lists__Int__eq,axiom,
! [X7,X8,X6] : c_List_Olistsp(X6,hAPP(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)),X8)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X7))) = hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_lists__Int__eq) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [X54,X17,X49,X48,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)),X48),X49)),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)),X49),X54)),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)),X48),X54)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_refl__on__def,axiom,
! [X17,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X17)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X6),X3),X8))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X3)),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [X12,X17,X49,X48,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)),X48),X49)),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),X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X49))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_lexord__trans) ).
fof(fact_append__listrel1I,axiom,
! [X57,X58,X17,X49,X48,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)),X48),X49)),c_List_Olistrel1(X6,X17)))
& X58 = X57 )
| ( X48 = X49
& 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)),X58),X57)),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),X48),X58)),hAPP(hAPP(c_List_Oappend(X6),X49),X57))),c_List_Olistrel1(X6,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__listrel1I) ).
fof(fact_lexord__append__leftI,axiom,
! [X12,X17,X60,X50,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)),X50),X60)),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),X50)),hAPP(hAPP(c_List_Oappend(X6),X12),X60))),c_List_Olexord(X6,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_listrel1I2,axiom,
! [X12,X17,X49,X48,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)),X48),X49)),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),X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X49))),c_List_Olistrel1(X6,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I2) ).
fof(fact_in__below,axiom,
! [X11,X12,X10,X23,X24] :
( X24 != X23
=> ( 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),X24),X23)))
<=> ( X12 != X11
& ( X11 = X24
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X23)),X10)) )
& ( X11 != X24
=> ( ( X12 = X24
=> ( X11 = X23
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X11)),X10)) ) )
& ( X12 != X24
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X11)),X10)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_in__above,axiom,
! [X11,X12,X10,X23,X24] :
( X24 != X23
=> ( 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,X24,X23)))
<=> ( X12 != X11
& ( X12 = X23
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X11)),X10)) )
& ( X12 != X23
=> ( ( X11 = X23
=> ( X12 = X24
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X24)),X10)) ) )
& ( X11 != X23
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_override__on__apply__in,axiom,
! [X1,X2,X14,X8,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X24) = hAPP(X1,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
fof(fact_listrel1I1,axiom,
! [X48,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),X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X48))),c_List_Olistrel1(X6,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I1) ).
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/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Domain__iff,axiom,
! [X17,X14,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),c_Relation_ODomain(X6,X14,X17)))
<=> ? [X62] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X62)),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
fof(fact_Cons__eq__append__conv,axiom,
! [X54,X49,X48,X12,X6] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48) = hAPP(hAPP(c_List_Oappend(X6),X49),X54)
<=> ( ( X49 = c_List_Olist_ONil(X6)
& hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48) = X54 )
| ? [X59] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X12),X59) = X49
& X48 = hAPP(hAPP(c_List_Oappend(X6),X59),X54) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append__eq__Cons__conv,axiom,
! [X48,X12,X54,X49,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X49),X54) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)
<=> ( ( X49 = c_List_Olist_ONil(X6)
& X54 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48) )
| ? [X59] :
( X49 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X59)
& hAPP(hAPP(c_List_Oappend(X6),X59),X54) = X48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_rotate1__def,axiom,
! [X48,X6] : c_List_Orotate1(X6,X48) = 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))),X48),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).
fof(fact_in__measures_I2_J,axiom,
! [X101,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),X101))))
<=> ( 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,X101))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_rtrancl__trans,axiom,
! [X5,X17,X23,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X23),X5)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X5)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_inf2D1,axiom,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
fof(fact_inf2D2,axiom,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [X5,X17,X23,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X23),X5)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X5)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [X5,X17,X23,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X23),X5)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X5)),c_Transitive__Closure_Ortrancl(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [X17,X49,X48,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)),X48),X49)),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)),X48),X49)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_listrel__reflcl__if__listrel1,axiom,
! [X17,X49,X48,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)),X48),X49)),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)),X48),X49)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14,tc_HOL_Obool)),X8),X7)),hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_image__Int__subset) ).
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/sandbox/benchmark/theBenchmark.p',fact_lexord__lex) ).
fof(fact_trans__def,axiom,
! [X17,X6] :
( c_Relation_Otrans(X6,X17)
<=> ! [X3,X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X62)),X17))
=> ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X62),X66)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X66)),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__def) ).
fof(fact_transD,axiom,
! [X5,X23,X24,X17,X6] :
( c_Relation_Otrans(X6,X17)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),X17))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X23),X5)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X5)),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transD) ).
fof(fact_measures__lesseq,axiom,
! [X101,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,X101)))
=> 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),X101)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__lesseq) ).
fof(fact_length__takeWhile__less__P__nth,axiom,
! [X48,X6,X16,X111] :
( ! [X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X111)
=> hBOOL(hAPP(X16,c_List_Onth(X6,X48,X4))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X111,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X111,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X48))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
fof(fact_listrel1I,axiom,
! [X49,X57,X58,X48,X17,X11,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X11)),X17))
=> ( X48 = hAPP(hAPP(c_List_Oappend(X6),X58),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X57))
=> ( X49 = hAPP(hAPP(c_List_Oappend(X6),X58),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X57))
=> 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)),X48),X49)),c_List_Olistrel1(X6,X17))) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_single__valuedI,axiom,
! [X17,X14,X6] :
( ! [X3,X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X62)),X17))
=> ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X66)),X17))
=> X62 = X66 ) )
=> c_Relation_Osingle__valued(X6,X14,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedI) ).
fof(fact_single__valued__def,axiom,
! [X17,X14,X6] :
( c_Relation_Osingle__valued(X6,X14,X17)
<=> ! [X3,X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X62)),X17))
=> ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X3),X66)),X17))
=> X62 = X66 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(fact_curryE,axiom,
! [X23,X24,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X6,X14,tc_HOL_Obool,X2),X24),X23))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
fof(fact_curryD,axiom,
! [X23,X24,X2,X14,X6] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X6,X14,tc_HOL_Obool,X2),X24),X23))
=> hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
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/sandbox/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))
<=> ? [X99] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),X99,X8)
& X7 = c_Set_Oimage(X14,X6,X2,X99) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_Times__Int__distrib1,axiom,
! [X90,X7,X8,X14,X6] : c_Product__Type_OSigma(X6,X14,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X90)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X14),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X14,X8,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X90))),c_Product__Type_OSigma(X6,X14,X7,c_COMBK(tc_fun(X14,tc_HOL_Obool),X6,X90))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_mem__Sigma__iff,axiom,
! [X7,X8,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),c_Product__Type_OSigma(X6,X14,X8,X7)))
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
& hBOOL(hAPP(hAPP(c_member(X14),X23),hAPP(X7,X24))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
fof(fact_SigmaD2,axiom,
! [X7,X8,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),c_Product__Type_OSigma(X6,X14,X8,X7)))
=> hBOOL(hAPP(hAPP(c_member(X14),X23),hAPP(X7,X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
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/sandbox/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_SigmaD1,axiom,
! [X7,X8,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),c_Product__Type_OSigma(X6,X14,X8,X7)))
=> hBOOL(hAPP(hAPP(c_member(X6),X24),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
fof(fact_trancl__subset__Sigma__aux,axiom,
! [X8,X17,X23,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))
=> ( X24 = X23
| hBOOL(hAPP(hAPP(c_member(X6),X24),X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
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)))
<=> ? [X19,X3] : X11 = hAPP(hAPP(c_List_Olist_OCons(X6),X19),X3) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
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(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_fun(X14,tc_HOL_Obool))),X8),X7),X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
fof(fact_Times__subset__cancel2,axiom,
! [X7,X8,X14,X90,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X90))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X14,X6),tc_HOL_Obool),c_Product__Type_OSigma(X14,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X14,X90)),c_Product__Type_OSigma(X14,X6,X7,c_COMBK(tc_fun(X6,tc_HOL_Obool),X14,X90)))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),X8,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
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/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_lexn__length,axiom,
! [X71,X17,X49,X48,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)),X48),X49)),c_List_Olexn(X6,X17,X71)))
=> ( c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48) = X71
& c_Nat_Osize__class_Osize(tc_List_Olist(X6),X49) = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn__length) ).
fof(fact_acc_OaccI,axiom,
! [X17,X12,X6] :
( ! [X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X62),X12)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X62),c_Wellfounded_Oacc(X6,X17))) )
=> hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(fact_acc_Osimps,axiom,
! [X17,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),c_Wellfounded_Oacc(X6,X17)))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X24)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X3),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_listrel__Nil1,axiom,
! [X17,X48,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)),X48)),c_List_Olistrel(X6,X17)))
=> X48 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_listrel__Nil2,axiom,
! [X17,X48,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)),X48),c_List_Olist_ONil(X6))),c_List_Olistrel(X6,X17)))
=> X48 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_listrel__subset,axiom,
! [X8,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8)))
=> 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_Product__Type_OSigma(tc_List_Olist(X6),tc_List_Olist(X6),c_List_Olists(X6,X8),c_COMBK(tc_fun(tc_List_Olist(X6),tc_HOL_Obool),tc_List_Olist(X6),c_List_Olists(X6,X8)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset) ).
fof(fact_listrel1__eq__len,axiom,
! [X17,X49,X48,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)),X48),X49)),c_List_Olistrel1(X6,X17)))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_listrel__eq__len,axiom,
! [X17,X49,X48,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)),X48),X49)),c_List_Olistrel(X6,X17)))
=> c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_split__paired__All,axiom,
! [X14,X6,X16] :
( ! [X18] : hBOOL(hAPP(X16,X18))
<=> ! [X19,X20] : hBOOL(hAPP(X16,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(fact_curryI,axiom,
! [X23,X24,X14,X6,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X6,X14,tc_HOL_Obool,X2),X24),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
fof(fact_transI,axiom,
! [X17,X6] :
( ! [X3,X62] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X62)),X17))
=> ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X62),X66)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X66)),X17)) ) )
=> c_Relation_Otrans(X6,X17) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_lexord__append__rightI,axiom,
! [X17,X12,X6,X11] :
( ? [X20,X66] : X11 = hAPP(hAPP(c_List_Olist_OCons(X6),X20),X66)
=> 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/sandbox/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X14,X6),tc_HOL_Obool)),X8),X7)),hAPP(hAPP(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/sandbox/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,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X14),tc_HOL_Obool)),X8),X7)),hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
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/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_SigmaI,axiom,
! [X7,X23,X14,X8,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> ( hBOOL(hAPP(hAPP(c_member(X14),X23),hAPP(X7,X24)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),c_Product__Type_OSigma(X6,X14,X8,X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
fof(fact_pred__subset__eq,axiom,
! [X31,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)),X31))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X13,X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_measures__less,axiom,
! [X101,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),X101)))) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [X90,X114,X113,X14,X6] : c_Product__Type_OSigma(X6,X14,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X113),X114),X90) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X14),tc_HOL_Obool)),c_Product__Type_OSigma(X6,X14,X113,X90)),c_Product__Type_OSigma(X6,X14,X114,X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
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/sandbox/benchmark/theBenchmark.p',fact_iff) ).
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/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_acc__downwards__aux,axiom,
! [X17,X24,X23,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X23),X24)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(X6),X24),c_Wellfounded_Oacc(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(X6),X23),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_acc__downwards,axiom,
! [X23,X17,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),c_Wellfounded_Oacc(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X23),X24)),c_Transitive__Closure_Ortrancl(X6,X17)))
=> hBOOL(hAPP(hAPP(c_member(X6),X23),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
fof(fact_dictator__def,axiom,
! [X41,X35] :
( c_Arrow__Order__Mirabelle_Odictator(X35,X41)
<=> ! [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(X35,X3) = hAPP(X3,X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_acc__downward,axiom,
! [X24,X17,X23,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X23),c_Wellfounded_Oacc(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X24),c_Wellfounded_Oacc(X6,X17))) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_DomainI,axiom,
! [X17,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),X17))
=> hBOOL(hAPP(hAPP(c_member(X6),X24),c_Relation_ODomain(X6,X14,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
fof(fact_RangeI,axiom,
! [X17,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),X17))
=> hBOOL(hAPP(hAPP(c_member(X14),X23),c_Relation_ORange(X6,X14,X17))) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [X17,X48,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)),X48),X48)),c_List_Olistrel(X6,c_Transitive__Closure_Ortrancl(X6,X17)))),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_takeWhile__not__last,axiom,
! [X6,X48] :
( X48 != c_List_Olist_ONil(X6)
=> ( c_List_Odistinct(X6,X48)
=> 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,X48))),X48) = c_List_Obutlast(X6,X48) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [X48,X17,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X17)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X48),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),X48)),c_Wellfounded_Oacc(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_image__image,axiom,
! [X8,X1,X33,X2,X6,X14] : c_Set_Oimage(X14,X6,X2,c_Set_Oimage(X33,X14,X1,X8)) = c_Set_Oimage(X33,X6,hAPP(hAPP(c_COMBB(X14,X6,X33),X2),X1),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_listsp__infI,axiom,
! [X7,X86,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),X86))
=> ( hBOOL(hAPP(c_List_Olistsp(X6,X7),X86))
=> hBOOL(hAPP(c_List_Olistsp(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)),X86)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__infI) ).
fof(fact_Times__eq__cancel2,axiom,
! [X7,X8,X14,X90,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X90))
=> ( c_Product__Type_OSigma(X14,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X14,X90)) = c_Product__Type_OSigma(X14,X6,X7,c_COMBK(tc_fun(X6,tc_HOL_Obool),X14,X90))
<=> X8 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
fof(fact_prod_Orecs,axiom,
! [X23,X24,X32,X6,X33,X14] : c_Product__Type_Oprod_Oprod__rec(X14,X33,X6,X32,hAPP(hAPP(c_Product__Type_OPair(X14,X33),X24),X23)) = hAPP(hAPP(X32,X24),X23),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_list_Osimps_I5_J,axiom,
! [X38,X24,X47,X32,X14,X6] : c_List_Olist_Olist__case(X6,X14,X32,X47,hAPP(hAPP(c_List_Olist_OCons(X14),X24),X38)) = hAPP(hAPP(X47,X24),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_dropWhile__nth,axiom,
! [X48,X16,X6,X111] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X111,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OdropWhile(X6,X16,X48)))
=> c_List_Onth(X6,c_List_OdropWhile(X6,X16,X48),X111) = c_List_Onth(X6,X48,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X111,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X48)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__nth) ).
fof(fact_image__eqI,axiom,
! [X6,X8,X14,X12,X2,X23] :
( X23 = hAPP(X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X14),X12),X8))
=> hBOOL(hAPP(hAPP(c_member(X6),X23),c_Set_Oimage(X14,X6,X2,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X14,X2,X23,X8,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
=> ( X23 = hAPP(X2,X12)
=> hBOOL(hAPP(hAPP(c_member(X14),X23),c_Set_Oimage(X6,X14,X2,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_append__in__lists__conv,axiom,
! [X8,X49,X48,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),hAPP(hAPP(c_List_Oappend(X6),X48),X49)),c_List_Olists(X6,X8)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X48),c_List_Olists(X6,X8)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X49),c_List_Olists(X6,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_Id__on__eqI,axiom,
! [X8,X6,X23,X24] :
( X24 = X23
=> ( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X23)),c_Relation_OId__on(X6,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Pi__anti__mono,axiom,
! [X7,X14,X8,X98,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X98,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,X98,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_curry__conv,axiom,
! [X23,X24,X2,X6,X33,X14] : hAPP(hAPP(c_Product__Type_Ocurry(X14,X33,X6,X2),X24),X23) = hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X14,X33),X24),X23)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
fof(fact_curry__def,axiom,
! [X11,X12,X5,X6,X33,X14] : hAPP(hAPP(c_Product__Type_Ocurry(X14,X33,X6,X5),X12),X11) = hAPP(X5,hAPP(hAPP(c_Product__Type_OPair(X14,X33),X12),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).
fof(fact_list_Osimps_I4_J,axiom,
! [X47,X32,X14,X6] : c_List_Olist_Olist__case(X6,X14,X32,X47,c_List_Olist_ONil(X14)) = X32,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_Cons__in__lists__iff,axiom,
! [X8,X48,X12,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)),c_List_Olists(X6,X8)))
<=> ( hBOOL(hAPP(hAPP(c_member(X6),X12),X8))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X48),c_List_Olists(X6,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_IntD1,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
fof(fact_Int__iff,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD2,axiom,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
fof(fact_Int__assoc,axiom,
! [X90,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)),X90) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
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/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
fof(fact_pred__equals__eq,axiom,
! [X31,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)),X31)
<=> X13 = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [X17,X24,X6] : hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X24),X24)),c_Transitive__Closure_Ortrancl(X6,X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_third__alt,axiom,
! [X27,X28] :
( X28 != X27
=> ? [X29] : c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X28),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X27),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X29),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_third__alt) ).
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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
fof(fact_inf1D1,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> hBOOL(hAPP(X8,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(fact_inf1D2,axiom,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12))
=> hBOOL(hAPP(X7,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [X67,X68,X69,X70,X17,X6] :
( c_List_Olistrelp(X6,X17,hAPP(hAPP(c_List_Olist_OCons(X6),X70),X69),hAPP(hAPP(c_List_Olist_OCons(X6),X68),X67))
<=> ( hBOOL(hAPP(hAPP(X17,X70),X68))
& c_List_Olistrelp(X6,X17,X69,X67) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_listrelp_OCons,axiom,
! [X49,X48,X6,X11,X12,X17] :
( hBOOL(hAPP(hAPP(X17,X12),X11))
=> ( c_List_Olistrelp(X6,X17,X48,X49)
=> c_List_Olistrelp(X6,X17,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_lists_Osimps,axiom,
! [X8,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X24),c_List_Olists(X6,X8)))
<=> ( X24 = c_List_Olist_ONil(X6)
| ? [X19,X76] :
( X24 = hAPP(hAPP(c_List_Olist_OCons(X6),X19),X76)
& hBOOL(hAPP(hAPP(c_member(X6),X19),X8))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X76),c_List_Olists(X6,X8))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_Osimps) ).
fof(fact_Id__on__subset__Times,axiom,
! [X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),c_Relation_OId__on(X6,X8),c_Product__Type_OSigma(X6,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X6,X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).
fof(fact_complete__Lin,axiom,
! [X23,X24] :
( X24 != X23
=> ? [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),X24),X23)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(fact_maps__simps_I1_J,axiom,
! [X48,X12,X2,X6,X14] : c_List_Omaps(X14,X6,X2,hAPP(hAPP(c_List_Olist_OCons(X14),X12),X48)) = hAPP(hAPP(c_List_Oappend(X6),hAPP(X2,X12)),c_List_Omaps(X14,X6,X2,X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).
fof(fact_Int__mono,axiom,
! [X95,X7,X90,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X90)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X7,X95)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X90),X95)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
fof(fact_r__into__rtrancl,axiom,
! [X17,X75,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X75),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),X75),c_Transitive__Closure_Ortrancl(X6,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_Int__left__commute,axiom,
! [X90,X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X90)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X90)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
fof(fact_lists__accI,axiom,
! [X17,X48,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X48),c_Wellfounded_Oacc(tc_List_Olist(X6),c_List_Olistrel1(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X48),c_List_Olists(X6,c_Wellfounded_Oacc(X6,X17)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accI) ).
fof(fact_lists__accD,axiom,
! [X17,X48,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X48),c_List_Olists(X6,c_Wellfounded_Oacc(X6,X17))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X6)),X48),c_Wellfounded_Oacc(tc_List_Olist(X6),c_List_Olistrel1(X6,X17)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accD) ).
fof(fact_trans__Int,axiom,
! [X42,X17,X6] :
( c_Relation_Otrans(X6,X17)
=> ( c_Relation_Otrans(X6,X42)
=> c_Relation_Otrans(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X6,X6),tc_HOL_Obool)),X17),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Int) ).
fof(fact_inf1I,axiom,
! [X6,X7,X12,X8] :
( hBOOL(hAPP(X8,X12))
=> ( hBOOL(hAPP(X7,X12))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
fof(fact_takeWhile__nth,axiom,
! [X48,X16,X6,X111] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X111,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X48)))
=> c_List_Onth(X6,c_List_OtakeWhile(X6,X16,X48),X111) = c_List_Onth(X6,X48,X111) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__nth) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [X45,X46,X39,X40,X6] : c_List_Osplice(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39),hAPP(hAPP(c_List_Olist_OCons(X6),X46),X45)) = hAPP(hAPP(c_List_Olist_OCons(X6),X40),hAPP(hAPP(c_List_Olist_OCons(X6),X46),c_List_Osplice(X6,X39,X45))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_Int__greatest,axiom,
! [X7,X8,X90,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X90,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X90,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X90,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
fof(fact_accp_Oequations,axiom,
! [X24,X17,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X24))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X17,X3),X24))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp_Osimps,axiom,
! [X24,X17,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X24))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X17,X3),X24))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(help_c__COMBS__1,axiom,
! [X13,X97,X16,X6,X33,X14] : hAPP(hAPP(hAPP(c_COMBS(X14,X33,X6),X16),X97),X13) = hAPP(hAPP(X16,X13),hAPP(X97,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_trans__lex__prod,axiom,
! [X73,X14,X74,X6] :
( c_Relation_Otrans(X6,X74)
=> ( c_Relation_Otrans(X14,X73)
=> c_Relation_Otrans(tc_prod(X6,X14),c_Wellfounded_Olex__prod(X6,X14,X74,X73)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
fof(fact_RangeP_Oequations,axiom,
! [X68,X17,X14,X6] :
( c_Predicate_ORangeP(X6,X14,X17,X68)
<=> ? [X19] : hBOOL(hAPP(hAPP(X17,X19),X68)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(fact_list__eq__iff__nth__eq,axiom,
! [X6,X49,X48] :
( X48 = X49
<=> ( c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X49)
& ! [X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> c_List_Onth(X6,X48,X4) = c_List_Onth(X6,X49,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).
fof(fact_Int__left__absorb,axiom,
! [X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_listsp__inf__eq,axiom,
! [X7,X8,X6] : c_List_Olistsp(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7)) = hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).
fof(help_c__COMBC__1,axiom,
! [X13,X97,X16,X6,X33,X14] : hAPP(hAPP(hAPP(c_COMBC(X14,X33,X6),X16),X97),X13) = hAPP(hAPP(X16,X13),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBB__1,axiom,
! [X13,X97,X16,X33,X6,X14] : hAPP(hAPP(hAPP(c_COMBB(X14,X6,X33),X16),X97),X13) = hAPP(X16,hAPP(X97,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_append__in__listsp__conv,axiom,
! [X49,X48,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),hAPP(hAPP(c_List_Oappend(X6),X48),X49)))
<=> ( hBOOL(hAPP(c_List_Olistsp(X6,X8),X48))
& hBOOL(hAPP(c_List_Olistsp(X6,X8),X49)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).
fof(fact_listsp_Oequations_I2_J,axiom,
! [X68,X70,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),hAPP(hAPP(c_List_Olist_OCons(X6),X70),X68)))
<=> ( hBOOL(hAPP(X8,X70))
& hBOOL(hAPP(c_List_Olistsp(X6,X8),X68)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).
fof(fact_append1__eq__conv,axiom,
! [X11,X49,X12,X48,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_Olist_ONil(X6))) = hAPP(hAPP(c_List_Oappend(X6),X49),hAPP(hAPP(c_List_Olist_OCons(X6),X11),c_List_Olist_ONil(X6)))
<=> ( X48 = X49
& X12 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_listsp_Osimps,axiom,
! [X24,X8,X6] :
( hBOOL(hAPP(c_List_Olistsp(X6,X8),X24))
<=> ( X24 = c_List_Olist_ONil(X6)
| ? [X19,X76] :
( X24 = hAPP(hAPP(c_List_Olist_OCons(X6),X19),X76)
& hBOOL(hAPP(X8,X19))
& hBOOL(hAPP(c_List_Olistsp(X6,X8),X76)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_Osimps) ).
fof(fact_Domain__mono,axiom,
! [X42,X17,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X17,X42)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Relation_ODomain(X6,X14,X17),c_Relation_ODomain(X6,X14,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
fof(fact_distinct__conv__nth,axiom,
! [X48,X6] :
( c_List_Odistinct(X6,X48)
<=> ! [X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> ! [X112] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X112,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> ( X4 != X112
=> c_List_Onth(X6,X48,X4) != c_List_Onth(X6,X48,X112) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
fof(fact_nth__eq__iff__index__eq,axiom,
! [X111,X41,X48,X6] :
( c_List_Odistinct(X6,X48)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X111,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> ( c_List_Onth(X6,X48,X41) = c_List_Onth(X6,X48,X111)
<=> X41 = X111 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).
fof(fact_rtrancl__subset,axiom,
! [X31,X13,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X13,X31)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X31,c_Transitive__Closure_Ortrancl(X6,X13))
=> c_Transitive__Closure_Ortrancl(X6,X31) = c_Transitive__Closure_Ortrancl(X6,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_internal__split__conv,axiom,
! [X23,X24,X5,X6,X33,X14] : hAPP(hAPP(c_Product__Type_Ointernal__split(X14,X33,X6),X5),hAPP(hAPP(c_Product__Type_OPair(X14,X33),X24),X23)) = hAPP(hAPP(X5,X24),X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
fof(fact_inf__apply,axiom,
! [X12,X1,X2,X14,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14,X6)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(X2,X12)),hAPP(X1,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).
fof(fact_inf__fun__def,axiom,
! [X12,X1,X2,X14,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X14,X6)),X2),X1),X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(X2,X12)),hAPP(X1,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__fun__def) ).
fof(fact_inf__mono,axiom,
! [X100,X27,X92,X28,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X28,X92)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X27,X100)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X92),X100)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
fof(fact_listrel1__mono,axiom,
! [X42,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,X42)
=> 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,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel__mono,axiom,
! [X42,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,X42)
=> 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,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__mono) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [X42,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,c_Transitive__Closure_Ortrancl(X6,X42))
=> 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,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_inf_Oassoc,axiom,
! [X92,X27,X28,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27)),X92) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X27),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__assoc,axiom,
! [X91,X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46)),X91) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),X91)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [X91,X46,X40,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46)),X91) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),X91)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_append__assoc,axiom,
! [X52,X45,X39,X6] : hAPP(hAPP(c_List_Oappend(X6),hAPP(hAPP(c_List_Oappend(X6),X39),X45)),X52) = hAPP(hAPP(c_List_Oappend(X6),X39),hAPP(hAPP(c_List_Oappend(X6),X45),X52)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).
fof(fact_append__Cons,axiom,
! [X45,X39,X40,X6] : hAPP(hAPP(c_List_Oappend(X6),hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39)),X45) = hAPP(hAPP(c_List_Olist_OCons(X6),X40),hAPP(hAPP(c_List_Oappend(X6),X39),X45)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Cons) ).
fof(fact_predicate2D,axiom,
! [X11,X12,X97,X16,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X14,tc_HOL_Obool)),X16,X97)
=> ( hBOOL(hAPP(hAPP(X16,X12),X11))
=> hBOOL(hAPP(hAPP(X97,X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X97,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,X97)
=> hBOOL(hAPP(hAPP(X97,X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_nth__append__length,axiom,
! [X45,X40,X39,X6] : c_List_Onth(X6,hAPP(hAPP(c_List_Oappend(X6),X39),hAPP(hAPP(c_List_Olist_OCons(X6),X40),X45)),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X39)) = X40,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
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/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
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/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
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/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_rtrancl__mono,axiom,
! [X42,X17,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X17,X42)
=> 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,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_DomainP_Ointros,axiom,
! [X14,X6,X23,X24,X17] :
( hBOOL(hAPP(hAPP(X17,X24),X23))
=> c_Predicate_ODomainP(X6,X14,X17,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_RangeP_Ointros,axiom,
! [X14,X6,X23,X24,X17] :
( hBOOL(hAPP(hAPP(X17,X24),X23))
=> c_Predicate_ORangeP(X6,X14,X17,X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_takeWhile__dropWhile__id,axiom,
! [X48,X16,X6] : hAPP(hAPP(c_List_Oappend(X6),c_List_OtakeWhile(X6,X16,X48)),c_List_OdropWhile(X6,X16,X48)) = X48,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).
fof(fact_Int__lower1,axiom,
! [X7,X8,X6] : c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X8),
file('/export/starexec/sandbox/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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
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/sandbox/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_butlast__snoc,axiom,
! [X40,X39,X6] : c_List_Obutlast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),hAPP(hAPP(c_List_Olist_OCons(X6),X40),c_List_Olist_ONil(X6)))) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__snoc) ).
fof(fact_last__snoc,axiom,
! [X40,X39,X6] : c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),hAPP(hAPP(c_List_Olist_OCons(X6),X40),c_List_Olist_ONil(X6)))) = X40,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__snoc) ).
fof(fact_single__valued__subset,axiom,
! [X42,X17,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X14),tc_HOL_Obool),X17,X42)
=> ( c_Relation_Osingle__valued(X6,X14,X42)
=> c_Relation_Osingle__valued(X6,X14,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
fof(fact_length__dropWhile__le,axiom,
! [X48,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,X48)),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).
fof(fact_length__takeWhile__le,axiom,
! [X48,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,X48)),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_accp__downward,axiom,
! [X24,X23,X17,X6] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X23))
=> ( hBOOL(hAPP(hAPP(X17,X24),X23))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X6,X17),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
fof(fact_le__inf__iff,axiom,
! [X9,X11,X12,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,hAPP(hAPP(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/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
fof(fact_le__infI,axiom,
! [X27,X28,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X28)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X27)
=> c_Orderings_Oord__class_Oless__eq(X6,X40,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
fof(fact_inf__greatest,axiom,
! [X91,X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X91)
=> c_Orderings_Oord__class_Oless__eq(X6,X40,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),X91)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
fof(fact_acc__subset,axiom,
! [X73,X74,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X6,X6),tc_HOL_Obool),X74,X73)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Wellfounded_Oacc(X6,X73),c_Wellfounded_Oacc(X6,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
fof(fact_append__butlast__last__id,axiom,
! [X6,X39] :
( X39 != c_List_Olist_ONil(X6)
=> hAPP(hAPP(c_List_Oappend(X6),c_List_Obutlast(X6,X39)),hAPP(hAPP(c_List_Olist_OCons(X6),c_List_Olast(X6,X39)),c_List_Olist_ONil(X6))) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
fof(fact_accp__subset,axiom,
! [X73,X74,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_fun(X6,tc_HOL_Obool)),X74,X73)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),c_Wellfounded_Oaccp(X6,X73),c_Wellfounded_Oaccp(X6,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
fof(fact_psubset__trans,axiom,
! [X90,X7,X8,X6] :
( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X7,X90)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_subset__psubset__trans,axiom,
! [X90,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,X90)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X90,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,X90)
=> c_Orderings_Oord__class_Oless(tc_fun(X6,tc_HOL_Obool),X8,X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_subset__trans,axiom,
! [X90,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,X90)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X90) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_inf_Oleft__commute,axiom,
! [X92,X28,X27,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X92)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X27),X92)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__left__commute,axiom,
! [X91,X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),X91)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X91)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [X91,X46,X40,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),X91)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X91)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
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/sandbox/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_Pair__inject,axiom,
! [X25,X26,X27,X28,X14,X6] :
( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X28),X27) = hAPP(hAPP(c_Product__Type_OPair(X6,X14),X26),X25)
=> ~ ( X28 = X26
=> X27 != X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(fact_Pair__eq,axiom,
! [X21,X22,X23,X24,X14,X6] :
( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23) = hAPP(hAPP(c_Product__Type_OPair(X6,X14),X22),X21)
<=> ( X24 = X22
& X23 = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
fof(fact_impossible__Cons,axiom,
! [X40,X45,X39,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X6),X39),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X45))
=> X39 != hAPP(hAPP(c_List_Olist_OCons(X6),X40),X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_impossible__Cons) ).
fof(fact_Int__commute,axiom,
! [X7,X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
fof(fact_rotate__simps,axiom,
! [X39,X40,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),X40),X39)) = hAPP(hAPP(c_List_Oappend(X14),X39),hAPP(hAPP(c_List_Olist_OCons(X14),X40),c_List_Olist_ONil(X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__simps) ).
fof(fact_snoc__eq__iff__butlast,axiom,
! [X49,X12,X48,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_Olist_ONil(X6))) = X49
<=> ( X49 != c_List_Olist_ONil(X6)
& c_List_Obutlast(X6,X49) = X48
& c_List_Olast(X6,X49) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_append__eq__appendI,axiom,
! [X51,X45,X52,X53,X39,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X39),X53) = X52
=> ( X45 = hAPP(hAPP(c_List_Oappend(X6),X53),X51)
=> hAPP(hAPP(c_List_Oappend(X6),X39),X45) = hAPP(hAPP(c_List_Oappend(X6),X52),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
fof(fact_Cons__eq__appendI,axiom,
! [X52,X39,X45,X53,X40,X6] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X40),X53) = X45
=> ( X39 = hAPP(hAPP(c_List_Oappend(X6),X53),X52)
=> hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39) = hAPP(hAPP(c_List_Oappend(X6),X45),X52) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
fof(fact_Int__absorb2,axiom,
! [X7,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X8,X7)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) = X8 ),
file('/export/starexec/sandbox/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)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).
fof(fact_image__ident,axiom,
! [X93,X6] : c_Set_Oimage(X6,X6,c_COMBI(X6),X93) = X93,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_less__infI1,axiom,
! [X27,X40,X28,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X28,X40)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27),X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI1) ).
fof(fact_less__infI2,axiom,
! [X28,X40,X27,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X27,X40)
=> c_Orderings_Oord__class_Oless(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27),X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI2) ).
fof(fact_le__infI1,axiom,
! [X27,X40,X28,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X28,X40)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27),X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
fof(fact_le__infI2,axiom,
! [X28,X40,X27,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X27,X40)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27),X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
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/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
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/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_order__less__trans,axiom,
! [X91,X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ( c_Orderings_Oord__class_Oless(X6,X46,X91)
=> c_Orderings_Oord__class_Oless(X6,X40,X91) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X91,X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> ( c_Orderings_Oord__class_Oless(X6,X46,X91)
=> c_Orderings_Oord__class_Oless(X6,X40,X91) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X91,X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X91)
=> c_Orderings_Oord__class_Oless(X6,X40,X91) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X91,X40,X46,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X46,X40)
=> ( c_Orderings_Oord__class_Oless(X6,X91,X46)
=> c_Orderings_Oord__class_Oless(X6,X91,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X91,X40,X46,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> ( c_Orderings_Oord__class_Oless(X6,X91,X46)
=> c_Orderings_Oord__class_Oless(X6,X91,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X91,X40,X46,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X46,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X91,X46)
=> c_Orderings_Oord__class_Oless(X6,X91,X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X91,X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X91)
=> c_Orderings_Oord__class_Oless__eq(X6,X40,X91) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X91,X40,X46,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X91,X46)
=> c_Orderings_Oord__class_Oless__eq(X6,X91,X40) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_lists_ONil) ).
fof(fact_le__trans,axiom,
! [X107,X108,X109] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X109,X108)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X108,X107)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X109,X107) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
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/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_splice_Osimps_I2_J,axiom,
! [X43,X44,X6] : c_List_Osplice(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X44),X43),c_List_Olist_ONil(X6)) = hAPP(hAPP(c_List_Olist_OCons(X6),X44),X43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
fof(fact_inf_Oleft__idem,axiom,
! [X27,X28,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__left__idem,axiom,
! [X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [X46,X40,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
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/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
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/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_predicate1D,axiom,
! [X12,X97,X16,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X16,X97)
=> ( hBOOL(hAPP(X16,X12))
=> hBOOL(hAPP(X97,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X97,X6,X12,X16] :
( hBOOL(hAPP(X16,X12))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool),X16,X97)
=> hBOOL(hAPP(X97,X12)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_butlast__append,axiom,
! [X39,X6,X45] :
( ( X45 = c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),X45)) = c_List_Obutlast(X6,X39) )
& ( X45 != c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),X45)) = hAPP(hAPP(c_List_Oappend(X6),X39),c_List_Obutlast(X6,X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__append) ).
fof(fact_butlast_Osimps_I2_J,axiom,
! [X40,X6,X39] :
( ( X39 = c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39)) = c_List_Olist_ONil(X6) )
& ( X39 != c_List_Olist_ONil(X6)
=> c_List_Obutlast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39)) = hAPP(hAPP(c_List_Olist_OCons(X6),X40),c_List_Obutlast(X6,X39)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_nat__less__cases,axiom,
! [X16,X71,X102] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X102,X71)
=> hBOOL(hAPP(hAPP(X16,X71),X102)) )
=> ( ( X102 = X71
=> hBOOL(hAPP(hAPP(X16,X71),X102)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X102)
=> hBOOL(hAPP(hAPP(X16,X71),X102)) )
=> hBOOL(hAPP(hAPP(X16,X71),X102)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
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/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
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/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X46,X40,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> X40 = X46 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X40,X46,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> X40 = X46 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_le__antisym,axiom,
! [X103,X104] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X104,X103)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X103,X104)
=> X104 = X103 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_list_Oinject,axiom,
! [X37,X22,X38,X24,X6] :
( hAPP(hAPP(c_List_Olist_OCons(X6),X24),X38) = hAPP(hAPP(c_List_Olist_OCons(X6),X22),X37)
<=> ( X24 = X22
& X38 = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).
fof(fact_append__same__eq,axiom,
! [X54,X48,X49,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X49),X48) = hAPP(hAPP(c_List_Oappend(X6),X54),X48)
<=> X49 = X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).
fof(fact_same__append__eq,axiom,
! [X54,X49,X48,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X48),X49) = hAPP(hAPP(c_List_Oappend(X6),X48),X54)
<=> X49 = X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).
fof(fact_inf__le1,axiom,
! [X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [X46,X40,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_inf__le2,axiom,
! [X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46),X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [X46,X40,X6] :
( class_Lattices_Olattice(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46),X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_xt1_I11_J,axiom,
! [X28,X27,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X27,X28)
=> ( X28 != X27
=> c_Orderings_Oord__class_Oless(X6,X27,X28) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X27,X28,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X28,X27)
=> ( X28 != X27
=> c_Orderings_Oord__class_Oless(X6,X28,X27) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X46,X40,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
| X40 = X46 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X27,X28,X6] :
( class_Orderings_Oorder(X6)
=> ( X28 != X27
=> ( c_Orderings_Oord__class_Oless__eq(X6,X28,X27)
=> c_Orderings_Oord__class_Oless(X6,X28,X27) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
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/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
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/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X27,X28,X6] :
( class_Orderings_Oorder(X6)
=> ( X28 != X27
=> ( c_Orderings_Oord__class_Oless__eq(X6,X27,X28)
=> c_Orderings_Oord__class_Oless(X6,X27,X28) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_order__less__imp__le,axiom,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> c_Orderings_Oord__class_Oless__eq(X6,X40,X46) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_le__iff__inf,axiom,
! [X11,X12,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X12,X11)
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X12),X11) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__absorb1,axiom,
! [X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46) = X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
fof(fact_inf__absorb2,axiom,
! [X40,X46,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46) = X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
fof(fact_Int__absorb,axiom,
! [X8,X6] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X8),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(fact_distinct__dropWhile,axiom,
! [X16,X48,X6] :
( c_List_Odistinct(X6,X48)
=> c_List_Odistinct(X6,c_List_OdropWhile(X6,X16,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).
fof(fact_distinct__takeWhile,axiom,
! [X16,X48,X6] :
( c_List_Odistinct(X6,X48)
=> c_List_Odistinct(X6,c_List_OtakeWhile(X6,X16,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
fof(fact_distinct__insert,axiom,
! [X40,X39,X6] :
( c_List_Odistinct(X6,X39)
=> c_List_Odistinct(X6,c_List_Oinsert(X6,X40,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insert) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X71,X102] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X102,X71)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X102,X71)
| X102 = X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X103,X104] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X104,X103)
=> ( X104 != X103
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X104,X103) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_nat__less__le,axiom,
! [X71,X102] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X102,X71)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X102,X71)
& X102 != X71 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_last__appendL,axiom,
! [X39,X6,X45] :
( X45 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),X45)) = c_List_Olast(X6,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendL) ).
fof(fact_last__append,axiom,
! [X39,X6,X45] :
( ( X45 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),X45)) = c_List_Olast(X6,X39) )
& ( X45 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),X45)) = c_List_Olast(X6,X45) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__append) ).
fof(fact_less__imp__le__nat,axiom,
! [X103,X104] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X104,X103)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X104,X103) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X103,X104] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X104,X103)
| X104 = X103 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X104,X103) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X46,X40] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X46)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_last__appendR,axiom,
! [X39,X6,X45] :
( X45 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Oappend(X6),X39),X45)) = c_List_Olast(X6,X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendR) ).
fof(fact_last__ConsR,axiom,
! [X40,X6,X39] :
( X39 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39)) = c_List_Olast(X6,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsR) ).
fof(fact_last_Osimps,axiom,
! [X40,X6,X39] :
( ( X39 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39)) = X40 )
& ( X39 != c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39)) = c_List_Olast(X6,X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last_Osimps) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_last__ConsL,axiom,
! [X40,X6,X39] :
( X39 = c_List_Olist_ONil(X6)
=> c_List_Olast(X6,hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39)) = X40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsL) ).
fof(help_c__COMBK__1,axiom,
! [X118,X117,X14,X6] : hAPP(c_COMBK(X6,X14,X117),X118) = X117,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
| X40 = X46
| c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_insert__Nil,axiom,
! [X40,X6] : c_List_Oinsert(X6,X40,c_List_Olist_ONil(X6)) = hAPP(hAPP(c_List_Olist_OCons(X6),X40),c_List_Olist_ONil(X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Nil) ).
fof(fact_linorder__le__less__linear,axiom,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
| c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
| c_Orderings_Oord__class_Oless__eq(X6,X46,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_inf_Ocommute,axiom,
! [X27,X28,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X27),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__commute,axiom,
! [X46,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [X46,X40,X6] :
( class_Lattices_Olattice(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X46) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X46),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_nat__neq__iff,axiom,
! [X71,X102] :
( X102 != X71
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X102,X71)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X102) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_nat__le__linear,axiom,
! [X103,X104] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X104,X103)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X103,X104) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_nat__add__commute,axiom,
! [X103,X104] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X104,X103) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X103,X104),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X46,X40,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> X46 != X40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X46,X40,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> X40 != X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X46,X40,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> X40 != X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_listsp_Oequations_I1_J,axiom,
! [X8,X6] : hBOOL(hAPP(c_List_Olistsp(X6,X8),c_List_Olist_ONil(X6))),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_listsp_ONil) ).
fof(fact_append__is__Nil__conv,axiom,
! [X49,X48,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X48),X49) = c_List_Olist_ONil(X6)
<=> ( X48 = c_List_Olist_ONil(X6)
& X49 = c_List_Olist_ONil(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_Nil__is__append__conv,axiom,
! [X49,X48,X6] :
( c_List_Olist_ONil(X6) = hAPP(hAPP(c_List_Oappend(X6),X48),X49)
<=> ( X48 = c_List_Olist_ONil(X6)
& X49 = c_List_Olist_ONil(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_append__self__conv2,axiom,
! [X49,X48,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X48),X49) = X49
<=> X48 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv2) ).
fof(fact_append__self__conv,axiom,
! [X49,X48,X6] :
( hAPP(hAPP(c_List_Oappend(X6),X48),X49) = X48
<=> X49 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv) ).
fof(fact_self__append__conv,axiom,
! [X49,X6,X48] :
( X48 = hAPP(hAPP(c_List_Oappend(X6),X48),X49)
<=> X49 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv) ).
fof(fact_self__append__conv2,axiom,
! [X48,X6,X49] :
( X49 = hAPP(hAPP(c_List_Oappend(X6),X48),X49)
<=> X48 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv2) ).
fof(fact_list_Osimps_I3_J,axiom,
! [X34,X26,X6] : hAPP(hAPP(c_List_Olist_OCons(X6),X26),X34) != c_List_Olist_ONil(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X34,X26,X6] : c_List_Olist_ONil(X6) != hAPP(hAPP(c_List_Olist_OCons(X6),X26),X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_less__not__refl3,axiom,
! [X105,X106] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X106,X105)
=> X106 != X105 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X104,X103] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X103,X104)
=> X104 != X103 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
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/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_not__Cons__self2,axiom,
! [X39,X40,X6] : hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39) != X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [X40,X6,X39] : X39 != hAPP(hAPP(c_List_Olist_OCons(X6),X40),X39),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_distinct1__rotate,axiom,
! [X48,X6] :
( c_List_Odistinct(X6,c_List_Orotate1(X6,X48))
<=> c_List_Odistinct(X6,X48) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_lexord__transI) ).
fof(fact_eq__Nil__appendI,axiom,
! [X6,X45,X39] :
( X39 = X45
=> X39 = hAPP(hAPP(c_List_Oappend(X6),c_List_Olist_ONil(X6)),X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
fof(fact_distinct__butlast,axiom,
! [X6,X39] :
( X39 != c_List_Olist_ONil(X6)
=> ( c_List_Odistinct(X6,X39)
=> c_List_Odistinct(X6,c_List_Obutlast(X6,X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__butlast) ).
fof(fact_length__rotate1,axiom,
! [X39,X6] : c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_Orotate1(X6,X39)) = c_Nat_Osize__class_Osize(tc_List_Olist(X6),X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate1) ).
fof(fact_order__eq__refl,axiom,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( X40 = X46
=> c_Orderings_Oord__class_Oless__eq(X6,X40,X46) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_append__Nil,axiom,
! [X45,X6] : hAPP(hAPP(c_List_Oappend(X6),c_List_Olist_ONil(X6)),X45) = X45,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(fact_order__refl,axiom,
! [X40,X6] :
( class_Orderings_Opreorder(X6)
=> c_Orderings_Oord__class_Oless__eq(X6,X40,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_splice_Osimps_I1_J,axiom,
! [X45,X6] : c_List_Osplice(X6,c_List_Olist_ONil(X6),X45) = X45,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(fact_splice__Nil2,axiom,
! [X39,X6] : c_List_Osplice(X6,X39,c_List_Olist_ONil(X6)) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice__Nil2) ).
fof(fact_inf_Oidem,axiom,
! [X28,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X28) = X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(fact_inf__idem,axiom,
! [X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X40),X40) = X40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(fact_append__Nil2,axiom,
! [X39,X6] : hAPP(hAPP(c_List_Oappend(X6),X39),c_List_Olist_ONil(X6)) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil2) ).
fof(fact_eq__imp__le,axiom,
! [X103,X104] :
( X104 = X103
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X104,X103) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_le__refl,axiom,
! [X103] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X103,X103),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_trans__Id__on,axiom,
! [X8,X6] : c_Relation_Otrans(X6,c_Relation_OId__on(X6,X8)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X115,X116] :
( class_Orderings_Oorder(X116)
=> class_Orderings_Oorder(tc_fun(X115,X116)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X115,X116] :
( class_Orderings_Oord(X116)
=> class_Orderings_Oord(tc_fun(X115,X116)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X115,X116] :
( class_Orderings_Opreorder(X116)
=> class_Orderings_Opreorder(tc_fun(X115,X116)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Lattices_Osemilattice__inf,axiom,
! [X115,X116] :
( class_Lattices_Olattice(X116)
=> class_Lattices_Osemilattice__inf(tc_fun(X115,X116)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(arity_fun__Lattices_Olattice,axiom,
! [X115,X116] :
( class_Lattices_Olattice(X116)
=> class_Lattices_Olattice(tc_fun(X115,X116)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(fact_rotate1__is__Nil__conv,axiom,
! [X48,X6] :
( c_List_Orotate1(X6,X48) = c_List_Olist_ONil(X6)
<=> X48 = c_List_Olist_ONil(X6) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
fof(help_c__COMBI__1,axiom,
! [X117,X6] : hAPP(c_COMBI(X6),X117) = X117,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_dist) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(arity_HOL__Obool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(i_0_509,plain,
! [X75,X5,X33,X14,X9,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X14,X33,tc_fun(X6,tc_HOL_Obool)),X5),X75)))
=> ~ ! [X3,X62] :
( X75 = hAPP(hAPP(c_Product__Type_OPair(X14,X33),X3),X62)
=> ~ hBOOL(hAPP(hAPP(c_member(X6),X9),hAPP(hAPP(X5,X3),X62))) ) ),
inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).
fof(i_0_510,plain,
! [X17,X83,X84,X85,X61,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),X61),X85)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X83))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17)))
=> ( hAPP(hAPP(c_Product__Type_OPair(X6,X14),X61),X85) != hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X83)
=> ~ ! [X19,X20] :
( 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),X61),X85)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X19),X20))),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),X19),X20)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X84),X83))),c_Transitive__Closure_Ortrancl(tc_prod(X6,X14),X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2]) ).
fof(i_0_511,plain,
! [X3053,X3054,X3055,X3056] : c_List_Opartition(X3056,X3055,hAPP(hAPP(c_List_Olist_OCons(X3056),X3054),X3053)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3056),tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056))),hAPP(hAPP(c_COMBS(tc_List_Olist(X3056),tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056))),tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3056),tc_fun(tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)))),tc_fun(tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056))),tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)))),tc_List_Olist(X3056)),c_COMBS(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056))),tc_fun(tc_List_Olist(X3056),tc_fun(tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)))),tc_List_Olist(X3056)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_fun(tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056))),tc_List_Olist(X3056)),c_If(tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)),hAPP(X3055,X3054)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X3056),tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056))),tc_List_Olist(X3056)),c_Product__Type_OPair(tc_List_Olist(X3056),tc_List_Olist(X3056))),hAPP(c_List_Olist_OCons(X3056),X3054))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3056),tc_fun(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056))),tc_fun(tc_fun(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_fun(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)))),tc_List_Olist(X3056)),c_COMBB(tc_List_Olist(X3056),tc_prod(tc_List_Olist(X3056),tc_List_Olist(X3056)),tc_List_Olist(X3056))),c_Product__Type_OPair(tc_List_Olist(X3056),tc_List_Olist(X3056)))),hAPP(c_List_Olist_OCons(X3056),X3054)))),c_List_Opartition(X3056,X3055,X3053)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).
fof(i_0_512,plain,
! [X3170,X3171,X3172] : c_Product__Type_Ointernal__split(X3172,X3171,X3170) = c_Product__Type_Oprod_Oprod__case(X3172,X3171,X3170),
inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).
fof(i_0_513,plain,
! [X3403,X3404,X3405,X3406,X3407,X3408] :
( ( X3408 = hAPP(hAPP(c_Product__Type_OPair(X3407,X3406),esk87_6(X3403,X3404,X3405,X3406,X3407,X3408)),esk88_6(X3403,X3404,X3405,X3406,X3407,X3408))
| hBOOL(hAPP(hAPP(c_member(X3405),X3404),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3407,X3406,tc_fun(X3405,tc_HOL_Obool)),X3403),X3408))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3405),X3404),hAPP(hAPP(X3403,esk87_6(X3403,X3404,X3405,X3406,X3407,X3408)),esk88_6(X3403,X3404,X3405,X3406,X3407,X3408))))
| hBOOL(hAPP(hAPP(c_member(X3405),X3404),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3407,X3406,tc_fun(X3405,tc_HOL_Obool)),X3403),X3408))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).
fof(i_0_514,plain,
! [X3381,X3382,X3383,X3384,X3385,X3386] :
( ( X3381 = hAPP(hAPP(c_Product__Type_OPair(X3384,X3383),esk85_6(X3381,X3382,X3383,X3384,X3385,X3386)),esk86_6(X3381,X3382,X3383,X3384,X3385,X3386))
| ~ hBOOL(hAPP(hAPP(c_member(X3386),X3385),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3384,X3383,tc_fun(X3386,tc_HOL_Obool)),X3382),X3381))) )
& ( hBOOL(hAPP(hAPP(c_member(X3386),X3385),hAPP(hAPP(X3382,esk85_6(X3381,X3382,X3383,X3384,X3385,X3386)),esk86_6(X3381,X3382,X3383,X3384,X3385,X3386))))
| ~ hBOOL(hAPP(hAPP(c_member(X3386),X3385),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3384,X3383,tc_fun(X3386,tc_HOL_Obool)),X3382),X3381))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_509])])])]) ).
fof(i_0_515,plain,
! [X17,X49,X11,X48,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)),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),c_List_Olistrel1(X6,X17)))
=> ( ! [X3] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X49)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X3),X11)),X17)) )
=> ~ ! [X72] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X72)
=> ~ 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)),X72),X49)),c_List_Olistrel1(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Cons__listrel1E2]) ).
fof(i_0_516,plain,
! [X17,X60,X50,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),X50)),hAPP(hAPP(c_List_Oappend(X6),X12),X60))),c_List_Olexord(X6,X17)))
=> ( ! [X19] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X19),X19)),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)),X50),X60)),c_List_Olexord(X6,X17))) ) ),
inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).
fof(i_0_517,plain,
! [X17,X49,X48,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),X48)),X49)),c_List_Olistrel1(X6,X17)))
=> ( ! [X62] :
( X49 = hAPP(hAPP(c_List_Olist_OCons(X6),X62),X48)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X12),X62)),X17)) )
=> ~ ! [X72] :
( X49 = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X72)
=> ~ 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)),X48),X72)),c_List_Olistrel1(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_Cons__listrel1E1]) ).
fof(i_0_518,plain,
! [X17,X49,X11,X48,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)),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))),c_List_Olistrel(X6,X17)))
=> ~ ! [X3,X64] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X3),X64)
=> ( 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)),X64),X49)),c_List_Olistrel(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).
fof(i_0_519,plain,
! [X3264,X3265] : c_Relation_OId__on(X3265,X3264) = hAPP(c_Product__Type_Oprod_Oprod__case(X3265,X3265,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X3265,tc_HOL_Obool,tc_fun(X3265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3265,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X3265,tc_HOL_Obool)),X3265),c_COMBC(X3265,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3265,tc_HOL_Obool),tc_fun(X3265,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X3265),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3265),c_fconj)),c_fequal))),X3264)),
inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).
fof(i_0_520,plain,
! [X17,X48,X49,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),X49)),X48)),c_List_Olistrel(X6,X17)))
=> ~ ! [X62,X63] :
( X48 = hAPP(hAPP(c_List_Olist_OCons(X6),X62),X63)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X11),X62)),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)),X49),X63)),c_List_Olistrel(X6,X17))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).
fof(i_0_521,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_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____))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_522,plain,
! [X3094,X3095,X3096,X3097,X3098,X3099,X3100,X3101] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3101,X3100,X3099),X3098),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3097,X3096,tc_prod(X3101,X3100)),X3095),X3094)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3097,X3096,X3099),hAPP(hAPP(c_COMBB(tc_fun(X3096,tc_prod(X3101,X3100)),tc_fun(X3096,X3099),X3097),hAPP(c_COMBB(tc_prod(X3101,X3100),X3099,X3096),hAPP(c_Product__Type_Oprod_Oprod__case(X3101,X3100,X3099),X3098))),X3095)),X3094),
inference(variable_rename,[status(thm)],[fact_split__twice]) ).
fof(i_0_523,plain,
! [X17,X14,X23,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X23),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),X23)),X17)) ),
inference(fof_simplification,[status(thm)],[fact_RangeE]) ).
fof(i_0_524,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_525,plain,
! [X1,X2,X14,X8,X24,X6] :
( ( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X24) = hAPP(X1,X24) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X24) = hAPP(X2,X24) ) ),
inference(fof_simplification,[status(thm)],[fact_override__on__def]) ).
fof(i_0_526,plain,
! [X1,X2,X14,X8,X24,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> c_Fun_Ooverride__on(X6,X14,X2,X1,X8,X24) = hAPP(X2,X24) ),
inference(fof_simplification,[status(thm)],[fact_override__on__apply__notin]) ).
fof(i_0_527,plain,
! [X17,X14,X24,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X24),c_Relation_ODomain(X6,X14,X17)))
=> ~ ! [X62] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X62)),X17)) ),
inference(fof_simplification,[status(thm)],[fact_DomainE]) ).
fof(i_0_528,plain,
! [X11,X12,X7,X8,X14,X6] :
( hBOOL(hAPP(hAPP(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_529,plain,
! [X3183,X3184,X3185,X3186,X3187,X3188,X3189] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3189,X3188)),hAPP(hAPP(c_Product__Type_OPair(X3189,X3188),X3187),X3186)),X3185))
| hBOOL(hAPP(hAPP(c_member(X3184),hAPP(hAPP(X3183,X3187),X3186)),c_Set_Oimage(tc_prod(X3189,X3188),X3184,hAPP(c_Product__Type_Oprod_Oprod__case(X3189,X3188,X3184),X3183),X3185))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).
fof(i_0_530,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_531,plain,
! [X23,X24,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),X24),X23)),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),X23),X24)),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_532,plain,
! [X3223,X3224,X3225,X3226,X3227,X3228,X3229] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3229,X3228,tc_fun(X3227,tc_HOL_Obool)),X3226),hAPP(hAPP(c_Product__Type_OPair(X3229,X3228),X3225),X3224)),X3223))
| hBOOL(hAPP(hAPP(hAPP(X3226,X3225),X3224),X3223)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).
fof(i_0_533,plain,
! [X7,X8,X23,X24,X14,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X14)),hAPP(hAPP(c_Product__Type_OPair(X6,X14),X24),X23)),c_Product__Type_OSigma(X6,X14,X8,X7)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X6),X24),X8))
=> ~ hBOOL(hAPP(hAPP(c_member(X14),X23),hAPP(X7,X24))) ) ),
inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).
fof(i_0_534,plain,
! [X13,X12,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X6),X12),c_Wellfounded_Oacc(X6,X13)))
=> ~ ! [X66] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X6,X6)),hAPP(hAPP(c_Product__Type_OPair(X6,X6),X66),X12)),X13))
=> hBOOL(hAPP(hAPP(c_member(X6),X66),c_Wellfounded_Oacc(X6,X13))) ) ),
inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).
fof(i_0_535,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_536,plain,
! [X17,X48,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)),X48)),c_List_Olistrel1(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).
fof(i_0_537,plain,
! [X17,X49,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)),X49)),c_List_Olex(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).
fof(i_0_538,plain,
! [X17,X48,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)),X48),c_List_Olist_ONil(X6))),c_List_Olistrel1(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).
fof(i_0_539,plain,
! [X17,X48,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)),X48),c_List_Olist_ONil(X6))),c_List_Olex(X6,X17))),
inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).
fof(i_0_540,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_541,plain,
! [X4142,X4143,X4144,X4145] : c_Set_Oimage(tc_prod(X4145,X4144),tc_prod(X4144,X4145),hAPP(c_Product__Type_Oprod_Oprod__case(X4145,X4144,tc_prod(X4144,X4145)),hAPP(c_COMBC(X4144,X4145,tc_prod(X4144,X4145)),c_Product__Type_OPair(X4144,X4145))),c_Product__Type_OSigma(X4145,X4144,X4143,c_COMBK(tc_fun(X4144,tc_HOL_Obool),X4145,X4142))) = c_Product__Type_OSigma(X4144,X4145,X4142,c_COMBK(tc_fun(X4145,tc_HOL_Obool),X4144,X4143)),
inference(variable_rename,[status(thm)],[fact_swap__product]) ).
fof(i_0_542,plain,
! [X3210,X3211,X3212,X3213,X3214,X3215,X3216] :
( ~ hBOOL(hAPP(hAPP(c_member(X3216),X3215),hAPP(hAPP(X3214,X3213),X3212)))
| hBOOL(hAPP(hAPP(c_member(X3216),X3215),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3211,X3210,tc_fun(X3216,tc_HOL_Obool)),X3214),hAPP(hAPP(c_Product__Type_OPair(X3211,X3210),X3213),X3212)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).
fof(i_0_543,plain,
! [X48,X16,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X48)),c_Nat_Osize__class_Osize(tc_List_Olist(X6),X48))
=> ~ hBOOL(hAPP(X16,c_List_Onth(X6,X48,c_Nat_Osize__class_Osize(tc_List_Olist(X6),c_List_OtakeWhile(X6,X16,X48))))) ),
inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile]) ).
fof(i_0_544,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_545,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_546,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_547,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_548,plain,
! [X3230,X3231,X3232,X3233,X3234] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3234,X3233,tc_HOL_Obool),X3232),hAPP(hAPP(c_Product__Type_OPair(X3234,X3233),X3231),X3230)))
| hBOOL(hAPP(hAPP(X3232,X3231),X3230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).
fof(i_0_549,plain,
! [X7,X8,X5,X6] :
( hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(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_550,plain,
! [X3205,X3206,X3207,X3208,X3209] :
( ~ hBOOL(hAPP(hAPP(X3209,X3208),X3207))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3206,X3205,tc_HOL_Obool),X3209),hAPP(hAPP(c_Product__Type_OPair(X3206,X3205),X3208),X3207))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).
fof(i_0_551,plain,
! [X3200,X3201,X3202,X3203,X3204] :
( ~ hBOOL(hAPP(hAPP(X3204,X3203),X3202))
| hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3201,X3200,tc_HOL_Obool),X3204),hAPP(hAPP(c_Product__Type_OPair(X3201,X3200),X3203),X3202))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).
fof(i_0_552,plain,
! [X12,X7,X8,X6] :
( hBOOL(hAPP(hAPP(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,
! [X49,X11,X48,X16,X6] :
( c_List_OdropWhile(X6,X16,X48) = hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49)
<=> ( X48 = hAPP(hAPP(c_List_Oappend(X6),c_List_OtakeWhile(X6,X16,X48)),hAPP(hAPP(c_List_Olist_OCons(X6),X11),X49))
& ~ hBOOL(hAPP(X16,X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).
fof(i_0_554,plain,
~ ! [X29] : ~ 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),X29),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_555,plain,
! [X3159,X3160,X3161,X3162] : hAPP(c_Product__Type_Oprod_Oprod__case(X3162,X3161,X3160),c_Product__Type_Ocurry(X3162,X3161,X3160,X3159)) = X3159,
inference(variable_rename,[status(thm)],[fact_split__curry]) ).
fof(i_0_556,plain,
! [X3163,X3164,X3165,X3166] : c_Product__Type_Ocurry(X3166,X3165,X3164,hAPP(c_Product__Type_Oprod_Oprod__case(X3166,X3165,X3164),X3163)) = X3163,
inference(variable_rename,[status(thm)],[fact_curry__split]) ).
fof(i_0_557,plain,
! [X3138,X3139,X3140,X3141,X3142,X3143] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3143,X3142,X3141),X3140),hAPP(hAPP(c_Product__Type_OPair(X3143,X3142),X3139),X3138)) = hAPP(hAPP(X3140,X3139),X3138),
inference(variable_rename,[status(thm)],[fact_split__conv]) ).
fof(i_0_558,plain,
! [X3132,X3133,X3134,X3135,X3136,X3137] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X3137,X3136,X3135),X3134),hAPP(hAPP(c_Product__Type_OPair(X3137,X3136),X3133),X3132)) = hAPP(hAPP(X3134,X3133),X3132),
inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(i_0_559,plain,
! [X86,X48,X6,X12,X16] :
( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Oappend(X6),X48),hAPP(hAPP(c_List_Olist_OCons(X6),X12),X86))) = c_List_OtakeWhile(X6,X16,X48) ),
inference(fof_simplification,[status(thm)],[fact_takeWhile__tail]) ).
fof(i_0_560,plain,
! [X48,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),c_List_OtakeWhile(X6,X16,X48)) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OtakeWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = c_List_Olist_ONil(X6) ) ),
inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).
fof(i_0_561,plain,
! [X27,X28,X40,X6] :
( class_Lattices_Osemilattice__inf(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X40,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X6),X28),X27))
=> ~ ( c_Orderings_Oord__class_Oless__eq(X6,X40,X28)
=> ~ c_Orderings_Oord__class_Oless__eq(X6,X40,X27) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__infE]) ).
fof(i_0_562,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_563,plain,
! [X48,X6,X12,X16] :
( ( hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = c_List_OdropWhile(X6,X16,X48) )
& ( ~ hBOOL(hAPP(X16,X12))
=> c_List_OdropWhile(X6,X16,hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48)) = hAPP(hAPP(c_List_Olist_OCons(X6),X12),X48) ) ),
inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).
fof(i_0_564,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_565,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_566,plain,
! [X28,X27,X6] :
( class_Orderings_Oorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X27,X28)
=> ~ c_Orderings_Oord__class_Oless(X6,X28,X27) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_567,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_568,plain,
! [X40,X46,X6] :
( class_Orderings_Olinorder(X6)
=> ( c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> ~ c_Orderings_Oord__class_Oless(X6,X40,X46) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_569,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_570,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_571,plain,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ~ c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_572,plain,
! [X27,X28,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X28,X27)
=> ~ c_Orderings_Oord__class_Oless(X6,X27,X28) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_573,plain,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ~ c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_574,plain,
! [X46,X40,X6] :
( class_Orderings_Opreorder(X6)
=> ( c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ~ c_Orderings_Oord__class_Oless(X6,X46,X40) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_575,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_576,plain,
! [X97,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X97))
| hBOOL(X16) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(i_0_577,plain,
! [X97,X16] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X16),X97))
| hBOOL(X97) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).
fof(i_0_578,plain,
! [X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X12),X11))
| X12 = X11 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_579,plain,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X40,X46)
=> ( X40 != X46
=> c_Orderings_Oord__class_Oless(X6,X46,X40) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_580,plain,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( X40 != X46
=> ( ~ c_Orderings_Oord__class_Oless(X6,X40,X46)
=> c_Orderings_Oord__class_Oless(X6,X46,X40) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_581,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_582,plain,
! [X40,X46,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X46,X40)
=> c_Orderings_Oord__class_Oless(X6,X40,X46) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_583,plain,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless(X6,X40,X46)
=> c_Orderings_Oord__class_Oless__eq(X6,X46,X40) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_584,plain,
! [X46,X40,X6] :
( class_Orderings_Olinorder(X6)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X6,X40,X46)
=> c_Orderings_Oord__class_Oless__eq(X6,X46,X40) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_585,plain,
! [X46,X40] :
( X40 != X46
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X40,X46)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X46,X40) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_586,plain,
! [X40,X6] :
( class_Orderings_Opreorder(X6)
=> ~ c_Orderings_Oord__class_Oless(X6,X40,X40) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_587,plain,
! [X97,X16] :
( ~ hBOOL(X16)
| ~ hBOOL(X97)
| hBOOL(hAPP(hAPP(c_fconj,X16),X97)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).
fof(i_0_588,plain,
! [X103] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X103,X103),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_589,plain,
! [X103] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X103,X103),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_590,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_591,plain,
! [X16] :
( ~ hBOOL(hAPP(c_fNot,X16))
| ~ hBOOL(X16) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(i_0_592,plain,
! [X16] :
( hBOOL(X16)
| hBOOL(hAPP(c_fNot,X16)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(i_0_593,plain,
! [X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3000,X2999),tc_prod(X3000,X2999))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3000,X2999),tc_prod(X3000,X2999)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2998),X2997)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),esk66_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)),esk67_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)))),c_Transitive__Closure_Ortrancl(tc_prod(X3000,X2999),X2994)))
| hBOOL(hAPP(hAPP(X2993,X2996),X2995))
| ~ hBOOL(hAPP(hAPP(X2993,X2998),X2997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3000,X2999),tc_prod(X3000,X2999))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3000,X2999),tc_prod(X3000,X2999)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2998),X2997)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2996),X2995))),c_Transitive__Closure_Ortrancl(tc_prod(X3000,X2999),X2994))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3000,X2999),tc_prod(X3000,X2999))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3000,X2999),tc_prod(X3000,X2999)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),esk66_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)),esk67_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000))),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),esk68_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)),esk69_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)))),X2994))
| hBOOL(hAPP(hAPP(X2993,X2996),X2995))
| ~ hBOOL(hAPP(hAPP(X2993,X2998),X2997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3000,X2999),tc_prod(X3000,X2999))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3000,X2999),tc_prod(X3000,X2999)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2998),X2997)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2996),X2995))),c_Transitive__Closure_Ortrancl(tc_prod(X3000,X2999),X2994))) )
& ( hBOOL(hAPP(hAPP(X2993,esk66_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)),esk67_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)))
| hBOOL(hAPP(hAPP(X2993,X2996),X2995))
| ~ hBOOL(hAPP(hAPP(X2993,X2998),X2997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3000,X2999),tc_prod(X3000,X2999))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3000,X2999),tc_prod(X3000,X2999)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2998),X2997)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2996),X2995))),c_Transitive__Closure_Ortrancl(tc_prod(X3000,X2999),X2994))) )
& ( ~ hBOOL(hAPP(hAPP(X2993,esk68_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)),esk69_8(X2993,X2994,X2995,X2996,X2997,X2998,X2999,X3000)))
| hBOOL(hAPP(hAPP(X2993,X2996),X2995))
| ~ hBOOL(hAPP(hAPP(X2993,X2998),X2997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3000,X2999),tc_prod(X3000,X2999))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3000,X2999),tc_prod(X3000,X2999)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2998),X2997)),hAPP(hAPP(c_Product__Type_OPair(X3000,X2999),X2996),X2995))),c_Transitive__Closure_Ortrancl(tc_prod(X3000,X2999),X2994))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2])])])]) ).
fof(i_0_594,plain,
! [X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3012,X3011),tc_prod(X3012,X3011))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3012,X3011),tc_prod(X3012,X3011)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),esk70_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)),esk71_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012))),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),esk72_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)),esk73_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)))),X3006))
| hBOOL(hAPP(hAPP(X3005,X3010),X3009))
| ~ hBOOL(hAPP(hAPP(X3005,X3008),X3007))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3012,X3011),tc_prod(X3012,X3011))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3012,X3011),tc_prod(X3012,X3011)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3010),X3009)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3008),X3007))),c_Transitive__Closure_Ortrancl(tc_prod(X3012,X3011),X3006))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3012,X3011),tc_prod(X3012,X3011))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3012,X3011),tc_prod(X3012,X3011)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),esk72_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)),esk73_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012))),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3008),X3007))),c_Transitive__Closure_Ortrancl(tc_prod(X3012,X3011),X3006)))
| hBOOL(hAPP(hAPP(X3005,X3010),X3009))
| ~ hBOOL(hAPP(hAPP(X3005,X3008),X3007))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3012,X3011),tc_prod(X3012,X3011))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3012,X3011),tc_prod(X3012,X3011)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3010),X3009)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3008),X3007))),c_Transitive__Closure_Ortrancl(tc_prod(X3012,X3011),X3006))) )
& ( hBOOL(hAPP(hAPP(X3005,esk72_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)),esk73_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)))
| hBOOL(hAPP(hAPP(X3005,X3010),X3009))
| ~ hBOOL(hAPP(hAPP(X3005,X3008),X3007))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3012,X3011),tc_prod(X3012,X3011))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3012,X3011),tc_prod(X3012,X3011)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3010),X3009)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3008),X3007))),c_Transitive__Closure_Ortrancl(tc_prod(X3012,X3011),X3006))) )
& ( ~ hBOOL(hAPP(hAPP(X3005,esk70_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)),esk71_8(X3005,X3006,X3007,X3008,X3009,X3010,X3011,X3012)))
| hBOOL(hAPP(hAPP(X3005,X3010),X3009))
| ~ hBOOL(hAPP(hAPP(X3005,X3008),X3007))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3012,X3011),tc_prod(X3012,X3011))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3012,X3011),tc_prod(X3012,X3011)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3010),X3009)),hAPP(hAPP(c_Product__Type_OPair(X3012,X3011),X3008),X3007))),c_Transitive__Closure_Ortrancl(tc_prod(X3012,X3011),X3006))) ) ),
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_595,plain,
! [X3033,X3034,X3035,X3036,X3037,X3038,X3039] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3039,X3038),tc_prod(X3039,X3038))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3039,X3038),tc_prod(X3039,X3038)),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3037),X3036)),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),esk74_7(X3033,X3034,X3035,X3036,X3037,X3038,X3039)),esk75_7(X3033,X3034,X3035,X3036,X3037,X3038,X3039)))),X3033))
| hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3037),X3036) = hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3035),X3034)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3039,X3038),tc_prod(X3039,X3038))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3039,X3038),tc_prod(X3039,X3038)),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3037),X3036)),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3035),X3034))),c_Transitive__Closure_Ortrancl(tc_prod(X3039,X3038),X3033))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3039,X3038),tc_prod(X3039,X3038))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3039,X3038),tc_prod(X3039,X3038)),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),esk74_7(X3033,X3034,X3035,X3036,X3037,X3038,X3039)),esk75_7(X3033,X3034,X3035,X3036,X3037,X3038,X3039))),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3035),X3034))),c_Transitive__Closure_Ortrancl(tc_prod(X3039,X3038),X3033)))
| hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3037),X3036) = hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3035),X3034)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X3039,X3038),tc_prod(X3039,X3038))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X3039,X3038),tc_prod(X3039,X3038)),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3037),X3036)),hAPP(hAPP(c_Product__Type_OPair(X3039,X3038),X3035),X3034))),c_Transitive__Closure_Ortrancl(tc_prod(X3039,X3038),X3033))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_510])])])]) ).
fof(i_0_596,plain,
! [X3266,X3267,X3268,X3269,X3270,X3271] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3271,tc_fun(X3270,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X3271,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),X3271),c_COMBC(X3270,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_prod(X3271,X3270)),tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),X3271),hAPP(c_COMBB(tc_prod(X3271,X3270),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool),X3270),c_member(tc_prod(X3271,X3270)))),c_Product__Type_OPair(X3271,X3270)))),X3269)),hAPP(hAPP(c_COMBC(X3271,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),X3271),c_COMBC(X3270,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_prod(X3271,X3270)),tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),X3271),hAPP(c_COMBB(tc_prod(X3271,X3270),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool),X3270),c_member(tc_prod(X3271,X3270)))),c_Product__Type_OPair(X3271,X3270)))),X3268)),X3267),X3266))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3271,X3270)),hAPP(hAPP(c_Product__Type_OPair(X3271,X3270),X3267),X3266)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool)),X3269),X3268))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3271,X3270)),hAPP(hAPP(c_Product__Type_OPair(X3271,X3270),X3267),X3266)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool)),X3269),X3268)))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3271,tc_fun(X3270,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X3271,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),X3271),c_COMBC(X3270,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_prod(X3271,X3270)),tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),X3271),hAPP(c_COMBB(tc_prod(X3271,X3270),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool),X3270),c_member(tc_prod(X3271,X3270)))),c_Product__Type_OPair(X3271,X3270)))),X3269)),hAPP(hAPP(c_COMBC(X3271,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_fun(X3270,tc_HOL_Obool)),X3271),c_COMBC(X3270,tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3270,tc_prod(X3271,X3270)),tc_fun(X3270,tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool)),X3271),hAPP(c_COMBB(tc_prod(X3271,X3270),tc_fun(tc_fun(tc_prod(X3271,X3270),tc_HOL_Obool),tc_HOL_Obool),X3270),c_member(tc_prod(X3271,X3270)))),c_Product__Type_OPair(X3271,X3270)))),X3268)),X3267),X3266)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).
fof(i_0_597,plain,
! [X2893,X2894,X2895] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2895,hAPP(hAPP(c_COMBC(X2895,tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_fun(X2895,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2895,tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_fun(X2895,tc_HOL_Obool)),X2895),c_COMBC(X2895,tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2895,tc_prod(X2895,X2895)),tc_fun(X2895,tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool)),X2895),hAPP(c_COMBB(tc_prod(X2895,X2895),tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool),X2895),c_member(tc_prod(X2895,X2895)))),c_Product__Type_OPair(X2895,X2895)))),X2894)),X2893))
| hBOOL(hAPP(hAPP(c_member(X2895),X2893),c_Wellfounded_Oacc(X2895,X2894))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2895),X2893),c_Wellfounded_Oacc(X2895,X2894)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2895,hAPP(hAPP(c_COMBC(X2895,tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_fun(X2895,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2895,tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_fun(X2895,tc_HOL_Obool)),X2895),c_COMBC(X2895,tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2895,tc_prod(X2895,X2895)),tc_fun(X2895,tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool)),X2895),hAPP(c_COMBB(tc_prod(X2895,X2895),tc_fun(tc_fun(tc_prod(X2895,X2895),tc_HOL_Obool),tc_HOL_Obool),X2895),c_member(tc_prod(X2895,X2895)))),c_Product__Type_OPair(X2895,X2895)))),X2894)),X2893)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).
cnf(i_0_598,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_511]) ).
cnf(i_0_599,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_512]) ).
fof(i_0_600,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_601,plain,
! [X3771,X3772,X3773,X3774] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3774,tc_fun(X3773,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3774,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),X3774),c_COMBC(X3773,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_prod(X3774,X3773)),tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),X3774),hAPP(c_COMBB(tc_prod(X3774,X3773),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool),X3773),c_member(tc_prod(X3774,X3773)))),c_Product__Type_OPair(X3774,X3773)))),X3772),hAPP(hAPP(c_COMBC(X3774,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),X3774),c_COMBC(X3773,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_prod(X3774,X3773)),tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),X3774),hAPP(c_COMBB(tc_prod(X3774,X3773),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool),X3773),c_member(tc_prod(X3774,X3773)))),c_Product__Type_OPair(X3774,X3773)))),X3771))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),X3772,X3771) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),X3772,X3771)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3774,tc_fun(X3773,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3774,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),X3774),c_COMBC(X3773,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_prod(X3774,X3773)),tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),X3774),hAPP(c_COMBB(tc_prod(X3774,X3773),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool),X3773),c_member(tc_prod(X3774,X3773)))),c_Product__Type_OPair(X3774,X3773)))),X3772),hAPP(hAPP(c_COMBC(X3774,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_fun(X3773,tc_HOL_Obool)),X3774),c_COMBC(X3773,tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X3773,tc_prod(X3774,X3773)),tc_fun(X3773,tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool)),X3774),hAPP(c_COMBB(tc_prod(X3774,X3773),tc_fun(tc_fun(tc_prod(X3774,X3773),tc_HOL_Obool),tc_HOL_Obool),X3773),c_member(tc_prod(X3774,X3773)))),c_Product__Type_OPair(X3774,X3773)))),X3771)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
cnf(i_0_602,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,esk87_6(X3,X2,X1,X4,X5,X6)),esk88_6(X3,X2,X1,X4,X5,X6)))) ),
inference(split_conjunct,[status(thm)],[i_0_513]) ).
fof(i_0_603,plain,
! [X2186,X2187,X2188,X2189,X2190,X2191] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(v_F,X2187)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(v_F,X2186)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(X2187,esk8_6(X2186,X2187,X2188,X2189,X2190,X2191))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(X2186,esk8_6(X2186,X2187,X2188,X2189,X2190,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))),X2186),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))),X2187),c_Arrow__Order__Mirabelle_OProf))
| X2190 = X2189
| X2191 = X2188
| X2189 = X2188
| X2191 = X2190 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(v_F,X2186)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(v_F,X2187)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(X2187,esk8_6(X2186,X2187,X2188,X2189,X2190,X2191))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(X2186,esk8_6(X2186,X2187,X2188,X2189,X2190,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))),X2186),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))),X2187),c_Arrow__Order__Mirabelle_OProf))
| X2190 = X2189
| X2191 = X2188
| X2189 = X2188
| X2191 = X2190 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(v_F,X2187)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(v_F,X2186)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(X2187,esk8_6(X2186,X2187,X2188,X2189,X2190,X2191))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(X2186,esk8_6(X2186,X2187,X2188,X2189,X2190,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))),X2186),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))),X2187),c_Arrow__Order__Mirabelle_OProf))
| X2190 = X2189
| X2191 = X2188
| X2189 = X2188
| X2191 = X2190 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(v_F,X2186)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(v_F,X2187)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2191),X2190)),hAPP(X2187,esk8_6(X2186,X2187,X2188,X2189,X2190,X2191))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2189),X2188)),hAPP(X2186,esk8_6(X2186,X2187,X2188,X2189,X2190,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))),X2186),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))),X2187),c_Arrow__Order__Mirabelle_OProf))
| X2190 = X2189
| X2191 = X2188
| X2189 = X2188
| X2191 = X2190 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_604,plain,
! [X2179,X2180,X2181,X2182,X2183,X2184] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2184),X2183)),hAPP(X2180,esk7_6(X2179,X2180,X2181,X2182,X2183,X2184))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2182),X2181)),hAPP(X2179,esk7_6(X2179,X2180,X2181,X2182,X2183,X2184))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2184),X2183)),hAPP(v_F,X2180)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2182),X2181)),hAPP(v_F,X2179)))
| ~ 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))),X2179),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))),X2180),c_Arrow__Order__Mirabelle_OProf))
| X2183 = X2182
| X2184 = X2181
| X2182 = X2181
| X2184 = X2183 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2184),X2183)),hAPP(X2180,esk7_6(X2179,X2180,X2181,X2182,X2183,X2184))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2182),X2181)),hAPP(X2179,esk7_6(X2179,X2180,X2181,X2182,X2183,X2184))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2184),X2183)),hAPP(v_F,X2180)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2182),X2181)),hAPP(v_F,X2179)))
| ~ 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))),X2179),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))),X2180),c_Arrow__Order__Mirabelle_OProf))
| X2183 = X2182
| X2184 = X2181
| X2182 = X2181
| X2184 = X2183 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).
fof(i_0_605,plain,
! [X2593,X2594,X2595,X2596] :
( ( ~ c_List_Olistrelp(X2596,hAPP(hAPP(c_COMBC(X2596,tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_fun(X2596,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2596,tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_fun(X2596,tc_HOL_Obool)),X2596),c_COMBC(X2596,tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2596,tc_prod(X2596,X2596)),tc_fun(X2596,tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool)),X2596),hAPP(c_COMBB(tc_prod(X2596,X2596),tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool),X2596),c_member(tc_prod(X2596,X2596)))),c_Product__Type_OPair(X2596,X2596)))),X2595),X2594,X2593)
| 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)),X2594),X2593)),c_List_Olistrel(X2596,X2595))) )
& ( ~ 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)),X2594),X2593)),c_List_Olistrel(X2596,X2595)))
| c_List_Olistrelp(X2596,hAPP(hAPP(c_COMBC(X2596,tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_fun(X2596,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2596,tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_fun(X2596,tc_HOL_Obool)),X2596),c_COMBC(X2596,tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2596,tc_prod(X2596,X2596)),tc_fun(X2596,tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool)),X2596),hAPP(c_COMBB(tc_prod(X2596,X2596),tc_fun(tc_fun(tc_prod(X2596,X2596),tc_HOL_Obool),tc_HOL_Obool),X2596),c_member(tc_prod(X2596,X2596)))),c_Product__Type_OPair(X2596,X2596)))),X2595),X2594,X2593) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).
fof(i_0_606,plain,
! [X2879,X2880,X2881,X2882] :
( ( ~ c_Predicate_ODomainP(X2882,X2881,hAPP(hAPP(c_COMBC(X2882,tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_fun(X2881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2881,tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_fun(X2881,tc_HOL_Obool)),X2882),c_COMBC(X2881,tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2881,tc_prod(X2882,X2881)),tc_fun(X2881,tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool)),X2882),hAPP(c_COMBB(tc_prod(X2882,X2881),tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool),X2881),c_member(tc_prod(X2882,X2881)))),c_Product__Type_OPair(X2882,X2881)))),X2880),X2879)
| hBOOL(hAPP(hAPP(c_member(X2882),X2879),c_Relation_ODomain(X2882,X2881,X2880))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2882),X2879),c_Relation_ODomain(X2882,X2881,X2880)))
| c_Predicate_ODomainP(X2882,X2881,hAPP(hAPP(c_COMBC(X2882,tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_fun(X2881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2881,tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_fun(X2881,tc_HOL_Obool)),X2882),c_COMBC(X2881,tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2881,tc_prod(X2882,X2881)),tc_fun(X2881,tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool)),X2882),hAPP(c_COMBB(tc_prod(X2882,X2881),tc_fun(tc_fun(tc_prod(X2882,X2881),tc_HOL_Obool),tc_HOL_Obool),X2881),c_member(tc_prod(X2882,X2881)))),c_Product__Type_OPair(X2882,X2881)))),X2880),X2879) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).
fof(i_0_607,plain,
! [X2875,X2876,X2877,X2878] :
( ( ~ c_Predicate_ORangeP(X2878,X2877,hAPP(hAPP(c_COMBC(X2878,tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_fun(X2877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2877,tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_fun(X2877,tc_HOL_Obool)),X2878),c_COMBC(X2877,tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2877,tc_prod(X2878,X2877)),tc_fun(X2877,tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool)),X2878),hAPP(c_COMBB(tc_prod(X2878,X2877),tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool),X2877),c_member(tc_prod(X2878,X2877)))),c_Product__Type_OPair(X2878,X2877)))),X2876),X2875)
| hBOOL(hAPP(hAPP(c_member(X2877),X2875),c_Relation_ORange(X2878,X2877,X2876))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2877),X2875),c_Relation_ORange(X2878,X2877,X2876)))
| c_Predicate_ORangeP(X2878,X2877,hAPP(hAPP(c_COMBC(X2878,tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_fun(X2877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2877,tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_fun(X2877,tc_HOL_Obool)),X2878),c_COMBC(X2877,tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2877,tc_prod(X2878,X2877)),tc_fun(X2877,tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool)),X2878),hAPP(c_COMBB(tc_prod(X2878,X2877),tc_fun(tc_fun(tc_prod(X2878,X2877),tc_HOL_Obool),tc_HOL_Obool),X2877),c_member(tc_prod(X2878,X2877)))),c_Product__Type_OPair(X2878,X2877)))),X2876),X2875) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).
fof(i_0_608,plain,
! [X2193,X2194,X2195,X2196] :
( ( hAPP(hAPP(c_COMBC(X2196,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),X2196),c_COMBC(X2195,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_prod(X2196,X2195)),tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),X2196),hAPP(c_COMBB(tc_prod(X2196,X2195),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool),X2195),c_member(tc_prod(X2196,X2195)))),c_Product__Type_OPair(X2196,X2195)))),X2194) != hAPP(hAPP(c_COMBC(X2196,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),X2196),c_COMBC(X2195,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_prod(X2196,X2195)),tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),X2196),hAPP(c_COMBB(tc_prod(X2196,X2195),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool),X2195),c_member(tc_prod(X2196,X2195)))),c_Product__Type_OPair(X2196,X2195)))),X2193)
| X2194 = X2193 )
& ( X2194 != X2193
| hAPP(hAPP(c_COMBC(X2196,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),X2196),c_COMBC(X2195,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_prod(X2196,X2195)),tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),X2196),hAPP(c_COMBB(tc_prod(X2196,X2195),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool),X2195),c_member(tc_prod(X2196,X2195)))),c_Product__Type_OPair(X2196,X2195)))),X2194) = hAPP(hAPP(c_COMBC(X2196,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_fun(X2195,tc_HOL_Obool)),X2196),c_COMBC(X2195,tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2195,tc_prod(X2196,X2195)),tc_fun(X2195,tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool)),X2196),hAPP(c_COMBB(tc_prod(X2196,X2195),tc_fun(tc_fun(tc_prod(X2196,X2195),tc_HOL_Obool),tc_HOL_Obool),X2195),c_member(tc_prod(X2196,X2195)))),c_Product__Type_OPair(X2196,X2195)))),X2193) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
cnf(i_0_609,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk85_6(X4,X3,X5,X6,X2,X1)),esk86_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_514]) ).
fof(i_0_610,plain,
! [X3046,X3047,X3048,X3049,X3050] :
( ( X3049 = hAPP(hAPP(c_List_Olist_OCons(X3050),X3048),esk77_5(X3046,X3047,X3048,X3049,X3050))
| X3049 = hAPP(hAPP(c_List_Olist_OCons(X3050),esk76_5(X3046,X3047,X3048,X3049,X3050)),X3047)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3050),tc_List_Olist(X3050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3050),tc_List_Olist(X3050)),X3049),hAPP(hAPP(c_List_Olist_OCons(X3050),X3048),X3047))),c_List_Olistrel1(X3050,X3046))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3050),tc_List_Olist(X3050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3050),tc_List_Olist(X3050)),esk77_5(X3046,X3047,X3048,X3049,X3050)),X3047)),c_List_Olistrel1(X3050,X3046)))
| X3049 = hAPP(hAPP(c_List_Olist_OCons(X3050),esk76_5(X3046,X3047,X3048,X3049,X3050)),X3047)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3050),tc_List_Olist(X3050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3050),tc_List_Olist(X3050)),X3049),hAPP(hAPP(c_List_Olist_OCons(X3050),X3048),X3047))),c_List_Olistrel1(X3050,X3046))) )
& ( X3049 = hAPP(hAPP(c_List_Olist_OCons(X3050),X3048),esk77_5(X3046,X3047,X3048,X3049,X3050))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3050,X3050)),hAPP(hAPP(c_Product__Type_OPair(X3050,X3050),esk76_5(X3046,X3047,X3048,X3049,X3050)),X3048)),X3046))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3050),tc_List_Olist(X3050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3050),tc_List_Olist(X3050)),X3049),hAPP(hAPP(c_List_Olist_OCons(X3050),X3048),X3047))),c_List_Olistrel1(X3050,X3046))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3050),tc_List_Olist(X3050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3050),tc_List_Olist(X3050)),esk77_5(X3046,X3047,X3048,X3049,X3050)),X3047)),c_List_Olistrel1(X3050,X3046)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3050,X3050)),hAPP(hAPP(c_Product__Type_OPair(X3050,X3050),esk76_5(X3046,X3047,X3048,X3049,X3050)),X3048)),X3046))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3050),tc_List_Olist(X3050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3050),tc_List_Olist(X3050)),X3049),hAPP(hAPP(c_List_Olist_OCons(X3050),X3048),X3047))),c_List_Olistrel1(X3050,X3046))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_515])])])]) ).
fof(i_0_611,plain,
! [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)),hAPP(hAPP(c_List_Oappend(X2623),X2622),X2621)),hAPP(hAPP(c_List_Oappend(X2623),X2622),X2620))),c_List_Olexord(X2623,X2619)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2623,X2623)),hAPP(hAPP(c_Product__Type_OPair(X2623,X2623),esk43_5(X2619,X2620,X2621,X2622,X2623)),esk43_5(X2619,X2620,X2621,X2622,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)),X2621),X2620)),c_List_Olexord(X2623,X2619))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_516])])]) ).
fof(i_0_612,plain,
! [X3482,X3483,X3484,X3485,X3486,X3487,X3488,X3489] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3489,X3488)),X3487),c_FuncSet_OPi(X3489,X3488,X3486,c_COMBK(tc_fun(X3488,tc_HOL_Obool),X3489,X3485))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3488,X3484)),X3483),c_FuncSet_OPi(X3488,X3484,X3485,c_COMBK(tc_fun(X3484,tc_HOL_Obool),X3488,X3482))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3489,X3484)),c_FuncSet_Ocompose(X3489,X3488,X3484,X3486,X3483,X3487)),c_FuncSet_OPi(X3489,X3484,X3486,c_COMBK(tc_fun(X3484,tc_HOL_Obool),X3489,X3482)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__compose])]) ).
fof(i_0_613,plain,
! [X3326,X3327,X3328,X3329,X3330,X3331] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3329),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3328),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hBOOL(hAPP(hAPP(c_member(X3331),esk84_6(X3326,X3327,X3328,X3329,X3330,X3331)),X3330)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3328),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3329),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hBOOL(hAPP(hAPP(c_member(X3331),esk84_6(X3326,X3327,X3328,X3329,X3330,X3331)),X3330)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3329),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3328),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hAPP(X3329,esk84_6(X3326,X3327,X3328,X3329,X3330,X3331)) != hAPP(X3328,esk84_6(X3326,X3327,X3328,X3329,X3330,X3331)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3328),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3331,X3327)),X3329),c_FuncSet_OPi(X3331,X3327,X3330,X3326)))
| hAPP(X3329,esk84_6(X3326,X3327,X3328,X3329,X3330,X3331)) != hAPP(X3328,esk84_6(X3326,X3327,X3328,X3329,X3330,X3331)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__cong])])])]) ).
fof(i_0_614,plain,
! [X3411,X3412,X3413,X3414,X3415] :
( ( hBOOL(hAPP(hAPP(c_member(X3415),esk89_5(X3411,X3412,X3413,X3414,X3415)),X3414))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3415,X3413)),X3412),c_FuncSet_OPi(X3415,X3413,X3414,X3411))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3413),hAPP(X3412,esk89_5(X3411,X3412,X3413,X3414,X3415))),hAPP(X3411,esk89_5(X3411,X3412,X3413,X3414,X3415))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3415,X3413)),X3412),c_FuncSet_OPi(X3415,X3413,X3414,X3411))) ) ),
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_615,plain,
! [X2331,X2332,X2333,X2334,X2335] :
( ( hBOOL(hAPP(hAPP(c_member(X2335),esk23_5(X2331,X2332,X2333,X2334,X2335)),X2334))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2335,X2333)),X2332),c_FuncSet_OPi(X2335,X2333,X2334,X2331))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2333),hAPP(X2332,esk23_5(X2331,X2332,X2333,X2334,X2335))),hAPP(X2331,esk23_5(X2331,X2332,X2333,X2334,X2335))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2335,X2333)),X2332),c_FuncSet_OPi(X2335,X2333,X2334,X2331))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_616,plain,
! [X2705,X2706,X2707,X2708,X2709] :
( ( X2706 = hAPP(hAPP(c_List_Olist_OCons(X2709),X2708),esk45_5(X2705,X2706,X2707,X2708,X2709))
| X2706 = hAPP(hAPP(c_List_Olist_OCons(X2709),esk44_5(X2705,X2706,X2707,X2708,X2709)),X2707)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2709),tc_List_Olist(X2709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2709),tc_List_Olist(X2709)),hAPP(hAPP(c_List_Olist_OCons(X2709),X2708),X2707)),X2706)),c_List_Olistrel1(X2709,X2705))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2709),tc_List_Olist(X2709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2709),tc_List_Olist(X2709)),X2707),esk45_5(X2705,X2706,X2707,X2708,X2709))),c_List_Olistrel1(X2709,X2705)))
| X2706 = hAPP(hAPP(c_List_Olist_OCons(X2709),esk44_5(X2705,X2706,X2707,X2708,X2709)),X2707)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2709),tc_List_Olist(X2709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2709),tc_List_Olist(X2709)),hAPP(hAPP(c_List_Olist_OCons(X2709),X2708),X2707)),X2706)),c_List_Olistrel1(X2709,X2705))) )
& ( X2706 = hAPP(hAPP(c_List_Olist_OCons(X2709),X2708),esk45_5(X2705,X2706,X2707,X2708,X2709))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2709,X2709)),hAPP(hAPP(c_Product__Type_OPair(X2709,X2709),X2708),esk44_5(X2705,X2706,X2707,X2708,X2709))),X2705))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2709),tc_List_Olist(X2709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2709),tc_List_Olist(X2709)),hAPP(hAPP(c_List_Olist_OCons(X2709),X2708),X2707)),X2706)),c_List_Olistrel1(X2709,X2705))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2709),tc_List_Olist(X2709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2709),tc_List_Olist(X2709)),X2707),esk45_5(X2705,X2706,X2707,X2708,X2709))),c_List_Olistrel1(X2709,X2705)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2709,X2709)),hAPP(hAPP(c_Product__Type_OPair(X2709,X2709),X2708),esk44_5(X2705,X2706,X2707,X2708,X2709))),X2705))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2709),tc_List_Olist(X2709))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2709),tc_List_Olist(X2709)),hAPP(hAPP(c_List_Olist_OCons(X2709),X2708),X2707)),X2706)),c_List_Olistrel1(X2709,X2705))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_517])])])]) ).
fof(i_0_617,plain,
! [X3471,X3472,X3473,X3474,X3475,X3476,X3477,X3478,X3479,X3480,X3481] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3481,X3480)),X3479),c_FuncSet_OPi(X3481,X3480,X3478,c_COMBK(tc_fun(X3480,tc_HOL_Obool),X3481,X3477))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3480,X3476)),X3475),c_FuncSet_OPi(X3480,X3476,X3477,c_COMBK(tc_fun(X3476,tc_HOL_Obool),X3480,X3474))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3476,X3473)),X3472),c_FuncSet_OPi(X3476,X3473,X3474,c_COMBK(tc_fun(X3473,tc_HOL_Obool),X3476,X3471))))
| c_FuncSet_Ocompose(X3481,X3476,X3473,X3478,X3472,c_FuncSet_Ocompose(X3481,X3480,X3476,X3478,X3475,X3479)) = c_FuncSet_Ocompose(X3481,X3480,X3473,X3478,c_FuncSet_Ocompose(X3480,X3476,X3473,X3477,X3472,X3475),X3479) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__assoc])]) ).
fof(i_0_618,plain,
! [X4030,X4031,X4032,X4033,X4034,X4035,X4036,X4037,X4038] :
( ( c_Nat_Osize__class_Osize(tc_List_Olist(X4033),X4032) = c_Nat_Osize__class_Osize(tc_List_Olist(X4033),X4031)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4033),tc_List_Olist(X4033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4033),tc_List_Olist(X4033)),X4032),X4031)),c_List_Olistrel(X4033,X4030))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4034,c_Nat_Osize__class_Osize(tc_List_Olist(X4033),X4032))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4033,X4033)),hAPP(hAPP(c_Product__Type_OPair(X4033,X4033),c_List_Onth(X4033,X4032,X4034)),c_List_Onth(X4033,X4031,X4034))),X4030))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4033),tc_List_Olist(X4033))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4033),tc_List_Olist(X4033)),X4032),X4031)),c_List_Olistrel(X4033,X4030))) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk96_4(X4035,X4036,X4037,X4038),c_Nat_Osize__class_Osize(tc_List_Olist(X4038),X4037))
| c_Nat_Osize__class_Osize(tc_List_Olist(X4038),X4037) != c_Nat_Osize__class_Osize(tc_List_Olist(X4038),X4036)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4038),tc_List_Olist(X4038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4038),tc_List_Olist(X4038)),X4037),X4036)),c_List_Olistrel(X4038,X4035))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4038,X4038)),hAPP(hAPP(c_Product__Type_OPair(X4038,X4038),c_List_Onth(X4038,X4037,esk96_4(X4035,X4036,X4037,X4038))),c_List_Onth(X4038,X4036,esk96_4(X4035,X4036,X4037,X4038)))),X4035))
| c_Nat_Osize__class_Osize(tc_List_Olist(X4038),X4037) != c_Nat_Osize__class_Osize(tc_List_Olist(X4038),X4036)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4038),tc_List_Olist(X4038))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4038),tc_List_Olist(X4038)),X4037),X4036)),c_List_Olistrel(X4038,X4035))) ) ),
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_listrel__iff__nth])])])])])]) ).
fof(i_0_619,plain,
! [X2604,X2605,X2606,X2607,X2608] :
( ( X2607 = hAPP(hAPP(c_List_Olist_OCons(X2608),esk37_5(X2604,X2605,X2606,X2607,X2608)),esk38_5(X2604,X2605,X2606,X2607,X2608))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2608),tc_List_Olist(X2608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2608),tc_List_Olist(X2608)),X2607),hAPP(hAPP(c_List_Olist_OCons(X2608),X2606),X2605))),c_List_Olistrel(X2608,X2604))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2608,X2608)),hAPP(hAPP(c_Product__Type_OPair(X2608,X2608),esk37_5(X2604,X2605,X2606,X2607,X2608)),X2606)),X2604))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2608),tc_List_Olist(X2608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2608),tc_List_Olist(X2608)),X2607),hAPP(hAPP(c_List_Olist_OCons(X2608),X2606),X2605))),c_List_Olistrel(X2608,X2604))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2608),tc_List_Olist(X2608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2608),tc_List_Olist(X2608)),esk38_5(X2604,X2605,X2606,X2607,X2608)),X2605)),c_List_Olistrel(X2608,X2604)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2608),tc_List_Olist(X2608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2608),tc_List_Olist(X2608)),X2607),hAPP(hAPP(c_List_Olist_OCons(X2608),X2606),X2605))),c_List_Olistrel(X2608,X2604))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_518])])])]) ).
fof(i_0_620,plain,
! [X2210,X2211,X2212,X2213,X2214,X2216,X2221,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),X2213),X2214)),hAPP(X2210,X2211)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2210,X2212)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2211,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2212,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| ~ 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))),X2212),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))),X2211),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2210) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2210,X2212)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2210,X2211)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2211,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2212,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| ~ 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))),X2212),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))),X2211),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2210) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2210,X2211)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2210,X2212)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2211,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2212,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| ~ 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))),X2212),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))),X2211),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2210) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2210,X2212)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2210,X2211)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2211,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2213),X2214)),hAPP(X2212,esk9_5(X2210,X2211,X2212,X2213,X2214))))
| ~ 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))),X2212),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))),X2211),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2210) )
& ( 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))),esk10_1(X2216)),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))),esk11_1(X2216)),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),esk12_1(X2216)),esk13_1(X2216))),hAPP(esk10_1(X2216),X2221)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X2216)),esk13_1(X2216))),hAPP(esk11_1(X2216),X2221)))
| 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),esk12_1(X2216)),esk13_1(X2216))),hAPP(esk11_1(X2216),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),esk12_1(X2216)),esk13_1(X2216))),hAPP(esk10_1(X2216),X2222)))
| 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),esk12_1(X2216)),esk13_1(X2216))),hAPP(X2216,esk10_1(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),esk12_1(X2216)),esk13_1(X2216))),hAPP(X2216,esk11_1(X2216))))
| 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),esk12_1(X2216)),esk13_1(X2216))),hAPP(X2216,esk10_1(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),esk12_1(X2216)),esk13_1(X2216))),hAPP(X2216,esk11_1(X2216))))
| c_Arrow__Order__Mirabelle_OIIA(X2216) ) ),
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])])])])])]) ).
cnf(i_0_621,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk85_6(X1,X4,X3,X2,X5,X6)),esk86_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_514]) ).
cnf(i_0_622,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk87_6(X4,X5,X6,X3,X2,X1)),esk88_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_513]) ).
fof(i_0_623,plain,
! [X2356,X2357,X2358,X2359,X2360] :
( ( hBOOL(hAPP(hAPP(c_member(X2360),esk25_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,esk25_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])])])]) ).
cnf(i_0_624,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_519]) ).
fof(i_0_625,plain,
! [X2597,X2598,X2599,X2600,X2601] :
( ( X2598 = hAPP(hAPP(c_List_Olist_OCons(X2601),esk35_5(X2597,X2598,X2599,X2600,X2601)),esk36_5(X2597,X2598,X2599,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)),hAPP(hAPP(c_List_Olist_OCons(X2601),X2600),X2599)),X2598)),c_List_Olistrel(X2601,X2597))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2601,X2601)),hAPP(hAPP(c_Product__Type_OPair(X2601,X2601),X2600),esk35_5(X2597,X2598,X2599,X2600,X2601))),X2597))
| ~ 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)),hAPP(hAPP(c_List_Olist_OCons(X2601),X2600),X2599)),X2598)),c_List_Olistrel(X2601,X2597))) )
& ( 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)),X2599),esk36_5(X2597,X2598,X2599,X2600,X2601))),c_List_Olistrel(X2601,X2597)))
| ~ 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)),hAPP(hAPP(c_List_Olist_OCons(X2601),X2600),X2599)),X2598)),c_List_Olistrel(X2601,X2597))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_520])])])]) ).
fof(i_0_626,plain,
! [X2413,X2414,X2415,X2416] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2416,X2416)),hAPP(hAPP(c_Product__Type_OPair(X2416,X2416),esk28_4(X2413,X2414,X2415,X2416)),esk29_4(X2413,X2414,X2415,X2416))),X2415))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2416),tc_List_Olist(X2416))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2416),tc_List_Olist(X2416)),X2414),X2413)),c_List_Olexord(X2416,X2415)))
| X2414 = X2413
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2416),tc_List_Olist(X2416))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2416),tc_List_Olist(X2416)),X2413),X2414)),c_List_Olexord(X2416,X2415))) )
& ( esk28_4(X2413,X2414,X2415,X2416) != esk29_4(X2413,X2414,X2415,X2416)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2416),tc_List_Olist(X2416))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2416),tc_List_Olist(X2416)),X2414),X2413)),c_List_Olexord(X2416,X2415)))
| X2414 = X2413
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2416),tc_List_Olist(X2416))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2416),tc_List_Olist(X2416)),X2413),X2414)),c_List_Olexord(X2416,X2415))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2416,X2416)),hAPP(hAPP(c_Product__Type_OPair(X2416,X2416),esk29_4(X2413,X2414,X2415,X2416)),esk28_4(X2413,X2414,X2415,X2416))),X2415))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2416),tc_List_Olist(X2416))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2416),tc_List_Olist(X2416)),X2414),X2413)),c_List_Olexord(X2416,X2415)))
| X2414 = X2413
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2416),tc_List_Olist(X2416))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2416),tc_List_Olist(X2416)),X2413),X2414)),c_List_Olexord(X2416,X2415))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])]) ).
fof(i_0_627,plain,
! [X4151,X4152,X4153,X4154,X4155] :
( ( hBOOL(hAPP(hAPP(c_member(X4155),esk101_5(X4151,X4152,X4153,X4154,X4155)),X4152))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4155,X4154)),X4153),c_Product__Type_OSigma(X4155,X4154,X4152,X4151))) )
& ( hBOOL(hAPP(hAPP(c_member(X4154),esk102_5(X4151,X4152,X4153,X4154,X4155)),hAPP(X4151,esk101_5(X4151,X4152,X4153,X4154,X4155))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4155,X4154)),X4153),c_Product__Type_OSigma(X4155,X4154,X4152,X4151))) )
& ( X4153 = hAPP(hAPP(c_Product__Type_OPair(X4155,X4154),esk101_5(X4151,X4152,X4153,X4154,X4155)),esk102_5(X4151,X4152,X4153,X4154,X4155))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4155,X4154)),X4153),c_Product__Type_OSigma(X4155,X4154,X4152,X4151))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaE])])])]) ).
fof(i_0_628,plain,
! [X3019,X3020,X3021,X3022] :
( ( hBOOL(hAPP(c_List_Olistsp(X3022,X3021),X3019))
| ~ hBOOL(hAPP(c_List_Olistsp(X3022,hAPP(hAPP(c_COMBS(X3022,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3022),c_fconj),X3021)),X3020)),X3019)) )
& ( hBOOL(hAPP(c_List_Olistsp(X3022,X3020),X3019))
| ~ hBOOL(hAPP(c_List_Olistsp(X3022,hAPP(hAPP(c_COMBS(X3022,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3022),c_fconj),X3021)),X3020)),X3019)) )
& ( ~ hBOOL(hAPP(c_List_Olistsp(X3022,X3021),X3019))
| ~ hBOOL(hAPP(c_List_Olistsp(X3022,X3020),X3019))
| hBOOL(hAPP(c_List_Olistsp(X3022,hAPP(hAPP(c_COMBS(X3022,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3022),c_fconj),X3021)),X3020)),X3019)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])]) ).
fof(i_0_629,plain,
! [X3042,X3043,X3044,X3045] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3045)),X3044),c_List_Olists(X3045,X3043)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X3045)),X3044),c_List_Olists(X3045,X3042)))
| hBOOL(hAPP(c_List_Olistsp(X3045,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3045,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3045,tc_fun(X3045,tc_HOL_Obool),tc_HOL_Obool),c_member(X3045)),X3043)),hAPP(hAPP(c_COMBC(X3045,tc_fun(X3045,tc_HOL_Obool),tc_HOL_Obool),c_member(X3045)),X3042))),X3044)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__IntI])]) ).
fof(i_0_630,plain,
! [X2564,X2565,X2566,X2567,X2568,X2569] :
( ( X2568 = X2566
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),X2568),X2566)),c_List_Olistrel1(X2569,X2564)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),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))))),c_List_Olistrel1(X2569,X2564))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2569,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2569,X2569),X2567),X2565)),X2564))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),X2568),X2566)),c_List_Olistrel1(X2569,X2564)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),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))))),c_List_Olistrel1(X2569,X2564))) )
& ( X2568 = X2566
| X2567 = X2565
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),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))))),c_List_Olistrel1(X2569,X2564))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2569,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2569,X2569),X2567),X2565)),X2564))
| X2567 = X2565
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),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))))),c_List_Olistrel1(X2569,X2564))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),X2568),X2566)),c_List_Olistrel1(X2569,X2564)))
| X2567 != X2565
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),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))))),c_List_Olistrel1(X2569,X2564))) )
& ( X2568 != X2566
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2569,X2569)),hAPP(hAPP(c_Product__Type_OPair(X2569,X2569),X2567),X2565)),X2564))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2569),tc_List_Olist(X2569))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2569),tc_List_Olist(X2569)),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))))),c_List_Olistrel1(X2569,X2564))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).
fof(i_0_631,plain,
! [X3790,X3791,X3792,X3793,X3794] :
( ( hBOOL(hAPP(hAPP(c_member(X3794),esk95_5(X3790,X3791,X3792,X3793,X3794)),X3793))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3794,X3792),tc_HOL_Obool),c_FuncSet_OPi(X3794,X3792,X3793,X3791),c_FuncSet_OPi(X3794,X3792,X3793,X3790)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3792,tc_HOL_Obool),hAPP(X3791,esk95_5(X3790,X3791,X3792,X3793,X3794)),hAPP(X3790,esk95_5(X3790,X3791,X3792,X3793,X3794)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3794,X3792),tc_HOL_Obool),c_FuncSet_OPi(X3794,X3792,X3793,X3791),c_FuncSet_OPi(X3794,X3792,X3793,X3790)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_632,plain,
! [X2299,X2300,X2301,X2302,X2303,X2304,X2305,X2306] :
( ( X2304 = X2302
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2306,X2306)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2306),X2304),X2302)),X2300))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2306,X2305),tc_prod(X2306,X2305))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2306,X2305),tc_prod(X2306,X2305)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2304),X2303)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2302),X2301))),c_Wellfounded_Olex__prod(X2306,X2305,X2300,X2299))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2305,X2305)),hAPP(hAPP(c_Product__Type_OPair(X2305,X2305),X2303),X2301)),X2299))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2306,X2306)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2306),X2304),X2302)),X2300))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2306,X2305),tc_prod(X2306,X2305))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2306,X2305),tc_prod(X2306,X2305)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2304),X2303)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2302),X2301))),c_Wellfounded_Olex__prod(X2306,X2305,X2300,X2299))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2306,X2306)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2306),X2304),X2302)),X2300))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2306,X2305),tc_prod(X2306,X2305))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2306,X2305),tc_prod(X2306,X2305)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2304),X2303)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2302),X2301))),c_Wellfounded_Olex__prod(X2306,X2305,X2300,X2299))) )
& ( X2304 != X2302
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2305,X2305)),hAPP(hAPP(c_Product__Type_OPair(X2305,X2305),X2303),X2301)),X2299))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2306,X2305),tc_prod(X2306,X2305))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2306,X2305),tc_prod(X2306,X2305)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2304),X2303)),hAPP(hAPP(c_Product__Type_OPair(X2306,X2305),X2302),X2301))),c_Wellfounded_Olex__prod(X2306,X2305,X2300,X2299))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_633,plain,
! [X2294,X2295] :
( ( 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))),esk18_2(X2294,X2295)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2295,X2294)
| ~ 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))),X2295),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)))) )
& ( esk19_2(X2294,X2295) != esk20_2(X2294,X2295)
| c_Arrow__Order__Mirabelle_Odictator(X2295,X2294)
| ~ 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))),X2295),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),esk19_2(X2294,X2295)),esk20_2(X2294,X2295))),hAPP(esk18_2(X2294,X2295),X2294)))
| c_Arrow__Order__Mirabelle_Odictator(X2295,X2294)
| ~ 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))),X2295),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),esk19_2(X2294,X2295)),esk20_2(X2294,X2295))),hAPP(X2295,esk18_2(X2294,X2295))))
| c_Arrow__Order__Mirabelle_Odictator(X2295,X2294)
| ~ 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))),X2295),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_634,plain,
! [X2611,X2612,X2613,X2614] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2614,X2614)),hAPP(hAPP(c_Product__Type_OPair(X2614,X2614),esk39_4(X2611,X2612,X2613,X2614)),esk40_4(X2611,X2612,X2613,X2614))),X2611))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2614),tc_List_Olist(X2614))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2614),tc_List_Olist(X2614)),X2613),X2612)),c_List_Olistrel1(X2614,X2611))) )
& ( X2613 = hAPP(hAPP(c_List_Oappend(X2614),esk41_4(X2611,X2612,X2613,X2614)),hAPP(hAPP(c_List_Olist_OCons(X2614),esk39_4(X2611,X2612,X2613,X2614)),esk42_4(X2611,X2612,X2613,X2614)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2614),tc_List_Olist(X2614))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2614),tc_List_Olist(X2614)),X2613),X2612)),c_List_Olistrel1(X2614,X2611))) )
& ( X2612 = hAPP(hAPP(c_List_Oappend(X2614),esk41_4(X2611,X2612,X2613,X2614)),hAPP(hAPP(c_List_Olist_OCons(X2614),esk40_4(X2611,X2612,X2613,X2614)),esk42_4(X2611,X2612,X2613,X2614)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2614),tc_List_Olist(X2614))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2614),tc_List_Olist(X2614)),X2613),X2612)),c_List_Olistrel1(X2614,X2611))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).
fof(i_0_635,plain,
! [X3151,X3152,X3153,X3154] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3154,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3154,tc_fun(X3154,tc_HOL_Obool),tc_HOL_Obool),c_member(X3154)),X3153)),hAPP(hAPP(c_COMBC(X3154,tc_fun(X3154,tc_HOL_Obool),tc_HOL_Obool),c_member(X3154)),X3152)),X3151))
| hBOOL(hAPP(hAPP(c_member(X3154),X3151),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3154,tc_HOL_Obool)),X3153),X3152))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3154),X3151),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3154,tc_HOL_Obool)),X3153),X3152)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3154,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3154,tc_fun(X3154,tc_HOL_Obool),tc_HOL_Obool),c_member(X3154)),X3153)),hAPP(hAPP(c_COMBC(X3154,tc_fun(X3154,tc_HOL_Obool),tc_HOL_Obool),c_member(X3154)),X3152)),X3151)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).
fof(i_0_636,plain,
! [X3672,X3673,X3674,X3675,X3676,X3677,X3678,X3679] :
( c_Set_Oimage(X3679,X3678,X3677,X3676) != X3675
| c_Set_Oimage(X3678,X3674,X3673,X3675) != X3672
| c_Set_Oimage(X3679,X3674,c_FuncSet_Ocompose(X3679,X3678,X3674,X3676,X3673,X3677),X3676) = X3672 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__compose])]) ).
fof(i_0_637,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_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk104_0)),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____,esk104_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_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk104_0)),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____,esk104_0)),v_c____),v_b____)),v_b____),v_a____))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])])]) ).
fof(i_0_638,plain,
! [X3499,X3500,X3501,X3502,X3503,X3504,X3505] :
( ~ hBOOL(hAPP(hAPP(c_member(X3505),X3504),X3503))
| hAPP(c_FuncSet_Ocompose(X3505,X3502,X3501,X3503,X3500,X3499),X3504) = hAPP(X3500,hAPP(X3499,X3504)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compose__eq])]) ).
fof(i_0_639,plain,
! [X2435,X2436,X2437,X2438,X2439,X2440,X2441] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2441,X2441)),hAPP(hAPP(c_Product__Type_OPair(X2441,X2441),X2440),X2439)),X2438))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2441),tc_List_Olist(X2441))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2441),tc_List_Olist(X2441)),hAPP(hAPP(c_List_Oappend(X2441),X2437),hAPP(hAPP(c_List_Olist_OCons(X2441),X2440),X2436))),hAPP(hAPP(c_List_Oappend(X2441),X2437),hAPP(hAPP(c_List_Olist_OCons(X2441),X2439),X2435)))),c_List_Olexord(X2441,X2438))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).
fof(i_0_640,plain,
! [X2126,X2127,X2128,X2129,X2130,X2131,X2132] :
( ~ hBOOL(hAPP(X2132,X2131))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2130,X2130)),hAPP(hAPP(c_Product__Type_OPair(X2130,X2130),X2129),X2128)),hAPP(X2127,X2131)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2126,X2130),tc_prod(X2126,X2130))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2126,X2130),tc_prod(X2126,X2130)),hAPP(hAPP(c_Product__Type_OPair(X2126,X2130),X2131),X2129)),hAPP(hAPP(c_Product__Type_OPair(X2126,X2130),X2131),X2128))),c_Recdef_Osame__fst(X2126,X2130,X2132,X2127))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
cnf(i_0_641,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_522]) ).
fof(i_0_642,plain,
! [X4119,X4120,X4121,X4122,X4123] : c_Product__Type_OSigma(X4123,X4122,X4121,hAPP(hAPP(c_COMBS(X4123,tc_fun(X4122,tc_HOL_Obool),tc_fun(X4122,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X4122,tc_HOL_Obool),tc_fun(tc_fun(X4122,tc_HOL_Obool),tc_fun(X4122,tc_HOL_Obool)),X4123),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4122,tc_HOL_Obool))),X4120)),X4119)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4123,X4122),tc_HOL_Obool)),c_Product__Type_OSigma(X4123,X4122,X4121,X4120)),c_Product__Type_OSigma(X4123,X4122,X4121,X4119)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).
fof(i_0_643,plain,
! [X2468,X2469,X2470,X2471,X2472,X2475,X2476,X2477,X2478,X2479,X2480,X2481] :
( ( hAPP(hAPP(c_List_Oappend(X2472),X2471),esk32_5(X2468,X2469,X2470,X2471,X2472)) = X2469
| X2471 = hAPP(hAPP(c_List_Oappend(X2472),X2469),esk31_5(X2468,X2469,X2470,X2471,X2472))
| hAPP(hAPP(c_List_Oappend(X2472),X2471),X2470) != hAPP(hAPP(c_List_Oappend(X2472),X2469),X2468) )
& ( X2470 = hAPP(hAPP(c_List_Oappend(X2472),esk32_5(X2468,X2469,X2470,X2471,X2472)),X2468)
| X2471 = hAPP(hAPP(c_List_Oappend(X2472),X2469),esk31_5(X2468,X2469,X2470,X2471,X2472))
| hAPP(hAPP(c_List_Oappend(X2472),X2471),X2470) != hAPP(hAPP(c_List_Oappend(X2472),X2469),X2468) )
& ( hAPP(hAPP(c_List_Oappend(X2472),X2471),esk32_5(X2468,X2469,X2470,X2471,X2472)) = X2469
| hAPP(hAPP(c_List_Oappend(X2472),esk31_5(X2468,X2469,X2470,X2471,X2472)),X2470) = X2468
| hAPP(hAPP(c_List_Oappend(X2472),X2471),X2470) != hAPP(hAPP(c_List_Oappend(X2472),X2469),X2468) )
& ( X2470 = hAPP(hAPP(c_List_Oappend(X2472),esk32_5(X2468,X2469,X2470,X2471,X2472)),X2468)
| hAPP(hAPP(c_List_Oappend(X2472),esk31_5(X2468,X2469,X2470,X2471,X2472)),X2470) = X2468
| hAPP(hAPP(c_List_Oappend(X2472),X2471),X2470) != hAPP(hAPP(c_List_Oappend(X2472),X2469),X2468) )
& ( X2478 != hAPP(hAPP(c_List_Oappend(X2479),X2476),X2480)
| hAPP(hAPP(c_List_Oappend(X2479),X2480),X2477) != X2475
| hAPP(hAPP(c_List_Oappend(X2479),X2478),X2477) = hAPP(hAPP(c_List_Oappend(X2479),X2476),X2475) )
& ( hAPP(hAPP(c_List_Oappend(X2479),X2478),X2481) != X2476
| X2477 != hAPP(hAPP(c_List_Oappend(X2479),X2481),X2475)
| hAPP(hAPP(c_List_Oappend(X2479),X2478),X2477) = hAPP(hAPP(c_List_Oappend(X2479),X2476),X2475) ) ),
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_644,plain,
! [X2883,X2884,X2885,X2886] :
( ~ hBOOL(hAPP(hAPP(c_member(X2886),X2885),c_Relation_ORange(X2884,X2886,X2883)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2884,X2886)),hAPP(hAPP(c_Product__Type_OPair(X2884,X2886),esk56_4(X2883,X2884,X2885,X2886)),X2885)),X2883)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])])]) ).
fof(i_0_645,plain,
! [X2853,X2854,X2855,X2856,X2858,X2859,X2860,X2861,X2862] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2856),X2855),c_Relation_ORange(X2854,X2856,X2853)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2854,X2856)),hAPP(hAPP(c_Product__Type_OPair(X2854,X2856),esk54_4(X2853,X2854,X2855,X2856)),X2855)),X2853)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2859,X2861)),hAPP(hAPP(c_Product__Type_OPair(X2859,X2861),X2862),X2860)),X2858))
| hBOOL(hAPP(hAPP(c_member(X2861),X2860),c_Relation_ORange(X2859,X2861,X2858))) ) ),
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_646,plain,
! [X2442,X2443,X2444,X2445,X2446,X2447] :
( ( X2446 = X2444
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2447,X2447)),hAPP(hAPP(c_Product__Type_OPair(X2447,X2447),X2446),X2444)),X2442))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2446),X2445)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2444),X2443))),c_List_Olistrel1(X2447,X2442))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),X2445),X2443)),c_List_Olistrel1(X2447,X2442)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2447,X2447)),hAPP(hAPP(c_Product__Type_OPair(X2447,X2447),X2446),X2444)),X2442))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2446),X2445)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2444),X2443))),c_List_Olistrel1(X2447,X2442))) )
& ( X2446 = X2444
| X2445 = X2443
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2446),X2445)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2444),X2443))),c_List_Olistrel1(X2447,X2442))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),X2445),X2443)),c_List_Olistrel1(X2447,X2442)))
| X2445 = X2443
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2446),X2445)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2444),X2443))),c_List_Olistrel1(X2447,X2442))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2447,X2447)),hAPP(hAPP(c_Product__Type_OPair(X2447,X2447),X2446),X2444)),X2442))
| X2445 != X2443
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2446),X2445)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2444),X2443))),c_List_Olistrel1(X2447,X2442))) )
& ( X2446 != X2444
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),X2445),X2443)),c_List_Olistrel1(X2447,X2442)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2447),tc_List_Olist(X2447))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2447),tc_List_Olist(X2447)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2446),X2445)),hAPP(hAPP(c_List_Olist_OCons(X2447),X2444),X2443))),c_List_Olistrel1(X2447,X2442))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).
fof(i_0_647,plain,
! [X2631,X2632,X2633,X2634,X2635,X2636] :
( ( X2635 = X2633
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2636,X2636)),hAPP(hAPP(c_Product__Type_OPair(X2636,X2636),X2635),X2633)),X2631))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2635),X2634)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2633),X2632))),c_List_Olex(X2636,X2631))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),X2634),X2632)),c_List_Olex(X2636,X2631)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2636,X2636)),hAPP(hAPP(c_Product__Type_OPair(X2636,X2636),X2635),X2633)),X2631))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2635),X2634)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2633),X2632))),c_List_Olex(X2636,X2631))) )
& ( X2635 = X2633
| c_Nat_Osize__class_Osize(tc_List_Olist(X2636),X2634) = c_Nat_Osize__class_Osize(tc_List_Olist(X2636),X2632)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2635),X2634)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2633),X2632))),c_List_Olex(X2636,X2631))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),X2634),X2632)),c_List_Olex(X2636,X2631)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2636),X2634) = c_Nat_Osize__class_Osize(tc_List_Olist(X2636),X2632)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2635),X2634)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2633),X2632))),c_List_Olex(X2636,X2631))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2636,X2636)),hAPP(hAPP(c_Product__Type_OPair(X2636,X2636),X2635),X2633)),X2631))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2636),X2634) != c_Nat_Osize__class_Osize(tc_List_Olist(X2636),X2632)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2635),X2634)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2633),X2632))),c_List_Olex(X2636,X2631))) )
& ( X2635 != X2633
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),X2634),X2632)),c_List_Olex(X2636,X2631)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2636),tc_List_Olist(X2636))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2636),tc_List_Olist(X2636)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2635),X2634)),hAPP(hAPP(c_List_Olist_OCons(X2636),X2633),X2632))),c_List_Olex(X2636,X2631))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).
fof(i_0_648,plain,
! [X2368,X2369,X2370,X2371,X2372,X2373] :
( ( X2372 = X2370
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2373,X2373)),hAPP(hAPP(c_Product__Type_OPair(X2373,X2373),X2372),X2370)),X2368))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2373),tc_List_Olist(X2373))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2373),tc_List_Olist(X2373)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2372),X2371)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2370),X2369))),c_List_Olexord(X2373,X2368))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2373),tc_List_Olist(X2373))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2373),tc_List_Olist(X2373)),X2371),X2369)),c_List_Olexord(X2373,X2368)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2373,X2373)),hAPP(hAPP(c_Product__Type_OPair(X2373,X2373),X2372),X2370)),X2368))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2373),tc_List_Olist(X2373))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2373),tc_List_Olist(X2373)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2372),X2371)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2370),X2369))),c_List_Olexord(X2373,X2368))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2373,X2373)),hAPP(hAPP(c_Product__Type_OPair(X2373,X2373),X2372),X2370)),X2368))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2373),tc_List_Olist(X2373))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2373),tc_List_Olist(X2373)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2372),X2371)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2370),X2369))),c_List_Olexord(X2373,X2368))) )
& ( X2372 != X2370
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2373),tc_List_Olist(X2373))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2373),tc_List_Olist(X2373)),X2371),X2369)),c_List_Olexord(X2373,X2368)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2373),tc_List_Olist(X2373))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2373),tc_List_Olist(X2373)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2372),X2371)),hAPP(hAPP(c_List_Olist_OCons(X2373),X2370),X2369))),c_List_Olexord(X2373,X2368))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).
fof(i_0_649,plain,
! [X2725,X2726,X2727,X2728,X2729,X2730] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2730,X2730)),hAPP(hAPP(c_Product__Type_OPair(X2730,X2730),X2729),X2728)),c_Transitive__Closure_Ortrancl(X2730,X2727)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),X2726),X2725)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2730),c_List_Olistrel1(X2730,X2727))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2730),tc_List_Olist(X2730))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2730),tc_List_Olist(X2730)),hAPP(hAPP(c_List_Olist_OCons(X2730),X2729),X2726)),hAPP(hAPP(c_List_Olist_OCons(X2730),X2728),X2725))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2730),c_List_Olistrel1(X2730,X2727)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).
fof(i_0_650,plain,
! [X2429,X2430,X2431,X2432,X2433,X2434] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2434,X2434)),hAPP(hAPP(c_Product__Type_OPair(X2434,X2434),X2433),X2432)),X2431))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2434),tc_List_Olist(X2434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2434),tc_List_Olist(X2434)),X2430),X2429)),c_List_Olistrel(X2434,X2431)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2434),tc_List_Olist(X2434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2434),tc_List_Olist(X2434)),hAPP(hAPP(c_List_Olist_OCons(X2434),X2433),X2430)),hAPP(hAPP(c_List_Olist_OCons(X2434),X2432),X2429))),c_List_Olistrel(X2434,X2431))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).
fof(i_0_651,plain,
! [X2223,X2224,X2225,X2226,X2228,X2232] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2223)
| ~ 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))),X2224),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),X2225),X2226)),hAPP(X2224,esk14_4(X2223,X2224,X2225,X2226))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2226)),hAPP(X2223,X2224))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk15_1(X2228)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(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),esk16_1(X2228)),esk17_1(X2228))),hAPP(esk15_1(X2228),X2232)))
| c_Arrow__Order__Mirabelle_Ounanimity(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),esk16_1(X2228)),esk17_1(X2228))),hAPP(X2228,esk15_1(X2228))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2228) ) ),
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_652,plain,
! [X3167,X3168,X3169] : c_List_Olistsp(X3169,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3169,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3169,tc_fun(X3169,tc_HOL_Obool),tc_HOL_Obool),c_member(X3169)),X3168)),hAPP(hAPP(c_COMBC(X3169,tc_fun(X3169,tc_HOL_Obool),tc_HOL_Obool),c_member(X3169)),X3167))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X3169),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X3169),tc_fun(tc_List_Olist(X3169),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X3169))),c_List_Olists(X3169,X3168))),hAPP(hAPP(c_COMBC(tc_List_Olist(X3169),tc_fun(tc_List_Olist(X3169),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X3169))),c_List_Olists(X3169,X3167))),
inference(variable_rename,[status(thm)],[fact_lists__Int__eq]) ).
fof(i_0_653,plain,
! [X2734,X2735,X2736,X2737,X2738] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2738),tc_List_Olist(X2738))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2738),tc_List_Olist(X2738)),X2737),X2736)),c_List_Olistrel(X2738,c_Transitive__Closure_Ortrancl(X2738,X2735))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2738),tc_List_Olist(X2738))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2738),tc_List_Olist(X2738)),X2736),X2734)),c_List_Olistrel(X2738,c_Transitive__Closure_Ortrancl(X2738,X2735))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2738),tc_List_Olist(X2738))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2738),tc_List_Olist(X2738)),X2737),X2734)),c_List_Olistrel(X2738,c_Transitive__Closure_Ortrancl(X2738,X2735)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).
fof(i_0_654,plain,
! [X4158,X4159,X4160,X4161,X4162,X4163,X4164] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4160,X4160),tc_HOL_Obool),X4158,c_Product__Type_OSigma(X4160,X4160,X4159,c_COMBK(tc_fun(X4160,tc_HOL_Obool),X4160,X4159)))
| ~ c_Relation_Orefl__on(X4160,X4159,X4158) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4160),X4161),X4159))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4160,X4160)),hAPP(hAPP(c_Product__Type_OPair(X4160,X4160),X4161),X4161)),X4158))
| ~ c_Relation_Orefl__on(X4160,X4159,X4158) )
& ( hBOOL(hAPP(hAPP(c_member(X4164),esk103_3(X4162,X4163,X4164)),X4163))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4164,X4164),tc_HOL_Obool),X4162,c_Product__Type_OSigma(X4164,X4164,X4163,c_COMBK(tc_fun(X4164,tc_HOL_Obool),X4164,X4163)))
| c_Relation_Orefl__on(X4164,X4163,X4162) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4164,X4164)),hAPP(hAPP(c_Product__Type_OPair(X4164,X4164),esk103_3(X4162,X4163,X4164)),esk103_3(X4162,X4163,X4164))),X4162))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4164,X4164),tc_HOL_Obool),X4162,c_Product__Type_OSigma(X4164,X4164,X4163,c_COMBK(tc_fun(X4164,tc_HOL_Obool),X4164,X4163)))
| c_Relation_Orefl__on(X4164,X4163,X4162) ) ),
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_refl__on__def])])])])])]) ).
fof(i_0_655,plain,
! [X2739,X2740,X2741,X2742,X2743] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2743),tc_List_Olist(X2743))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2743),tc_List_Olist(X2743)),X2742),X2741)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2743),c_List_Olistrel1(X2743,X2740))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2743),tc_List_Olist(X2743))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2743),tc_List_Olist(X2743)),hAPP(hAPP(c_List_Olist_OCons(X2743),X2739),X2742)),hAPP(hAPP(c_List_Olist_OCons(X2743),X2739),X2741))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2743),c_List_Olistrel1(X2743,X2740)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).
fof(i_0_656,plain,
! [X2692,X2693,X2694,X2695,X2696] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2695),X2694)),c_List_Olexord(X2696,X2693)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2694),X2692)),c_List_Olexord(X2696,X2693)))
| ~ c_Relation_Otrans(X2696,X2693)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2696),tc_List_Olist(X2696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2696),tc_List_Olist(X2696)),X2695),X2692)),c_List_Olexord(X2696,X2693))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__trans])]) ).
fof(i_0_657,plain,
! [X2521,X2522,X2523,X2524,X2525,X2526] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2526),tc_List_Olist(X2526))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2526),tc_List_Olist(X2526)),X2525),X2524)),c_List_Olistrel1(X2526,X2523)))
| X2522 != X2521
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2526),tc_List_Olist(X2526))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2526),tc_List_Olist(X2526)),hAPP(hAPP(c_List_Oappend(X2526),X2525),X2522)),hAPP(hAPP(c_List_Oappend(X2526),X2524),X2521))),c_List_Olistrel1(X2526,X2523))) )
& ( X2525 != X2524
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2526),tc_List_Olist(X2526))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2526),tc_List_Olist(X2526)),X2522),X2521)),c_List_Olistrel1(X2526,X2523)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2526),tc_List_Olist(X2526))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2526),tc_List_Olist(X2526)),hAPP(hAPP(c_List_Oappend(X2526),X2525),X2522)),hAPP(hAPP(c_List_Oappend(X2526),X2524),X2521))),c_List_Olistrel1(X2526,X2523))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).
fof(i_0_658,plain,
! [X2570,X2571,X2572,X2573,X2574] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2574),tc_List_Olist(X2574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2574),tc_List_Olist(X2574)),X2573),X2572)),c_List_Olexord(X2574,X2571)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2574),tc_List_Olist(X2574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2574),tc_List_Olist(X2574)),hAPP(hAPP(c_List_Oappend(X2574),X2570),X2573)),hAPP(hAPP(c_List_Oappend(X2574),X2570),X2572))),c_List_Olexord(X2574,X2571))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).
fof(i_0_659,plain,
! [X2575,X2576,X2577,X2578,X2579] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2579),tc_List_Olist(X2579))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2579),tc_List_Olist(X2579)),X2578),X2577)),c_List_Olistrel1(X2579,X2576)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2579),tc_List_Olist(X2579))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2579),tc_List_Olist(X2579)),hAPP(hAPP(c_List_Olist_OCons(X2579),X2575),X2578)),hAPP(hAPP(c_List_Olist_OCons(X2579),X2575),X2577))),c_List_Olistrel1(X2579,X2576))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).
fof(i_0_660,plain,
! [X2264,X2265,X2266,X2267,X2268] :
( ( X2265 != X2264
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2264 != X2268
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 != X2268
| X2264 = X2267
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2267),X2264)),X2266))
| X2264 = X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 = X2268
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),X2266))
| X2264 = X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2264 != X2268
| X2264 = X2268
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 != X2268
| X2265 = X2268
| X2264 = X2268
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),X2266))
| X2265 = X2268
| X2264 = X2268
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 != X2268
| X2264 != X2267
| X2264 = X2268
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),X2266))
| X2264 != X2267
| X2264 = X2268
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 != X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2267),X2264)),X2266))
| X2264 = X2268
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),X2266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2267),X2264)),X2266))
| X2264 = X2268
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2264 != X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 != X2268
| X2265 = X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),X2266))
| X2265 = X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 != X2268
| X2264 != X2267
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),X2266))
| X2264 != X2267
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( X2265 != X2268
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2267),X2264)),X2266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),X2266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2267),X2264)),X2266))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2267)),X2266))
| X2265 = X2264
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2265),X2264)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,X2266),X2268),X2267)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2266),c_Arrow__Order__Mirabelle_OLin))
| X2268 = X2267 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_661,plain,
! [X2281,X2282,X2283,X2284,X2285] :
( ( 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2282 != X2284
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 != X2284
| X2282 = X2285
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2285)),X2283))
| X2282 = X2284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 = X2284
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),X2283))
| X2282 = X2284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2282 != X2284
| X2282 = X2284
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 != X2284
| X2281 = X2284
| X2282 = X2284
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),X2283))
| X2281 = X2284
| X2282 = X2284
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 != X2284
| X2282 != X2285
| X2282 = X2284
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),X2283))
| X2282 != X2285
| X2282 = X2284
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 != X2284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2285)),X2283))
| X2282 = X2284
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),X2283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2285)),X2283))
| X2282 = X2284
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2282 != X2284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 != X2284
| X2281 = X2284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),X2283))
| X2281 = X2284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 != X2284
| X2282 != X2285
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),X2283))
| X2282 != X2285
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( X2281 != X2284
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2285)),X2283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2281)),X2283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2282),X2285)),X2283))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2285),X2281)),X2283))
| 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),X2282),X2281)),c_Arrow__Order__Mirabelle_Oabove(X2283,X2285,X2284)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2283),c_Arrow__Order__Mirabelle_OLin))
| X2285 = X2284 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_662,plain,
! [X2419,X2420,X2421] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2421,X2421)),hAPP(hAPP(c_Product__Type_OPair(X2421,X2421),esk30_3(X2419,X2420,X2421)),esk30_3(X2419,X2420,X2421))),X2420))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2421),tc_List_Olist(X2421))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2421),tc_List_Olist(X2421)),X2419),X2419)),c_List_Olexord(X2421,X2420))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])])]) ).
fof(i_0_663,plain,
! [X3456,X3457,X3458,X3459,X3460,X3461] :
( ~ hBOOL(hAPP(hAPP(c_member(X3461),X3460),X3459))
| c_Fun_Ooverride__on(X3461,X3458,X3457,X3456,X3459,X3460) = hAPP(X3456,X3460) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_override__on__apply__in])]) ).
fof(i_0_664,plain,
! [X3441,X3442,X3443,X3444,X3445,X3446] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3446),X3445),X3444))
| c_Fun_Ooverride__on(X3446,X3443,X3442,X3441,X3444,X3445) = hAPP(X3441,X3445) )
& ( hBOOL(hAPP(hAPP(c_member(X3446),X3445),X3444))
| c_Fun_Ooverride__on(X3446,X3443,X3442,X3441,X3444,X3445) = hAPP(X3442,X3445) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])]) ).
fof(i_0_665,plain,
! [X3462,X3463,X3464,X3465,X3466,X3467] :
( hBOOL(hAPP(hAPP(c_member(X3467),X3466),X3465))
| c_Fun_Ooverride__on(X3467,X3464,X3463,X3462,X3465,X3466) = hAPP(X3463,X3466) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])]) ).
fof(i_0_666,plain,
! [X2588,X2589,X2590,X2591,X2592] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2592,X2592)),hAPP(hAPP(c_Product__Type_OPair(X2592,X2592),X2591),X2590)),X2589))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2592),tc_List_Olist(X2592))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2592),tc_List_Olist(X2592)),hAPP(hAPP(c_List_Olist_OCons(X2592),X2591),X2588)),hAPP(hAPP(c_List_Olist_OCons(X2592),X2590),X2588))),c_List_Olistrel1(X2592,X2589))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).
fof(i_0_667,plain,
! [X2802,X2803,X2804,X2805,X2806] :
( ~ c_Relation_Osingle__valued(X2806,X2806,X2805)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2806,X2806)),hAPP(hAPP(c_Product__Type_OPair(X2806,X2806),X2804),X2803)),c_Transitive__Closure_Ortrancl(X2806,X2805)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2806,X2806)),hAPP(hAPP(c_Product__Type_OPair(X2806,X2806),X2804),X2802)),c_Transitive__Closure_Ortrancl(X2806,X2805)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2806,X2806)),hAPP(hAPP(c_Product__Type_OPair(X2806,X2806),X2803),X2802)),c_Transitive__Closure_Ortrancl(X2806,X2805)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2806,X2806)),hAPP(hAPP(c_Product__Type_OPair(X2806,X2806),X2802),X2803)),c_Transitive__Closure_Ortrancl(X2806,X2805))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).
fof(i_0_668,plain,
! [X2888,X2889,X2890,X2891] :
( ~ hBOOL(hAPP(hAPP(c_member(X2891),X2890),c_Relation_ODomain(X2891,X2889,X2888)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2891,X2889)),hAPP(hAPP(c_Product__Type_OPair(X2891,X2889),X2890),esk57_4(X2888,X2889,X2890,X2891))),X2888)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])])]) ).
fof(i_0_669,plain,
! [X2843,X2844,X2845,X2846,X2848,X2849,X2850,X2851,X2852] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2846),X2845),c_Relation_ODomain(X2846,X2844,X2843)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2846,X2844)),hAPP(hAPP(c_Product__Type_OPair(X2846,X2844),X2845),esk53_4(X2843,X2844,X2845,X2846))),X2843)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2851,X2849)),hAPP(hAPP(c_Product__Type_OPair(X2851,X2849),X2850),X2852)),X2848))
| hBOOL(hAPP(hAPP(c_member(X2851),X2850),c_Relation_ODomain(X2851,X2849,X2848))) ) ),
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,
! [X2539,X2540,X2541,X2542,X2543,X2545,X2546,X2547,X2548,X2549,X2550] :
( ( hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),esk34_5(X2539,X2540,X2541,X2542,X2543)) = X2540
| X2540 = c_List_Olist_ONil(X2543)
| hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),X2541) != hAPP(hAPP(c_List_Oappend(X2543),X2540),X2539) )
& ( X2541 = hAPP(hAPP(c_List_Oappend(X2543),esk34_5(X2539,X2540,X2541,X2542,X2543)),X2539)
| X2540 = c_List_Olist_ONil(X2543)
| hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),X2541) != hAPP(hAPP(c_List_Oappend(X2543),X2540),X2539) )
& ( hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),esk34_5(X2539,X2540,X2541,X2542,X2543)) = X2540
| hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),X2541) = X2539
| hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),X2541) != hAPP(hAPP(c_List_Oappend(X2543),X2540),X2539) )
& ( X2541 = hAPP(hAPP(c_List_Oappend(X2543),esk34_5(X2539,X2540,X2541,X2542,X2543)),X2539)
| hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),X2541) = X2539
| hAPP(hAPP(c_List_Olist_OCons(X2543),X2542),X2541) != hAPP(hAPP(c_List_Oappend(X2543),X2540),X2539) )
& ( X2546 != c_List_Olist_ONil(X2549)
| hAPP(hAPP(c_List_Olist_OCons(X2549),X2548),X2547) != X2545
| hAPP(hAPP(c_List_Olist_OCons(X2549),X2548),X2547) = hAPP(hAPP(c_List_Oappend(X2549),X2546),X2545) )
& ( hAPP(hAPP(c_List_Olist_OCons(X2549),X2548),X2550) != X2546
| X2547 != hAPP(hAPP(c_List_Oappend(X2549),X2550),X2545)
| hAPP(hAPP(c_List_Olist_OCons(X2549),X2548),X2547) = hAPP(hAPP(c_List_Oappend(X2549),X2546),X2545) ) ),
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,
! [X2527,X2528,X2529,X2530,X2531,X2533,X2534,X2535,X2536,X2537,X2538] :
( ( X2530 = hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),esk33_5(X2527,X2528,X2529,X2530,X2531))
| X2530 = c_List_Olist_ONil(X2531)
| hAPP(hAPP(c_List_Oappend(X2531),X2530),X2529) != hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),X2527) )
& ( hAPP(hAPP(c_List_Oappend(X2531),esk33_5(X2527,X2528,X2529,X2530,X2531)),X2529) = X2527
| X2530 = c_List_Olist_ONil(X2531)
| hAPP(hAPP(c_List_Oappend(X2531),X2530),X2529) != hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),X2527) )
& ( X2530 = hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),esk33_5(X2527,X2528,X2529,X2530,X2531))
| X2529 = hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),X2527)
| hAPP(hAPP(c_List_Oappend(X2531),X2530),X2529) != hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),X2527) )
& ( hAPP(hAPP(c_List_Oappend(X2531),esk33_5(X2527,X2528,X2529,X2530,X2531)),X2529) = X2527
| X2529 = hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),X2527)
| hAPP(hAPP(c_List_Oappend(X2531),X2530),X2529) != hAPP(hAPP(c_List_Olist_OCons(X2531),X2528),X2527) )
& ( X2536 != c_List_Olist_ONil(X2537)
| X2535 != hAPP(hAPP(c_List_Olist_OCons(X2537),X2534),X2533)
| hAPP(hAPP(c_List_Oappend(X2537),X2536),X2535) = hAPP(hAPP(c_List_Olist_OCons(X2537),X2534),X2533) )
& ( X2536 != hAPP(hAPP(c_List_Olist_OCons(X2537),X2534),X2538)
| hAPP(hAPP(c_List_Oappend(X2537),X2538),X2535) != X2533
| hAPP(hAPP(c_List_Oappend(X2537),X2536),X2535) = hAPP(hAPP(c_List_Olist_OCons(X2537),X2534),X2533) ) ),
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,
! [X2637,X2638] : c_List_Orotate1(X2638,X2637) = c_List_Olist_Olist__case(tc_List_Olist(X2638),X2638,c_List_Olist_ONil(X2638),hAPP(hAPP(c_COMBB(tc_List_Olist(X2638),tc_fun(tc_List_Olist(X2638),tc_List_Olist(X2638)),X2638),hAPP(c_COMBC(tc_List_Olist(X2638),tc_List_Olist(X2638),tc_List_Olist(X2638)),c_List_Oappend(X2638))),hAPP(hAPP(c_COMBC(X2638,tc_List_Olist(X2638),tc_List_Olist(X2638)),c_List_Olist_OCons(X2638)),c_List_Olist_ONil(X2638))),X2637),
inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).
fof(i_0_673,plain,
! [X2990,X2991,X2992] :
( ( ~ hBOOL(hAPP(c_List_Olistsp(X2992,hAPP(hAPP(c_COMBC(X2992,tc_fun(X2992,tc_HOL_Obool),tc_HOL_Obool),c_member(X2992)),X2991)),X2990))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),X2990),c_List_Olists(X2992,X2991))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2992)),X2990),c_List_Olists(X2992,X2991)))
| hBOOL(hAPP(c_List_Olistsp(X2992,hAPP(hAPP(c_COMBC(X2992,tc_fun(X2992,tc_HOL_Obool),tc_HOL_Obool),c_member(X2992)),X2991)),X2990)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])]) ).
fof(i_0_674,plain,
! [X3808,X3809,X3810,X3811,X3812] :
( ( hAPP(X3809,X3811) = hAPP(X3809,X3810)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3809,X3811),hAPP(X3809,X3810))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3812,X3812)),hAPP(hAPP(c_Product__Type_OPair(X3812,X3812),X3811),X3810)),c_List_Omeasures(X3812,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X3812,tc_Nat_Onat)),X3809),X3808)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3812,X3812)),hAPP(hAPP(c_Product__Type_OPair(X3812,X3812),X3811),X3810)),c_List_Omeasures(X3812,X3808)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3809,X3811),hAPP(X3809,X3810))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3812,X3812)),hAPP(hAPP(c_Product__Type_OPair(X3812,X3812),X3811),X3810)),c_List_Omeasures(X3812,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X3812,tc_Nat_Onat)),X3809),X3808)))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3809,X3811),hAPP(X3809,X3810))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3812,X3812)),hAPP(hAPP(c_Product__Type_OPair(X3812,X3812),X3811),X3810)),c_List_Omeasures(X3812,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X3812,tc_Nat_Onat)),X3809),X3808)))) )
& ( hAPP(X3809,X3811) != hAPP(X3809,X3810)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3812,X3812)),hAPP(hAPP(c_Product__Type_OPair(X3812,X3812),X3811),X3810)),c_List_Omeasures(X3812,X3808)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3812,X3812)),hAPP(hAPP(c_Product__Type_OPair(X3812,X3812),X3811),X3810)),c_List_Omeasures(X3812,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X3812,tc_Nat_Onat)),X3809),X3808)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).
fof(i_0_675,plain,
! [X2769,X2770,X2771,X2772,X2773] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2772),X2771)),c_Transitive__Closure_Ortrancl(X2773,X2770)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2771),X2769)),c_Transitive__Closure_Ortrancl(X2773,X2770)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2773,X2773)),hAPP(hAPP(c_Product__Type_OPair(X2773,X2773),X2772),X2769)),c_Transitive__Closure_Ortrancl(X2773,X2770))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).
fof(i_0_676,plain,
! [X3333,X3334,X3335,X3336,X3337,X3338] :
( ( hBOOL(hAPP(hAPP(X3336,X3334),X3333))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3338,tc_fun(X3337,tc_HOL_Obool))),X3336),X3335),X3334),X3333)) )
& ( hBOOL(hAPP(hAPP(X3335,X3334),X3333))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3338,tc_fun(X3337,tc_HOL_Obool))),X3336),X3335),X3334),X3333)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).
fof(i_0_677,plain,
! [X3351,X3352,X3353,X3354,X3355,X3356] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3356,tc_fun(X3355,tc_HOL_Obool))),X3354),X3353),X3352),X3351))
| hBOOL(hAPP(hAPP(X3354,X3352),X3351)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).
fof(i_0_678,plain,
! [X3345,X3346,X3347,X3348,X3349,X3350] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3350,tc_fun(X3349,tc_HOL_Obool))),X3348),X3347),X3346),X3345))
| hBOOL(hAPP(hAPP(X3347,X3346),X3345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).
fof(i_0_679,plain,
! [X2783,X2784,X2785,X2786,X2787] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2787,X2787)),hAPP(hAPP(c_Product__Type_OPair(X2787,X2787),X2786),X2785)),X2784))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2787,X2787)),hAPP(hAPP(c_Product__Type_OPair(X2787,X2787),X2785),X2783)),c_Transitive__Closure_Ortrancl(X2787,X2784)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2787,X2787)),hAPP(hAPP(c_Product__Type_OPair(X2787,X2787),X2786),X2783)),c_Transitive__Closure_Ortrancl(X2787,X2784))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).
fof(i_0_680,plain,
! [X2774,X2775,X2776,X2777,X2778] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2778,X2778)),hAPP(hAPP(c_Product__Type_OPair(X2778,X2778),X2777),X2776)),c_Transitive__Closure_Ortrancl(X2778,X2775)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2778,X2778)),hAPP(hAPP(c_Product__Type_OPair(X2778,X2778),X2776),X2774)),X2775))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2778,X2778)),hAPP(hAPP(c_Product__Type_OPair(X2778,X2778),X2777),X2774)),c_Transitive__Closure_Ortrancl(X2778,X2775))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).
fof(i_0_681,plain,
! [X2697,X2698,X2699,X2700] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2700),tc_List_Olist(X2700))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2700),tc_List_Olist(X2700)),X2699),X2698)),c_List_Olistrel(X2700,X2697)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2700),tc_List_Olist(X2700))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2700),tc_List_Olist(X2700)),X2699),X2698)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2700),c_List_Olistrel1(X2700,X2697)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).
fof(i_0_682,plain,
! [X2701,X2702,X2703,X2704] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2704),tc_List_Olist(X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2704),tc_List_Olist(X2704)),X2703),X2702)),c_List_Olistrel1(X2704,X2701)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2704),tc_List_Olist(X2704))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2704),tc_List_Olist(X2704)),X2703),X2702)),c_List_Olistrel(X2704,c_Transitive__Closure_Ortrancl(X2704,X2701)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).
fof(i_0_683,plain,
! [X3680,X3681,X3682,X3683,X3684] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3684,tc_HOL_Obool),c_Set_Oimage(X3683,X3684,X3682,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3683,tc_HOL_Obool)),X3681),X3680)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3684,tc_HOL_Obool)),c_Set_Oimage(X3683,X3684,X3682,X3681)),c_Set_Oimage(X3683,X3684,X3682,X3680))),
inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).
fof(i_0_684,plain,
! [X2672,X2673,X2674,X2675] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2675),tc_List_Olist(X2675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2675),tc_List_Olist(X2675)),X2674),X2673)),c_List_Olexord(X2675,X2672)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2675),tc_List_Olist(X2675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2675),tc_List_Olist(X2675)),X2674),X2673)),c_List_Olex(X2675,X2672))) )
& ( c_Nat_Osize__class_Osize(tc_List_Olist(X2675),X2674) = c_Nat_Osize__class_Osize(tc_List_Olist(X2675),X2673)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2675),tc_List_Olist(X2675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2675),tc_List_Olist(X2675)),X2674),X2673)),c_List_Olex(X2675,X2672))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2675),tc_List_Olist(X2675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2675),tc_List_Olist(X2675)),X2674),X2673)),c_List_Olexord(X2675,X2672)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2675),X2674) != c_Nat_Osize__class_Osize(tc_List_Olist(X2675),X2673)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2675),tc_List_Olist(X2675))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2675),tc_List_Olist(X2675)),X2674),X2673)),c_List_Olex(X2675,X2672))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).
fof(i_0_685,plain,
! [X2759,X2760,X2761,X2762,X2763,X2764,X2765] :
( ( ~ c_Relation_Otrans(X2760,X2759)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2760,X2760)),hAPP(hAPP(c_Product__Type_OPair(X2760,X2760),X2761),X2762)),X2759))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2760,X2760)),hAPP(hAPP(c_Product__Type_OPair(X2760,X2760),X2762),X2763)),X2759))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2760,X2760)),hAPP(hAPP(c_Product__Type_OPair(X2760,X2760),X2761),X2763)),X2759)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2765,X2765)),hAPP(hAPP(c_Product__Type_OPair(X2765,X2765),esk46_2(X2764,X2765)),esk47_2(X2764,X2765))),X2764))
| c_Relation_Otrans(X2765,X2764) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2765,X2765)),hAPP(hAPP(c_Product__Type_OPair(X2765,X2765),esk47_2(X2764,X2765)),esk48_2(X2764,X2765))),X2764))
| c_Relation_Otrans(X2765,X2764) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2765,X2765)),hAPP(hAPP(c_Product__Type_OPair(X2765,X2765),esk46_2(X2764,X2765)),esk48_2(X2764,X2765))),X2764))
| c_Relation_Otrans(X2765,X2764) ) ),
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_686,plain,
! [X2754,X2755,X2756,X2757,X2758] :
( ~ c_Relation_Otrans(X2758,X2757)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2758)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2758),X2756),X2755)),X2757))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2758)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2758),X2755),X2754)),X2757))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2758,X2758)),hAPP(hAPP(c_Product__Type_OPair(X2758,X2758),X2756),X2754)),X2757)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transD])]) ).
fof(i_0_687,plain,
! [X3775,X3776,X3777,X3778,X3779] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X3779,X3778),hAPP(X3779,X3777))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3776,X3776)),hAPP(hAPP(c_Product__Type_OPair(X3776,X3776),X3778),X3777)),c_List_Omeasures(X3776,X3775)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3776,X3776)),hAPP(hAPP(c_Product__Type_OPair(X3776,X3776),X3778),X3777)),c_List_Omeasures(X3776,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X3776,tc_Nat_Onat)),X3779),X3775)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).
cnf(i_0_688,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_529]) ).
fof(i_0_689,plain,
! [X4146,X4147,X4148,X4149] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk100_4(X4146,X4147,X4148,X4149),X4149)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4149,c_Nat_Osize__class_Osize(tc_List_Olist(X4147),X4146))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4149,c_Nat_Osize__class_Osize(tc_List_Olist(X4147),c_List_OtakeWhile(X4147,X4148,X4146))) )
& ( ~ hBOOL(hAPP(X4148,c_List_Onth(X4147,X4146,esk100_4(X4146,X4147,X4148,X4149))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4149,c_Nat_Osize__class_Osize(tc_List_Olist(X4147),X4146))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4149,c_Nat_Osize__class_Osize(tc_List_Olist(X4147),c_List_OtakeWhile(X4147,X4148,X4146))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__takeWhile__less__P__nth])])])]) ).
fof(i_0_690,plain,
! [X2556,X2557,X2558,X2559,X2560,X2561,X2562,X2563] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2563,X2563)),hAPP(hAPP(c_Product__Type_OPair(X2563,X2563),X2562),X2561)),X2560))
| X2559 != hAPP(hAPP(c_List_Oappend(X2563),X2558),hAPP(hAPP(c_List_Olist_OCons(X2563),X2562),X2557))
| X2556 != hAPP(hAPP(c_List_Oappend(X2563),X2558),hAPP(hAPP(c_List_Olist_OCons(X2563),X2561),X2557))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2563),tc_List_Olist(X2563))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2563),tc_List_Olist(X2563)),X2559),X2556)),c_List_Olistrel1(X2563,X2560))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).
fof(i_0_691,plain,
! [X3241,X3242,X3243,X3244,X3245,X3247,X3248,X3249,X3250,X3251,X3252] :
( ( hBOOL(hAPP(hAPP(c_member(X3243),esk83_4(X3241,X3242,X3243,X3244)),X3241))
| ~ hBOOL(hAPP(hAPP(c_member(X3245),X3244),c_Set_Oimage(X3243,X3245,X3242,X3241))) )
& ( X3244 = hAPP(X3242,esk83_4(X3241,X3242,X3243,X3244))
| ~ hBOOL(hAPP(hAPP(c_member(X3245),X3244),c_Set_Oimage(X3243,X3245,X3242,X3241))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3249),X3251),X3247))
| X3250 != hAPP(X3248,X3251)
| hBOOL(hAPP(hAPP(c_member(X3252),X3250),c_Set_Oimage(X3249,X3252,X3248,X3247))) ) ),
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_692,plain,
! [X2254,X2255,X2256] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2255),X2254)),X2256))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2254),X2255)),X2256))
| X2255 = X2254
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2256),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),X2254),X2255)),X2256))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2255),X2254)),X2256))
| X2255 = X2254
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2256),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])])]) ).
fof(i_0_693,plain,
! [X2257,X2258,X2259] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2259),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),X2258),X2257)),X2259))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2257),X2258)),X2259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])]) ).
fof(i_0_694,plain,
! [X3057,X3058,X3059] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3059,X3058)),hAPP(hAPP(c_Product__Type_OPair(X3059,X3058),esk78_3(X3057,X3058,X3059)),esk79_3(X3057,X3058,X3059))),X3057))
| c_Relation_Osingle__valued(X3059,X3058,X3057) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3059,X3058)),hAPP(hAPP(c_Product__Type_OPair(X3059,X3058),esk78_3(X3057,X3058,X3059)),esk80_3(X3057,X3058,X3059))),X3057))
| c_Relation_Osingle__valued(X3059,X3058,X3057) )
& ( esk79_3(X3057,X3058,X3059) != esk80_3(X3057,X3058,X3059)
| c_Relation_Osingle__valued(X3059,X3058,X3057) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedI])])])]) ).
fof(i_0_695,plain,
! [X2831,X2832,X2833,X2834,X2835,X2836,X2837,X2838,X2839] :
( ( ~ c_Relation_Osingle__valued(X2833,X2832,X2831)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2833,X2832)),hAPP(hAPP(c_Product__Type_OPair(X2833,X2832),X2834),X2835)),X2831))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2833,X2832)),hAPP(hAPP(c_Product__Type_OPair(X2833,X2832),X2834),X2836)),X2831))
| X2835 = X2836 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2839,X2838)),hAPP(hAPP(c_Product__Type_OPair(X2839,X2838),esk50_3(X2837,X2838,X2839)),esk51_3(X2837,X2838,X2839))),X2837))
| c_Relation_Osingle__valued(X2839,X2838,X2837) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2839,X2838)),hAPP(hAPP(c_Product__Type_OPair(X2839,X2838),esk50_3(X2837,X2838,X2839)),esk52_3(X2837,X2838,X2839))),X2837))
| c_Relation_Osingle__valued(X2839,X2838,X2837) )
& ( esk51_3(X2837,X2838,X2839) != esk52_3(X2837,X2838,X2839)
| c_Relation_Osingle__valued(X2839,X2838,X2837) ) ),
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_696,plain,
! [X2389,X2390,X2391,X2392,X2393] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2393,X2392,tc_HOL_Obool,X2391),X2390),X2389))
| hBOOL(hAPP(X2391,hAPP(hAPP(c_Product__Type_OPair(X2393,X2392),X2390),X2389))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryE])]) ).
fof(i_0_697,plain,
! [X2384,X2385,X2386,X2387,X2388] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2388,X2387,tc_HOL_Obool,X2386),X2385),X2384))
| hBOOL(hAPP(X2386,hAPP(hAPP(c_Product__Type_OPair(X2388,X2387),X2385),X2384))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryD])]) ).
fof(i_0_698,plain,
! [X3693,X3694,X3695,X3696,X3697] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3697,X3696)),X3695),c_FuncSet_OPi(X3697,X3696,X3694,c_COMBK(tc_fun(X3696,tc_HOL_Obool),X3697,X3693))))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3696,tc_HOL_Obool),c_Set_Oimage(X3697,X3696,X3695,X3694),X3693) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_699,plain,
! [X3589,X3590,X3591,X3592,X3593,X3595,X3596,X3597,X3598,X3599,X3600] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3591,tc_HOL_Obool),esk93_5(X3589,X3590,X3591,X3592,X3593),X3589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3593,tc_HOL_Obool),X3592,c_Set_Oimage(X3591,X3593,X3590,X3589)) )
& ( X3592 = c_Set_Oimage(X3591,X3593,X3590,esk93_5(X3589,X3590,X3591,X3592,X3593))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3593,tc_HOL_Obool),X3592,c_Set_Oimage(X3591,X3593,X3590,X3589)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3597,tc_HOL_Obool),X3600,X3595)
| X3598 != c_Set_Oimage(X3597,X3599,X3596,X3600)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3599,tc_HOL_Obool),X3598,c_Set_Oimage(X3597,X3599,X3596,X3595)) ) ),
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])])])])])]) ).
cnf(i_0_700,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_532]) ).
fof(i_0_701,plain,
! [X4124,X4125,X4126,X4127,X4128] : c_Product__Type_OSigma(X4128,X4127,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4128,tc_HOL_Obool)),X4126),X4125),c_COMBK(tc_fun(X4127,tc_HOL_Obool),X4128,X4124)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4128,X4127),tc_HOL_Obool)),c_Product__Type_OSigma(X4128,X4127,X4126,c_COMBK(tc_fun(X4127,tc_HOL_Obool),X4128,X4124))),c_Product__Type_OSigma(X4128,X4127,X4125,c_COMBK(tc_fun(X4127,tc_HOL_Obool),X4128,X4124))),
inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).
fof(i_0_702,plain,
! [X2275,X2276,X2277,X2278,X2279,X2280] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2280,X2279)),X2278),c_FuncSet_OPi(X2280,X2279,X2277,c_COMBK(tc_fun(X2279,tc_HOL_Obool),X2280,X2276))))
| ~ hBOOL(hAPP(hAPP(c_member(X2280),X2275),X2277))
| hBOOL(hAPP(hAPP(c_member(X2279),hAPP(X2278,X2275)),X2276)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_703,plain,
! [X2825,X2826,X2827,X2828,X2829,X2830] :
( ~ c_Relation_Osingle__valued(X2830,X2829,X2828)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2830,X2829)),hAPP(hAPP(c_Product__Type_OPair(X2830,X2829),X2827),X2826)),X2828))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2830,X2829)),hAPP(hAPP(c_Product__Type_OPair(X2830,X2829),X2827),X2825)),X2828))
| X2826 = X2825 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).
fof(i_0_704,plain,
! [X3702,X3703,X3704,X3705,X3706] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3704,X3705),X3703,X3702)
| c_Orderings_Oord__class_Oless__eq(X3705,hAPP(X3703,X3706),hAPP(X3702,X3706))
| ~ class_Orderings_Oord(X3705) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3705,hAPP(X3703,esk94_4(X3702,X3703,X3704,X3705)),hAPP(X3702,esk94_4(X3702,X3703,X3704,X3705)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3704,X3705),X3703,X3702)
| ~ class_Orderings_Oord(X3705) ) ),
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_705,plain,
! [X4081,X4082,X4083,X4084,X4085,X4086] :
( ( hBOOL(hAPP(hAPP(c_member(X4086),X4084),X4082))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4086,X4085)),hAPP(hAPP(c_Product__Type_OPair(X4086,X4085),X4084),X4083)),c_Product__Type_OSigma(X4086,X4085,X4082,X4081))) )
& ( hBOOL(hAPP(hAPP(c_member(X4085),X4083),hAPP(X4081,X4084)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4086,X4085)),hAPP(hAPP(c_Product__Type_OPair(X4086,X4085),X4084),X4083)),c_Product__Type_OSigma(X4086,X4085,X4082,X4081))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X4086),X4084),X4082))
| ~ hBOOL(hAPP(hAPP(c_member(X4085),X4083),hAPP(X4081,X4084)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4086,X4085)),hAPP(hAPP(c_Product__Type_OPair(X4086,X4085),X4084),X4083)),c_Product__Type_OSigma(X4086,X4085,X4082,X4081))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).
fof(i_0_706,plain,
! [X4063,X4064,X4065,X4066,X4067,X4068] :
( ( hBOOL(hAPP(hAPP(c_member(X4068),X4066),X4064))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4068,X4067)),hAPP(hAPP(c_Product__Type_OPair(X4068,X4067),X4066),X4065)),c_Product__Type_OSigma(X4068,X4067,X4064,X4063))) )
& ( hBOOL(hAPP(hAPP(c_member(X4067),X4065),hAPP(X4063,X4066)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4068,X4067)),hAPP(hAPP(c_Product__Type_OPair(X4068,X4067),X4066),X4065)),c_Product__Type_OSigma(X4068,X4067,X4064,X4063))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])])]) ).
fof(i_0_707,plain,
! [X4069,X4070,X4071,X4072,X4073,X4074] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4074,X4073)),hAPP(hAPP(c_Product__Type_OPair(X4074,X4073),X4072),X4071)),c_Product__Type_OSigma(X4074,X4073,X4070,X4069)))
| hBOOL(hAPP(hAPP(c_member(X4073),X4071),hAPP(X4069,X4072))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).
fof(i_0_708,plain,
! [X2108] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2108)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2108)),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____,X2108)),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____,X2108))) ) ),
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_709,plain,
! [X4075,X4076,X4077,X4078,X4079,X4080] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4080,X4079)),hAPP(hAPP(c_Product__Type_OPair(X4080,X4079),X4078),X4077)),c_Product__Type_OSigma(X4080,X4079,X4076,X4075)))
| hBOOL(hAPP(hAPP(c_member(X4080),X4078),X4076)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).
fof(i_0_710,plain,
! [X4040,X4041,X4042,X4043,X4044] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4044,X4044)),hAPP(hAPP(c_Product__Type_OPair(X4044,X4044),X4043),X4042)),c_Transitive__Closure_Ortrancl(X4044,X4041)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4044,X4044),tc_HOL_Obool),X4041,c_Product__Type_OSigma(X4044,X4044,X4040,c_COMBK(tc_fun(X4044,tc_HOL_Obool),X4044,X4040)))
| X4043 = X4042
| hBOOL(hAPP(hAPP(c_member(X4044),X4043),X4040)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).
fof(i_0_711,plain,
! [X2403,X2404,X2405,X2408,X2409,X2410,X2411,X2412] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2405),tc_List_Olist(X2405))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2405),tc_List_Olist(X2405)),c_List_Olist_ONil(X2405)),X2404)),c_List_Olexord(X2405,X2403)))
| X2404 = hAPP(hAPP(c_List_Olist_OCons(X2405),esk26_3(X2403,X2404,X2405)),esk27_3(X2403,X2404,X2405)) )
& ( X2409 != hAPP(hAPP(c_List_Olist_OCons(X2410),X2411),X2412)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2410),tc_List_Olist(X2410))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2410),tc_List_Olist(X2410)),c_List_Olist_ONil(X2410)),X2409)),c_List_Olexord(X2410,X2408))) ) ),
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_712,plain,
! [X2263] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2263),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,X2263)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_713,plain,
! [X3785,X3786,X3787,X3788,X3789] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X3789,X3788),hAPP(X3789,X3787))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3786,X3786)),hAPP(hAPP(c_Product__Type_OPair(X3786,X3786),X3788),X3787)),X3785))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3786,X3786)),hAPP(hAPP(c_Product__Type_OPair(X3786,X3786),X3788),X3787)),c_Wellfounded_Omlex__prod(X3786,X3789,X3785))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_714,plain,
! [X3339,X3340,X3341,X3342,X3343,X3344] :
( ~ hBOOL(hAPP(hAPP(X3344,X3343),X3342))
| ~ hBOOL(hAPP(hAPP(X3341,X3343),X3342))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3340,tc_fun(X3339,tc_HOL_Obool))),X3344),X3341),X3343),X3342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).
fof(i_0_715,plain,
! [X4110,X4111,X4112,X4113,X4114,X4115] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4112,X4115),tc_HOL_Obool),c_Product__Type_OSigma(X4112,X4115,X4111,c_COMBK(tc_fun(X4115,tc_HOL_Obool),X4112,X4113)),c_Product__Type_OSigma(X4112,X4115,X4110,c_COMBK(tc_fun(X4115,tc_HOL_Obool),X4112,X4113)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4112,tc_HOL_Obool),X4111,X4110)
| ~ hBOOL(hAPP(hAPP(c_member(X4115),X4114),X4113)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4112,tc_HOL_Obool),X4111,X4110)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4112,X4115),tc_HOL_Obool),c_Product__Type_OSigma(X4112,X4115,X4111,c_COMBK(tc_fun(X4115,tc_HOL_Obool),X4112,X4113)),c_Product__Type_OSigma(X4112,X4115,X4110,c_COMBK(tc_fun(X4115,tc_HOL_Obool),X4112,X4113)))
| ~ hBOOL(hAPP(hAPP(c_member(X4115),X4114),X4113)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2])])]) ).
fof(i_0_716,plain,
! [X2121,X2122,X2123,X2124,X2125] :
( ( ~ c_FunDef_Oin__rel(X2125,X2124,X2123,X2122,X2121)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2125,X2124)),hAPP(hAPP(c_Product__Type_OPair(X2125,X2124),X2122),X2121)),X2123)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2125,X2124)),hAPP(hAPP(c_Product__Type_OPair(X2125,X2124),X2122),X2121)),X2123))
| c_FunDef_Oin__rel(X2125,X2124,X2123,X2122,X2121) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_717,plain,
! [X2680,X2681,X2682,X2683,X2684] :
( ( c_Nat_Osize__class_Osize(tc_List_Olist(X2684),X2683) = X2680
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2684),tc_List_Olist(X2684))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2684),tc_List_Olist(X2684)),X2683),X2682)),c_List_Olexn(X2684,X2681,X2680))) )
& ( c_Nat_Osize__class_Osize(tc_List_Olist(X2684),X2682) = X2680
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2684),tc_List_Olist(X2684))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2684),tc_List_Olist(X2684)),X2683),X2682)),c_List_Olexn(X2684,X2681,X2680))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).
fof(i_0_718,plain,
! [X2946,X2947,X2948] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2948,X2948)),hAPP(hAPP(c_Product__Type_OPair(X2948,X2948),esk62_3(X2946,X2947,X2948)),X2947)),X2946))
| hBOOL(hAPP(hAPP(c_member(X2948),X2947),c_Wellfounded_Oacc(X2948,X2946))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2948),esk62_3(X2946,X2947,X2948)),c_Wellfounded_Oacc(X2948,X2946)))
| hBOOL(hAPP(hAPP(c_member(X2948),X2947),c_Wellfounded_Oacc(X2948,X2946))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_534])])])]) ).
fof(i_0_719,plain,
! [X2942,X2943,X2944] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2944,X2944)),hAPP(hAPP(c_Product__Type_OPair(X2944,X2944),esk61_3(X2942,X2943,X2944)),X2943)),X2942))
| hBOOL(hAPP(hAPP(c_member(X2944),X2943),c_Wellfounded_Oacc(X2944,X2942))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2944),esk61_3(X2942,X2943,X2944)),c_Wellfounded_Oacc(X2944,X2942)))
| hBOOL(hAPP(hAPP(c_member(X2944),X2943),c_Wellfounded_Oacc(X2944,X2942))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).
fof(i_0_720,plain,
! [X2867,X2868,X2869,X2870,X2871,X2872,X2873] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2869),X2868),c_Wellfounded_Oacc(X2869,X2867)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2869,X2869)),hAPP(hAPP(c_Product__Type_OPair(X2869,X2869),X2870),X2868)),X2867))
| hBOOL(hAPP(hAPP(c_member(X2869),X2870),c_Wellfounded_Oacc(X2869,X2867))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2873,X2873)),hAPP(hAPP(c_Product__Type_OPair(X2873,X2873),esk55_3(X2871,X2872,X2873)),X2872)),X2871))
| hBOOL(hAPP(hAPP(c_member(X2873),X2872),c_Wellfounded_Oacc(X2873,X2871))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2873),esk55_3(X2871,X2872,X2873)),c_Wellfounded_Oacc(X2873,X2871)))
| hBOOL(hAPP(hAPP(c_member(X2873),X2872),c_Wellfounded_Oacc(X2873,X2871))) ) ),
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])])])])])]) ).
cnf(i_0_721,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_535]) ).
fof(i_0_722,plain,
! [X2744,X2745,X2746,X2747] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2747),tc_List_Olist(X2747))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2747),tc_List_Olist(X2747)),X2746),X2745)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X2747),c_List_Olistrel1(X2747,X2744))))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2747),X2746) = c_Nat_Osize__class_Osize(tc_List_Olist(X2747),X2745) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).
fof(i_0_723,plain,
! [X2448,X2449,X2450] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2450),tc_List_Olist(X2450))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2450),tc_List_Olist(X2450)),c_List_Olist_ONil(X2450)),X2449)),c_List_Olistrel(X2450,X2448)))
| X2449 = c_List_Olist_ONil(X2450) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).
fof(i_0_724,plain,
! [X2580,X2581,X2582] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2582),tc_List_Olist(X2582))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2582),tc_List_Olist(X2582)),c_List_Olist_ONil(X2582)),X2581)),c_List_Olistrel1(X2582,X2580))),
inference(variable_rename,[status(thm)],[i_0_536]) ).
fof(i_0_725,plain,
! [X2426,X2427,X2428] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2428),tc_List_Olist(X2428))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2428),tc_List_Olist(X2428)),c_List_Olist_ONil(X2428)),X2427)),c_List_Olex(X2428,X2426))),
inference(variable_rename,[status(thm)],[i_0_537]) ).
fof(i_0_726,plain,
! [X2451,X2452,X2453] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2453),tc_List_Olist(X2453))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2453),tc_List_Olist(X2453)),X2452),c_List_Olist_ONil(X2453))),c_List_Olistrel(X2453,X2451)))
| X2452 = c_List_Olist_ONil(X2453) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).
fof(i_0_727,plain,
! [X2583,X2584,X2585] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2585),tc_List_Olist(X2585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2585),tc_List_Olist(X2585)),X2584),c_List_Olist_ONil(X2585))),c_List_Olistrel1(X2585,X2583))),
inference(variable_rename,[status(thm)],[i_0_538]) ).
fof(i_0_728,plain,
! [X2423,X2424,X2425] : ~ 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)),X2424),c_List_Olist_ONil(X2425))),c_List_Olex(X2425,X2423))),
inference(variable_rename,[status(thm)],[i_0_539]) ).
fof(i_0_729,plain,
! [X2381,X2382,X2383] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2383),tc_List_Olist(X2383))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2383),tc_List_Olist(X2383)),X2382),c_List_Olist_ONil(X2383))),c_List_Olexord(X2383,X2381))),
inference(variable_rename,[status(thm)],[i_0_540]) ).
fof(i_0_730,plain,
! [X4116,X4117,X4118] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4118,X4118),tc_HOL_Obool),X4117,c_Product__Type_OSigma(X4118,X4118,X4116,c_COMBK(tc_fun(X4118,tc_HOL_Obool),X4118,X4116)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X4118),tc_List_Olist(X4118)),tc_HOL_Obool),c_List_Olistrel(X4118,X4117),c_Product__Type_OSigma(tc_List_Olist(X4118),tc_List_Olist(X4118),c_List_Olists(X4118,X4116),c_COMBK(tc_fun(tc_List_Olist(X4118),tc_HOL_Obool),tc_List_Olist(X4118),c_List_Olists(X4118,X4116)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])]) ).
fof(i_0_731,plain,
! [X2664,X2665,X2666,X2667] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2667),tc_List_Olist(X2667))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2667),tc_List_Olist(X2667)),X2666),X2665)),c_List_Olistrel1(X2667,X2664)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2667),X2666) = c_Nat_Osize__class_Osize(tc_List_Olist(X2667),X2665) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).
fof(i_0_732,plain,
! [X2668,X2669,X2670,X2671] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2671),tc_List_Olist(X2671))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2671),tc_List_Olist(X2671)),X2670),X2669)),c_List_Olistrel(X2671,X2668)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X2671),X2670) = c_Nat_Osize__class_Osize(tc_List_Olist(X2671),X2669) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).
fof(i_0_733,plain,
! [X2139,X2140,X2141,X2143,X2144,X2145,X2146,X2147,X2150] :
( ( ~ hBOOL(hAPP(X2141,esk3_3(X2139,X2140,X2141)))
| hBOOL(hAPP(X2141,hAPP(hAPP(c_Product__Type_OPair(X2140,X2139),X2143),X2144))) )
& ( ~ hBOOL(hAPP(X2147,hAPP(hAPP(c_Product__Type_OPair(X2146,X2145),esk4_3(X2145,X2146,X2147)),esk5_3(X2145,X2146,X2147))))
| hBOOL(hAPP(X2147,X2150)) ) ),
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_734,plain,
! [X2376,X2377,X2378,X2379,X2380] :
( ~ hBOOL(hAPP(X2380,hAPP(hAPP(c_Product__Type_OPair(X2379,X2378),X2377),X2376)))
| hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2379,X2378,tc_HOL_Obool,X2380),X2377),X2376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).
cnf(i_0_735,plain,
c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))),c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4))) = c_Product__Type_OSigma(X2,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_541]) ).
fof(i_0_736,plain,
! [X3436,X3437] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3437,X3437)),hAPP(hAPP(c_Product__Type_OPair(X3437,X3437),esk90_2(X3436,X3437)),esk91_2(X3436,X3437))),X3436))
| c_Relation_Otrans(X3437,X3436) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3437,X3437)),hAPP(hAPP(c_Product__Type_OPair(X3437,X3437),esk91_2(X3436,X3437)),esk92_2(X3436,X3437))),X3436))
| c_Relation_Otrans(X3437,X3436) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3437,X3437)),hAPP(hAPP(c_Product__Type_OPair(X3437,X3437),esk90_2(X3436,X3437)),esk92_2(X3436,X3437))),X3436))
| c_Relation_Otrans(X3437,X3436) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transI])])])]) ).
fof(i_0_737,plain,
! [X2133,X2134,X2135,X2136,X2137] :
( ( ~ c_Nitpick_Orefl_H(X2134,X2133)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2134,X2134)),hAPP(hAPP(c_Product__Type_OPair(X2134,X2134),X2135),X2135)),X2133)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2137,X2137)),hAPP(hAPP(c_Product__Type_OPair(X2137,X2137),esk2_2(X2136,X2137)),esk2_2(X2136,X2137))),X2136))
| c_Nitpick_Orefl_H(X2137,X2136) ) ),
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])])])])]) ).
cnf(i_0_738,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_542]) ).
fof(i_0_739,plain,
! [X2625,X2626,X2627,X2628,X2629,X2630] :
( X2628 != hAPP(hAPP(c_List_Olist_OCons(X2627),X2629),X2630)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2627),tc_List_Olist(X2627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2627),tc_List_Olist(X2627)),X2626),hAPP(hAPP(c_List_Oappend(X2627),X2626),X2628))),c_List_Olexord(X2627,X2625))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).
fof(i_0_740,plain,
! [X3689,X3690,X3691,X3692] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3692,tc_HOL_Obool),c_Relation_ORange(X3691,X3692,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3691,X3692),tc_HOL_Obool)),X3690),X3689)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3692,tc_HOL_Obool)),c_Relation_ORange(X3691,X3692,X3690)),c_Relation_ORange(X3691,X3692,X3689))),
inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).
fof(i_0_741,plain,
! [X3685,X3686,X3687,X3688] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3688,tc_HOL_Obool),c_Relation_ODomain(X3688,X3687,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3688,X3687),tc_HOL_Obool)),X3686),X3685)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3688,tc_HOL_Obool)),c_Relation_ODomain(X3688,X3687,X3686)),c_Relation_ODomain(X3688,X3687,X3685))),
inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).
fof(i_0_742,plain,
! [X4103,X4104,X4105] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X4105),c_List_OtakeWhile(X4105,X4104,X4103)),c_Nat_Osize__class_Osize(tc_List_Olist(X4105),X4103))
| ~ hBOOL(hAPP(X4104,c_List_Onth(X4105,X4103,c_Nat_Osize__class_Osize(tc_List_Olist(X4105),c_List_OtakeWhile(X4105,X4104,X4103))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])]) ).
fof(i_0_743,plain,
! [X2286,X2287,X2288,X2289,X2290,X2291] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2291,X2290)),X2289),c_FuncSet_OPi(X2291,X2290,X2288,X2287)))
| ~ hBOOL(hAPP(hAPP(c_member(X2291),X2286),X2288))
| hBOOL(hAPP(hAPP(c_member(X2290),hAPP(X2289,X2286)),hAPP(X2287,X2286))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_744,plain,
! [X2269,X2270,X2271,X2272,X2273,X2274] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2274,X2273)),X2272),c_FuncSet_OPi(X2274,X2273,X2271,X2270)))
| hBOOL(hAPP(hAPP(c_member(X2273),hAPP(X2272,X2269)),hAPP(X2270,X2269)))
| ~ hBOOL(hAPP(hAPP(c_member(X2274),X2269),X2271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).
fof(i_0_745,plain,
! [X4045,X4046,X4047,X4048,X4049,X4050] :
( ~ hBOOL(hAPP(hAPP(c_member(X4050),X4049),X4048))
| ~ hBOOL(hAPP(hAPP(c_member(X4047),X4046),hAPP(X4045,X4049)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4050,X4047)),hAPP(hAPP(c_Product__Type_OPair(X4050,X4047),X4049),X4046)),c_Product__Type_OSigma(X4050,X4047,X4048,X4045))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).
fof(i_0_746,plain,
! [X3581,X3582,X3583] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3583,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3583,tc_fun(X3583,tc_HOL_Obool),tc_HOL_Obool),c_member(X3583)),X3582),hAPP(hAPP(c_COMBC(X3583,tc_fun(X3583,tc_HOL_Obool),tc_HOL_Obool),c_member(X3583)),X3581))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3583,tc_HOL_Obool),X3582,X3581) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3583,tc_HOL_Obool),X3582,X3581)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3583,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X3583,tc_fun(X3583,tc_HOL_Obool),tc_HOL_Obool),c_member(X3583)),X3582),hAPP(hAPP(c_COMBC(X3583,tc_fun(X3583,tc_HOL_Obool),tc_HOL_Obool),c_member(X3583)),X3581)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_747,plain,
! [X3813,X3814,X3815,X3816,X3817] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3817,X3816),hAPP(X3817,X3815))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3814,X3814)),hAPP(hAPP(c_Product__Type_OPair(X3814,X3814),X3816),X3815)),c_List_Omeasures(X3814,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X3814,tc_Nat_Onat)),X3817),X3813)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).
fof(i_0_748,plain,
! [X2113,X2114,X2115,X2116] :
( ( X2115 != X2113
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),c_Arrow__Order__Mirabelle_Omkbot(X2114,X2113))) )
& ( X2116 != X2113
| X2116 != X2115
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),c_Arrow__Order__Mirabelle_Omkbot(X2114,X2113))) )
& ( X2116 = X2113
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),X2114))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),c_Arrow__Order__Mirabelle_Omkbot(X2114,X2113))) )
& ( X2116 != X2113
| X2116 = X2113
| X2115 = X2113
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),c_Arrow__Order__Mirabelle_Omkbot(X2114,X2113))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),X2114))
| X2116 = X2113
| X2115 = X2113
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),c_Arrow__Order__Mirabelle_Omkbot(X2114,X2113))) )
& ( X2116 != X2113
| X2116 = X2115
| X2115 = X2113
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),c_Arrow__Order__Mirabelle_Omkbot(X2114,X2113))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),X2114))
| X2116 = X2115
| X2115 = X2113
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2116),X2115)),c_Arrow__Order__Mirabelle_Omkbot(X2114,X2113))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_749,plain,
! [X2117,X2118,X2119,X2120] :
( ( X2120 != X2117
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),c_Arrow__Order__Mirabelle_Omktop(X2118,X2117))) )
& ( X2119 != X2117
| X2120 != X2119
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),c_Arrow__Order__Mirabelle_Omktop(X2118,X2117))) )
& ( X2119 = X2117
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),X2118))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),c_Arrow__Order__Mirabelle_Omktop(X2118,X2117))) )
& ( X2119 != X2117
| X2119 = X2117
| X2120 = X2117
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),c_Arrow__Order__Mirabelle_Omktop(X2118,X2117))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),X2118))
| X2119 = X2117
| X2120 = X2117
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),c_Arrow__Order__Mirabelle_Omktop(X2118,X2117))) )
& ( X2119 != X2117
| X2120 = X2119
| X2120 = X2117
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),c_Arrow__Order__Mirabelle_Omktop(X2118,X2117))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),X2118))
| X2120 = X2119
| X2120 = X2117
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2120),X2119)),c_Arrow__Order__Mirabelle_Omktop(X2118,X2117))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_750,plain,
! [X4129,X4130,X4131,X4132,X4133] : c_Product__Type_OSigma(X4133,X4132,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4133,tc_HOL_Obool)),X4131),X4130),X4129) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4133,X4132),tc_HOL_Obool)),c_Product__Type_OSigma(X4133,X4132,X4131,X4129)),c_Product__Type_OSigma(X4133,X4132,X4130,X4129)),
inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).
fof(i_0_751,plain,
! [X2107] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2107)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2107))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2107)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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____,X2107))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iff])]) ).
fof(i_0_752,plain,
! [X2233,X2234,X2235] :
( X2235 = X2234
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2233),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,X2233),X2235),X2234)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_753,plain,
! [X2798,X2799,X2800,X2801] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2801,X2801)),hAPP(hAPP(c_Product__Type_OPair(X2801,X2801),X2800),X2799)),c_Transitive__Closure_Ortrancl(X2801,X2798)))
| ~ hBOOL(hAPP(hAPP(c_member(X2801),X2799),c_Wellfounded_Oacc(X2801,X2798)))
| hBOOL(hAPP(hAPP(c_member(X2801),X2800),c_Wellfounded_Oacc(X2801,X2798))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).
fof(i_0_754,plain,
! [X2794,X2795,X2796,X2797] :
( ~ hBOOL(hAPP(hAPP(c_member(X2797),X2796),c_Wellfounded_Oacc(X2797,X2795)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2797,X2797)),hAPP(hAPP(c_Product__Type_OPair(X2797,X2797),X2794),X2796)),c_Transitive__Closure_Ortrancl(X2797,X2795)))
| hBOOL(hAPP(hAPP(c_member(X2797),X2794),c_Wellfounded_Oacc(X2797,X2795))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).
fof(i_0_755,plain,
! [X2310,X2311,X2312,X2313,X2314] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2311,X2310)
| ~ 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))),X2312),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2311,X2312) = hAPP(X2312,X2310) )
& ( 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))),esk22_2(X2313,X2314)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2314,X2313) )
& ( hAPP(X2314,esk22_2(X2313,X2314)) != hAPP(esk22_2(X2313,X2314),X2313)
| c_Arrow__Order__Mirabelle_Odictator(X2314,X2313) ) ),
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_756,plain,
! [X2863,X2864,X2865,X2866] :
( ~ hBOOL(hAPP(hAPP(c_member(X2866),X2865),c_Wellfounded_Oacc(X2866,X2864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2866,X2866)),hAPP(hAPP(c_Product__Type_OPair(X2866,X2866),X2863),X2865)),X2864))
| hBOOL(hAPP(hAPP(c_member(X2866),X2863),c_Wellfounded_Oacc(X2866,X2864))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).
fof(i_0_757,plain,
! [X3323,X3324,X3325] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3325,X3325)),hAPP(hAPP(c_Product__Type_OPair(X3325,X3325),X3324),X3323)),c_List_Omeasures(X3325,c_List_Olist_ONil(tc_fun(X3325,tc_Nat_Onat))))),
inference(variable_rename,[status(thm)],[i_0_545]) ).
fof(i_0_758,plain,
! [X2807,X2808,X2809,X2810] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2810,X2810)),hAPP(hAPP(c_Product__Type_OPair(X2810,X2810),X2809),X2807)),c_Transitive__Closure_Ortrancl(X2810,X2808)))
| X2809 = X2807
| hBOOL(hAPP(hAPP(c_member(X2810),X2809),c_Relation_ODomain(X2810,X2810,X2808))) )
& ( X2809 != X2807
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2810,X2810)),hAPP(hAPP(c_Product__Type_OPair(X2810,X2810),X2809),X2807)),c_Transitive__Closure_Ortrancl(X2810,X2808)))
| hBOOL(hAPP(hAPP(c_member(X2810),X2809),c_Relation_ODomain(X2810,X2810,X2808))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])])]) ).
fof(i_0_759,plain,
! [X2328,X2329,X2330] :
( X2330 = X2329
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2328),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(X2328,X2330,X2329)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_760,plain,
! [X2816,X2817,X2818,X2819,X2820] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2820,X2819)),hAPP(hAPP(c_Product__Type_OPair(X2820,X2819),X2818),X2817)),X2816))
| hBOOL(hAPP(hAPP(c_member(X2820),X2818),c_Relation_ODomain(X2820,X2819,X2816))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).
fof(i_0_761,plain,
! [X2811,X2812,X2813,X2814,X2815] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2815,X2814)),hAPP(hAPP(c_Product__Type_OPair(X2815,X2814),X2813),X2812)),X2811))
| hBOOL(hAPP(hAPP(c_member(X2814),X2812),c_Relation_ORange(X2815,X2814,X2811))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).
fof(i_0_762,plain,
! [X2292,X2293] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2293,X2293)),c_COMBI(X2293)),c_FuncSet_OPi(X2293,X2293,X2292,c_COMBK(tc_fun(X2293,tc_HOL_Obool),X2293,X2292)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_763,plain,
! [X2586,X2587] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2587),tc_List_Olist(X2587))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2587),tc_List_Olist(X2587)),c_List_Olist_ONil(X2587)),c_List_Olist_ONil(X2587))),c_List_Olistrel(X2587,X2586))),
inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).
fof(i_0_764,plain,
! [X2950,X2951,X2952,X2953] :
( ( X2952 = X2951
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2953,X2953)),hAPP(hAPP(c_Product__Type_OPair(X2953,X2953),X2952),X2951)),c_Relation_OId__on(X2953,X2950))) )
& ( hBOOL(hAPP(hAPP(c_member(X2953),X2952),X2950))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2953,X2953)),hAPP(hAPP(c_Product__Type_OPair(X2953,X2953),X2952),X2951)),c_Relation_OId__on(X2953,X2950))) )
& ( X2952 != X2951
| ~ hBOOL(hAPP(hAPP(c_member(X2953),X2952),X2950))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2953,X2953)),hAPP(hAPP(c_Product__Type_OPair(X2953,X2953),X2952),X2951)),c_Relation_OId__on(X2953,X2950))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).
fof(i_0_765,plain,
! [X3968,X3969,X3970,X3971] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3971,X3971)),hAPP(hAPP(c_Product__Type_OPair(X3971,X3971),X3970),X3969)),c_Wellfounded_Omeasure(X3971,X3968)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3968,X3970),hAPP(X3968,X3969)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3968,X3970),hAPP(X3968,X3969))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3971,X3971)),hAPP(hAPP(c_Product__Type_OPair(X3971,X3971),X3970),X3969)),c_Wellfounded_Omeasure(X3971,X3968))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_766,plain,
! [X2716,X2717,X2718] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X2718),tc_List_Olist(X2718))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2718),tc_List_Olist(X2718)),X2717),X2717)),c_List_Olistrel(X2718,c_Transitive__Closure_Ortrancl(X2718,X2716)))),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).
fof(i_0_767,plain,
! [X2788,X2789,X2790,X2791,X2792] :
( ( ~ c_Relation_Oirrefl(X2789,X2788)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2789,X2789)),hAPP(hAPP(c_Product__Type_OPair(X2789,X2789),X2790),X2790)),X2788)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2792,X2792)),hAPP(hAPP(c_Product__Type_OPair(X2792,X2792),esk49_2(X2791,X2792)),esk49_2(X2791,X2792))),X2791))
| c_Relation_Oirrefl(X2792,X2791) ) ),
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_547])])])])]) ).
fof(i_0_768,plain,
! [X2236,X2237] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2237),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(X2237,X2236)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_769,plain,
! [X2238,X2239] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2239),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(X2239,X2238)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_770,plain,
! [X3401,X3402] :
( X3402 = c_List_Olist_ONil(X3401)
| ~ c_List_Odistinct(X3401,X3402)
| c_List_OtakeWhile(X3401,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3401),c_fNot),hAPP(hAPP(c_COMBC(X3401,X3401,tc_HOL_Obool),c_fequal),c_List_Olast(X3401,X3402))),X3402) = c_List_Obutlast(X3401,X3402) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last])]) ).
fof(i_0_771,plain,
! [X2821,X2822,X2823,X2824] :
( ~ hBOOL(hAPP(hAPP(c_member(X2824),X2823),c_Wellfounded_Oacc(X2824,X2822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2824)),X2821),c_Wellfounded_Oacc(tc_List_Olist(X2824),c_List_Olistrel1(X2824,X2822))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2824)),hAPP(hAPP(c_List_Olist_OCons(X2824),X2823),X2821)),c_Wellfounded_Oacc(tc_List_Olist(X2824),c_List_Olistrel1(X2824,X2822)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).
fof(i_0_772,plain,
! [X3235,X3236,X3237,X3238,X3239,X3240] : c_Set_Oimage(X3240,X3239,X3238,c_Set_Oimage(X3237,X3240,X3236,X3235)) = c_Set_Oimage(X3237,X3239,hAPP(hAPP(c_COMBB(X3240,X3239,X3237),X3238),X3236),X3235),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_773,plain,
! [X3147,X3148,X3149,X3150] :
( ~ hBOOL(hAPP(c_List_Olistsp(X3150,X3149),X3148))
| ~ hBOOL(hAPP(c_List_Olistsp(X3150,X3147),X3148))
| hBOOL(hAPP(c_List_Olistsp(X3150,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3150,tc_HOL_Obool)),X3149),X3147)),X3148)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])]) ).
cnf(i_0_774,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_548]) ).
fof(i_0_775,plain,
! [X4136,X4137,X4138,X4139,X4140,X4141] :
( ( c_Product__Type_OSigma(X4138,X4141,X4137,c_COMBK(tc_fun(X4141,tc_HOL_Obool),X4138,X4139)) != c_Product__Type_OSigma(X4138,X4141,X4136,c_COMBK(tc_fun(X4141,tc_HOL_Obool),X4138,X4139))
| X4137 = X4136
| ~ hBOOL(hAPP(hAPP(c_member(X4141),X4140),X4139)) )
& ( X4137 != X4136
| c_Product__Type_OSigma(X4138,X4141,X4137,c_COMBK(tc_fun(X4141,tc_HOL_Obool),X4138,X4139)) = c_Product__Type_OSigma(X4138,X4141,X4136,c_COMBK(tc_fun(X4141,tc_HOL_Obool),X4138,X4139))
| ~ hBOOL(hAPP(hAPP(c_member(X4141),X4140),X4139)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).
fof(i_0_776,plain,
! [X2197,X2198,X2199,X2200,X2201,X2202] : c_Product__Type_Oprod_Oprod__rec(X2202,X2201,X2200,X2199,hAPP(hAPP(c_Product__Type_OPair(X2202,X2201),X2198),X2197)) = hAPP(hAPP(X2199,X2198),X2197),
inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).
fof(i_0_777,plain,
! [X3963,X3964,X3965,X3966,X3967] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X3967,X3966),hAPP(X3967,X3965))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3964,X3964)),hAPP(hAPP(c_Product__Type_OPair(X3964,X3964),X3966),X3965)),c_Wellfounded_Omlex__prod(X3964,X3967,X3963))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_778,plain,
! [X3253,X3254,X3255,X3256,X3257] :
( ~ hBOOL(hAPP(hAPP(c_member(X3257),X3256),X3255))
| hBOOL(hAPP(hAPP(c_member(X3254),hAPP(X3253,X3256)),c_Set_Oimage(X3257,X3254,X3253,X3255))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_779,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_780,plain,
! [X4166,X4167,X4168,X4169] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4169,c_Nat_Osize__class_Osize(tc_List_Olist(X4168),c_List_OdropWhile(X4168,X4167,X4166)))
| c_List_Onth(X4168,c_List_OdropWhile(X4168,X4167,X4166),X4169) = c_List_Onth(X4168,X4166,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4169,c_Nat_Osize__class_Osize(tc_List_Olist(X4168),c_List_OtakeWhile(X4168,X4167,X4166)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__nth])]) ).
fof(i_0_781,plain,
! [X3217,X3218,X3219,X3220,X3221,X3222] :
( X3222 != hAPP(X3221,X3220)
| ~ hBOOL(hAPP(hAPP(c_member(X3219),X3220),X3218))
| hBOOL(hAPP(hAPP(c_member(X3217),X3222),c_Set_Oimage(X3219,X3217,X3221,X3218))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_782,plain,
! [X3258,X3259,X3260,X3261,X3262,X3263] :
( ~ hBOOL(hAPP(hAPP(c_member(X3263),X3262),X3261))
| X3260 != hAPP(X3259,X3262)
| hBOOL(hAPP(hAPP(c_member(X3258),X3260),c_Set_Oimage(X3263,X3258,X3259,X3261))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_783,plain,
! [X2964,X2965,X2966,X2967] :
( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2967)),X2966),c_List_Olists(X2967,X2964)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2967)),hAPP(hAPP(c_List_Oappend(X2967),X2966),X2965)),c_List_Olists(X2967,X2964))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2967)),X2965),c_List_Olists(X2967,X2964)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2967)),hAPP(hAPP(c_List_Oappend(X2967),X2966),X2965)),c_List_Olists(X2967,X2964))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2967)),X2966),c_List_Olists(X2967,X2964)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2967)),X2965),c_List_Olists(X2967,X2964)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2967)),hAPP(hAPP(c_List_Oappend(X2967),X2966),X2965)),c_List_Olists(X2967,X2964))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).
fof(i_0_784,plain,
! [X2972,X2973,X2974,X2975] :
( X2975 != X2974
| ~ hBOOL(hAPP(hAPP(c_member(X2973),X2975),X2972))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2973,X2973)),hAPP(hAPP(c_Product__Type_OPair(X2973,X2973),X2975),X2974)),c_Relation_OId__on(X2973,X2972))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).
fof(i_0_785,plain,
! [X3551,X3552,X3553,X3554,X3555] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3555,tc_HOL_Obool),X3554,X3553)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X3555,X3552),tc_HOL_Obool),c_FuncSet_OPi(X3555,X3552,X3553,X3551),c_FuncSet_OPi(X3555,X3552,X3554,X3551)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_786,plain,
! [X2397,X2398,X2399,X2400,X2401,X2402] : hAPP(hAPP(c_Product__Type_Ocurry(X2402,X2401,X2400,X2399),X2398),X2397) = hAPP(X2399,hAPP(hAPP(c_Product__Type_OPair(X2402,X2401),X2398),X2397)),
inference(variable_rename,[status(thm)],[fact_curry__conv]) ).
fof(i_0_787,plain,
! [X2362,X2363,X2364,X2365,X2366,X2367] : hAPP(hAPP(c_Product__Type_Ocurry(X2367,X2366,X2365,X2364),X2363),X2362) = hAPP(X2364,hAPP(hAPP(c_Product__Type_OPair(X2367,X2366),X2363),X2362)),
inference(variable_rename,[status(thm)],[fact_curry__def]) ).
fof(i_0_788,plain,
! [X2337,X2338,X2339,X2340] : c_List_Olist_Olist__case(X2340,X2339,X2338,X2337,c_List_Olist_ONil(X2339)) = X2338,
inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).
fof(i_0_789,plain,
! [X3584,X3585,X3586,X3587,X3588] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3588,tc_HOL_Obool),X3587,X3586)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3585,tc_HOL_Obool),c_Set_Oimage(X3588,X3585,X3584,X3587),c_Set_Oimage(X3588,X3585,X3584,X3586)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_790,plain,
! [X2968,X2969,X2970,X2971] :
( ( hBOOL(hAPP(hAPP(c_member(X2971),X2970),X2968))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2971)),hAPP(hAPP(c_List_Olist_OCons(X2971),X2970),X2969)),c_List_Olists(X2971,X2968))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2971)),X2969),c_List_Olists(X2971,X2968)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2971)),hAPP(hAPP(c_List_Olist_OCons(X2971),X2970),X2969)),c_List_Olists(X2971,X2968))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2971),X2970),X2968))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2971)),X2969),c_List_Olists(X2971,X2968)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2971)),hAPP(hAPP(c_List_Olist_OCons(X2971),X2970),X2969)),c_List_Olists(X2971,X2968))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).
fof(i_0_791,plain,
! [X3086,X3087,X3088,X3089] :
( ~ hBOOL(hAPP(hAPP(c_member(X3089),X3088),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3089,tc_HOL_Obool)),X3087),X3086)))
| hBOOL(hAPP(hAPP(c_member(X3089),X3088),X3087)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).
fof(i_0_792,plain,
! [X3082,X3083,X3084,X3085] :
( ( hBOOL(hAPP(hAPP(c_member(X3085),X3084),X3083))
| ~ hBOOL(hAPP(hAPP(c_member(X3085),X3084),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3085,tc_HOL_Obool)),X3083),X3082))) )
& ( hBOOL(hAPP(hAPP(c_member(X3085),X3084),X3082))
| ~ hBOOL(hAPP(hAPP(c_member(X3085),X3084),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3085,tc_HOL_Obool)),X3083),X3082))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3085),X3084),X3083))
| ~ hBOOL(hAPP(hAPP(c_member(X3085),X3084),X3082))
| hBOOL(hAPP(hAPP(c_member(X3085),X3084),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3085,tc_HOL_Obool)),X3083),X3082))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).
fof(i_0_793,plain,
! [X3071,X3072,X3073,X3074] :
( ( hBOOL(hAPP(hAPP(c_member(X3074),X3073),X3072))
| ~ hBOOL(hAPP(hAPP(c_member(X3074),X3073),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3074,tc_HOL_Obool)),X3072),X3071))) )
& ( hBOOL(hAPP(hAPP(c_member(X3074),X3073),X3071))
| ~ hBOOL(hAPP(hAPP(c_member(X3074),X3073),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3074,tc_HOL_Obool)),X3072),X3071))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])])]) ).
fof(i_0_794,plain,
! [X3090,X3091,X3092,X3093] :
( ~ hBOOL(hAPP(hAPP(c_member(X3093),X3092),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3093,tc_HOL_Obool)),X3091),X3090)))
| hBOOL(hAPP(hAPP(c_member(X3093),X3092),X3090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).
fof(i_0_795,plain,
! [X3116,X3117,X3118,X3119] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3119,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3119,tc_HOL_Obool)),X3118),X3117)),X3116) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3119,tc_HOL_Obool)),X3118),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3119,tc_HOL_Obool)),X3117),X3116)),
inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).
fof(i_0_796,plain,
! [X2986,X2987,X2988] :
( ( hBOOL(hAPP(hAPP(c_member(X2988),esk65_3(X2986,X2987,X2988)),X2986))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2988,X2988)),X2987),c_Relation_OId__on(X2988,X2986))) )
& ( X2987 = hAPP(hAPP(c_Product__Type_OPair(X2988,X2988),esk65_3(X2986,X2987,X2988)),esk65_3(X2986,X2987,X2988))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2988,X2988)),X2987),c_Relation_OId__on(X2988,X2986))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).
fof(i_0_797,plain,
! [X2260,X2261,X2262] :
( ( hAPP(hAPP(c_COMBC(X2262,tc_fun(X2262,tc_HOL_Obool),tc_HOL_Obool),c_member(X2262)),X2261) != hAPP(hAPP(c_COMBC(X2262,tc_fun(X2262,tc_HOL_Obool),tc_HOL_Obool),c_member(X2262)),X2260)
| X2261 = X2260 )
& ( X2261 != X2260
| hAPP(hAPP(c_COMBC(X2262,tc_fun(X2262,tc_HOL_Obool),tc_HOL_Obool),c_member(X2262)),X2261) = hAPP(hAPP(c_COMBC(X2262,tc_fun(X2262,tc_HOL_Obool),tc_HOL_Obool),c_member(X2262)),X2260) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_798,plain,
! [X2748,X2749,X2750] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2750,X2750)),hAPP(hAPP(c_Product__Type_OPair(X2750,X2750),X2749),X2749)),c_Transitive__Closure_Ortrancl(X2750,X2748))),
inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
fof(i_0_799,plain,
! [X2307,X2308] :
( X2308 = X2307
| c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X2308),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),X2307),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),esk21_2(X2307,X2308)),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_800,plain,
! [X3075,X3076,X3077,X3078] :
( ~ hBOOL(hAPP(hAPP(c_member(X3078),X3077),X3076))
| ~ hBOOL(hAPP(hAPP(c_member(X3078),X3077),X3075))
| hBOOL(hAPP(hAPP(c_member(X3078),X3077),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3078,tc_HOL_Obool)),X3076),X3075))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).
cnf(i_0_801,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_550]) ).
cnf(i_0_802,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_551]) ).
fof(i_0_803,plain,
! [X3063,X3064,X3065,X3066] :
( ( hBOOL(hAPP(X3065,X3063))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3066,tc_HOL_Obool)),X3065),X3064),X3063)) )
& ( hBOOL(hAPP(X3064,X3063))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3066,tc_HOL_Obool)),X3065),X3064),X3063)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])])]) ).
fof(i_0_804,plain,
! [X3106,X3107,X3108,X3109] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3109,tc_HOL_Obool)),X3108),X3107),X3106))
| hBOOL(hAPP(X3108,X3106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).
fof(i_0_805,plain,
! [X3102,X3103,X3104,X3105] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3105,tc_HOL_Obool)),X3104),X3103),X3102))
| hBOOL(hAPP(X3103,X3102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).
fof(i_0_806,plain,
! [X2654,X2655,X2656,X2657,X2658,X2659] :
( ( hBOOL(hAPP(hAPP(X2658,X2657),X2655))
| ~ c_List_Olistrelp(X2659,X2658,hAPP(hAPP(c_List_Olist_OCons(X2659),X2657),X2656),hAPP(hAPP(c_List_Olist_OCons(X2659),X2655),X2654)) )
& ( c_List_Olistrelp(X2659,X2658,X2656,X2654)
| ~ c_List_Olistrelp(X2659,X2658,hAPP(hAPP(c_List_Olist_OCons(X2659),X2657),X2656),hAPP(hAPP(c_List_Olist_OCons(X2659),X2655),X2654)) )
& ( ~ hBOOL(hAPP(hAPP(X2658,X2657),X2655))
| ~ c_List_Olistrelp(X2659,X2658,X2656,X2654)
| c_List_Olistrelp(X2659,X2658,hAPP(hAPP(c_List_Olist_OCons(X2659),X2657),X2656),hAPP(hAPP(c_List_Olist_OCons(X2659),X2655),X2654)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).
fof(i_0_807,plain,
! [X2648,X2649,X2650,X2651,X2652,X2653] :
( ~ hBOOL(hAPP(hAPP(X2653,X2652),X2651))
| ~ c_List_Olistrelp(X2650,X2653,X2649,X2648)
| c_List_Olistrelp(X2650,X2653,hAPP(hAPP(c_List_Olist_OCons(X2650),X2652),X2649),hAPP(hAPP(c_List_Olist_OCons(X2650),X2651),X2648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).
fof(i_0_808,plain,
! [X2976,X2977,X2978,X2981,X2982,X2983,X2984,X2985] :
( ( X2977 = hAPP(hAPP(c_List_Olist_OCons(X2978),esk63_3(X2976,X2977,X2978)),esk64_3(X2976,X2977,X2978))
| X2977 = c_List_Olist_ONil(X2978)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2978)),X2977),c_List_Olists(X2978,X2976))) )
& ( hBOOL(hAPP(hAPP(c_member(X2978),esk63_3(X2976,X2977,X2978)),X2976))
| X2977 = c_List_Olist_ONil(X2978)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2978)),X2977),c_List_Olists(X2978,X2976))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2978)),esk64_3(X2976,X2977,X2978)),c_List_Olists(X2978,X2976)))
| X2977 = c_List_Olist_ONil(X2978)
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2978)),X2977),c_List_Olists(X2978,X2976))) )
& ( X2982 != c_List_Olist_ONil(X2983)
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2983)),X2982),c_List_Olists(X2983,X2981))) )
& ( X2982 != hAPP(hAPP(c_List_Olist_OCons(X2983),X2984),X2985)
| ~ hBOOL(hAPP(hAPP(c_member(X2983),X2984),X2981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2983)),X2985),c_List_Olists(X2983,X2981)))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2983)),X2982),c_List_Olists(X2983,X2981))) ) ),
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_809,plain,
! [X4134,X4135] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X4135,X4135),tc_HOL_Obool),c_Relation_OId__on(X4135,X4134),c_Product__Type_OSigma(X4135,X4135,X4134,c_COMBK(tc_fun(X4135,tc_HOL_Obool),X4135,X4134))),
inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).
fof(i_0_810,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)),esk24_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)),esk24_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_811,plain,
! [X2685,X2686,X2687,X2688,X2689] : c_List_Omaps(X2689,X2688,X2687,hAPP(hAPP(c_List_Olist_OCons(X2689),X2686),X2685)) = hAPP(hAPP(c_List_Oappend(X2688),hAPP(X2687,X2686)),c_List_Omaps(X2689,X2688,X2687,X2685)),
inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J]) ).
fof(i_0_812,plain,
! [X3617,X3618,X3619,X3620,X3621] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3621,tc_HOL_Obool),X3620,X3619)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3621,tc_HOL_Obool),X3618,X3617)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3621,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3621,tc_HOL_Obool)),X3620),X3618),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3621,tc_HOL_Obool)),X3619),X3617)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).
fof(i_0_813,plain,
! [X2751,X2752,X2753] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2753,X2753)),X2752),X2751))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2753,X2753)),X2752),c_Transitive__Closure_Ortrancl(X2753,X2751))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).
fof(i_0_814,plain,
! [X3120,X3121,X3122,X3123] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3123,tc_HOL_Obool)),X3122),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3123,tc_HOL_Obool)),X3121),X3120)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3123,tc_HOL_Obool)),X3121),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3123,tc_HOL_Obool)),X3122),X3120)),
inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).
fof(i_0_815,plain,
! [X2939,X2940,X2941] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2941)),X2940),c_Wellfounded_Oacc(tc_List_Olist(X2941),c_List_Olistrel1(X2941,X2939))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2941)),X2940),c_List_Olists(X2941,c_Wellfounded_Oacc(X2941,X2939)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).
fof(i_0_816,plain,
! [X2936,X2937,X2938] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2938)),X2937),c_List_Olists(X2938,c_Wellfounded_Oacc(X2938,X2936))))
| hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2938)),X2937),c_Wellfounded_Oacc(tc_List_Olist(X2938),c_List_Olistrel1(X2938,X2936)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).
fof(i_0_817,plain,
! [X3144,X3145,X3146] :
( ~ c_Relation_Otrans(X3146,X3145)
| ~ c_Relation_Otrans(X3146,X3144)
| c_Relation_Otrans(X3146,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X3146,X3146),tc_HOL_Obool)),X3145),X3144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__Int])]) ).
fof(i_0_818,plain,
! [X3431,X3432,X3433,X3434,X3435] :
( ( X3433 = hAPP(hAPP(c_List_Oappend(X3435),c_List_OtakeWhile(X3435,X3434,X3433)),hAPP(hAPP(c_List_Olist_OCons(X3435),X3432),X3431))
| c_List_OdropWhile(X3435,X3434,X3433) != hAPP(hAPP(c_List_Olist_OCons(X3435),X3432),X3431) )
& ( ~ hBOOL(hAPP(X3434,X3432))
| c_List_OdropWhile(X3435,X3434,X3433) != hAPP(hAPP(c_List_Olist_OCons(X3435),X3432),X3431) )
& ( X3433 != hAPP(hAPP(c_List_Oappend(X3435),c_List_OtakeWhile(X3435,X3434,X3433)),hAPP(hAPP(c_List_Olist_OCons(X3435),X3432),X3431))
| hBOOL(hAPP(X3434,X3432))
| c_List_OdropWhile(X3435,X3434,X3433) = hAPP(hAPP(c_List_Olist_OCons(X3435),X3432),X3431) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])])]) ).
fof(i_0_819,plain,
! [X3067,X3068,X3069,X3070] :
( ~ hBOOL(hAPP(X3070,X3069))
| ~ hBOOL(hAPP(X3068,X3069))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3067,tc_HOL_Obool)),X3070),X3068),X3069)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).
fof(i_0_820,plain,
! [X4106,X4107,X4108,X4109] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4109,c_Nat_Osize__class_Osize(tc_List_Olist(X4108),c_List_OtakeWhile(X4108,X4107,X4106)))
| c_List_Onth(X4108,c_List_OtakeWhile(X4108,X4107,X4106),X4109) = c_List_Onth(X4108,X4106,X4109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__nth])]) ).
fof(i_0_821,plain,
! [X2319,X2320,X2321,X2322,X2323] : c_List_Osplice(X2323,hAPP(hAPP(c_List_Olist_OCons(X2323),X2322),X2321),hAPP(hAPP(c_List_Olist_OCons(X2323),X2320),X2319)) = hAPP(hAPP(c_List_Olist_OCons(X2323),X2322),hAPP(hAPP(c_List_Olist_OCons(X2323),X2320),c_List_Osplice(X2323,X2321,X2319))),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).
fof(i_0_822,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),esk6_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_554])])]) ).
cnf(i_0_823,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_555]) ).
fof(i_0_824,plain,
! [X3613,X3614,X3615,X3616] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3616,tc_HOL_Obool),X3615,X3614)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3616,tc_HOL_Obool),X3615,X3613)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3616,tc_HOL_Obool),X3615,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3616,tc_HOL_Obool)),X3614),X3613)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).
fof(i_0_825,plain,
! [X2914,X2915,X2916,X2917,X2918,X2919,X2920] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2916,X2915),X2914))
| ~ hBOOL(hAPP(hAPP(X2915,X2917),X2914))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2916,X2915),X2917)) )
& ( hBOOL(hAPP(hAPP(X2919,esk59_3(X2918,X2919,X2920)),X2918))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2920,X2919),X2918)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2920,X2919),esk59_3(X2918,X2919,X2920)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2920,X2919),X2918)) ) ),
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_826,plain,
! [X2906,X2907,X2908,X2909,X2910,X2911,X2912] :
( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2908,X2907),X2906))
| ~ hBOOL(hAPP(hAPP(X2907,X2909),X2906))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2908,X2907),X2909)) )
& ( hBOOL(hAPP(hAPP(X2911,esk58_3(X2910,X2911,X2912)),X2910))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2912,X2911),X2910)) )
& ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2912,X2911),esk58_3(X2910,X2911,X2912)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2912,X2911),X2910)) ) ),
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_827,plain,
! [X4200,X4201,X4202,X4203,X4204,X4205] : hAPP(hAPP(hAPP(c_COMBS(X4205,X4204,X4203),X4202),X4201),X4200) = hAPP(hAPP(X4202,X4200),hAPP(X4201,X4200)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_828,plain,
! [X2712,X2713,X2714,X2715] :
( ~ c_Relation_Otrans(X2715,X2714)
| ~ c_Relation_Otrans(X2713,X2712)
| c_Relation_Otrans(tc_prod(X2715,X2713),c_Wellfounded_Olex__prod(X2715,X2713,X2714,X2712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__lex__prod])]) ).
fof(i_0_829,plain,
! [X2926,X2927,X2928,X2929,X2931,X2932,X2933,X2934,X2935] :
( ( ~ c_Predicate_ORangeP(X2929,X2928,X2927,X2926)
| hBOOL(hAPP(hAPP(X2927,esk60_2(X2926,X2927)),X2926)) )
& ( ~ hBOOL(hAPP(hAPP(X2932,X2933),X2931))
| c_Predicate_ORangeP(X2935,X2934,X2932,X2931) ) ),
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_830,plain,
! [X4055,X4056,X4057,X4058,X4059,X4060,X4061] :
( ( c_Nat_Osize__class_Osize(tc_List_Olist(X4055),X4057) = c_Nat_Osize__class_Osize(tc_List_Olist(X4055),X4056)
| X4057 != X4056 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4058,c_Nat_Osize__class_Osize(tc_List_Olist(X4055),X4057))
| c_List_Onth(X4055,X4057,X4058) = c_List_Onth(X4055,X4056,X4058)
| X4057 != X4056 )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk97_3(X4059,X4060,X4061),c_Nat_Osize__class_Osize(tc_List_Olist(X4059),X4061))
| c_Nat_Osize__class_Osize(tc_List_Olist(X4059),X4061) != c_Nat_Osize__class_Osize(tc_List_Olist(X4059),X4060)
| X4061 = X4060 )
& ( c_List_Onth(X4059,X4061,esk97_3(X4059,X4060,X4061)) != c_List_Onth(X4059,X4060,esk97_3(X4059,X4060,X4061))
| c_Nat_Osize__class_Osize(tc_List_Olist(X4059),X4061) != c_Nat_Osize__class_Osize(tc_List_Olist(X4059),X4060)
| X4061 = X4060 ) ),
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_list__eq__iff__nth__eq])])])])])]) ).
fof(i_0_831,plain,
! [X3124,X3125,X3126] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3126,tc_HOL_Obool)),X3125),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3126,tc_HOL_Obool)),X3125),X3124)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3126,tc_HOL_Obool)),X3125),X3124),
inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).
fof(i_0_832,plain,
! [X3079,X3080,X3081] : c_List_Olistsp(X3081,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3081,tc_HOL_Obool)),X3080),X3079)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X3081),tc_HOL_Obool)),c_List_Olistsp(X3081,X3080)),c_List_Olistsp(X3081,X3079)),
inference(variable_rename,[status(thm)],[fact_listsp__inf__eq]) ).
fof(i_0_833,plain,
! [X4194,X4195,X4196,X4197,X4198,X4199] : hAPP(hAPP(hAPP(c_COMBC(X4199,X4198,X4197),X4196),X4195),X4194) = hAPP(hAPP(X4196,X4194),X4195),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_834,plain,
! [X4188,X4189,X4190,X4191,X4192,X4193] : hAPP(hAPP(hAPP(c_COMBB(X4193,X4192,X4191),X4190),X4189),X4188) = hAPP(X4190,hAPP(X4189,X4188)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_835,plain,
! [X3029,X3030,X3031,X3032] :
( ( hBOOL(hAPP(c_List_Olistsp(X3032,X3031),X3030))
| ~ hBOOL(hAPP(c_List_Olistsp(X3032,X3031),hAPP(hAPP(c_List_Oappend(X3032),X3030),X3029))) )
& ( hBOOL(hAPP(c_List_Olistsp(X3032,X3031),X3029))
| ~ hBOOL(hAPP(c_List_Olistsp(X3032,X3031),hAPP(hAPP(c_List_Oappend(X3032),X3030),X3029))) )
& ( ~ hBOOL(hAPP(c_List_Olistsp(X3032,X3031),X3030))
| ~ hBOOL(hAPP(c_List_Olistsp(X3032,X3031),X3029))
| hBOOL(hAPP(c_List_Olistsp(X3032,X3031),hAPP(hAPP(c_List_Oappend(X3032),X3030),X3029))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])]) ).
fof(i_0_836,plain,
! [X3023,X3024,X3025,X3026] :
( ( hBOOL(hAPP(X3025,X3024))
| ~ hBOOL(hAPP(c_List_Olistsp(X3026,X3025),hAPP(hAPP(c_List_Olist_OCons(X3026),X3024),X3023))) )
& ( hBOOL(hAPP(c_List_Olistsp(X3026,X3025),X3023))
| ~ hBOOL(hAPP(c_List_Olistsp(X3026,X3025),hAPP(hAPP(c_List_Olist_OCons(X3026),X3024),X3023))) )
& ( ~ hBOOL(hAPP(X3025,X3024))
| ~ hBOOL(hAPP(c_List_Olistsp(X3026,X3025),X3023))
| hBOOL(hAPP(c_List_Olistsp(X3026,X3025),hAPP(hAPP(c_List_Olist_OCons(X3026),X3024),X3023))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])]) ).
fof(i_0_837,plain,
! [X2551,X2552,X2553,X2554,X2555] :
( ( X2554 = X2552
| hAPP(hAPP(c_List_Oappend(X2555),X2554),hAPP(hAPP(c_List_Olist_OCons(X2555),X2553),c_List_Olist_ONil(X2555))) != hAPP(hAPP(c_List_Oappend(X2555),X2552),hAPP(hAPP(c_List_Olist_OCons(X2555),X2551),c_List_Olist_ONil(X2555))) )
& ( X2553 = X2551
| hAPP(hAPP(c_List_Oappend(X2555),X2554),hAPP(hAPP(c_List_Olist_OCons(X2555),X2553),c_List_Olist_ONil(X2555))) != hAPP(hAPP(c_List_Oappend(X2555),X2552),hAPP(hAPP(c_List_Olist_OCons(X2555),X2551),c_List_Olist_ONil(X2555))) )
& ( X2554 != X2552
| X2553 != X2551
| hAPP(hAPP(c_List_Oappend(X2555),X2554),hAPP(hAPP(c_List_Olist_OCons(X2555),X2553),c_List_Olist_ONil(X2555))) = hAPP(hAPP(c_List_Oappend(X2555),X2552),hAPP(hAPP(c_List_Olist_OCons(X2555),X2551),c_List_Olist_ONil(X2555))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).
fof(i_0_838,plain,
! [X3190,X3191,X3192,X3195,X3196,X3197,X3198,X3199] :
( ( X3190 = hAPP(hAPP(c_List_Olist_OCons(X3192),esk81_3(X3190,X3191,X3192)),esk82_3(X3190,X3191,X3192))
| X3190 = c_List_Olist_ONil(X3192)
| ~ hBOOL(hAPP(c_List_Olistsp(X3192,X3191),X3190)) )
& ( hBOOL(hAPP(X3191,esk81_3(X3190,X3191,X3192)))
| X3190 = c_List_Olist_ONil(X3192)
| ~ hBOOL(hAPP(c_List_Olistsp(X3192,X3191),X3190)) )
& ( hBOOL(hAPP(c_List_Olistsp(X3192,X3191),esk82_3(X3190,X3191,X3192)))
| X3190 = c_List_Olist_ONil(X3192)
| ~ hBOOL(hAPP(c_List_Olistsp(X3192,X3191),X3190)) )
& ( X3195 != c_List_Olist_ONil(X3197)
| hBOOL(hAPP(c_List_Olistsp(X3197,X3196),X3195)) )
& ( X3195 != hAPP(hAPP(c_List_Olist_OCons(X3197),X3198),X3199)
| ~ hBOOL(hAPP(X3196,X3198))
| ~ hBOOL(hAPP(c_List_Olistsp(X3197,X3196),X3199))
| hBOOL(hAPP(c_List_Olistsp(X3197,X3196),X3195)) ) ),
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_839,plain,
! [X3562,X3563,X3564,X3565] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3565,X3564),tc_HOL_Obool),X3563,X3562)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3565,tc_HOL_Obool),c_Relation_ODomain(X3565,X3564,X3563),c_Relation_ODomain(X3565,X3564,X3562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).
cnf(i_0_840,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_556]) ).
fof(i_0_841,plain,
! [X4095,X4096,X4097,X4098,X4099,X4100] :
( ( ~ c_List_Odistinct(X4096,X4095)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4097,c_Nat_Osize__class_Osize(tc_List_Olist(X4096),X4095))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4098,c_Nat_Osize__class_Osize(tc_List_Olist(X4096),X4095))
| X4097 = X4098
| c_List_Onth(X4096,X4095,X4097) != c_List_Onth(X4096,X4095,X4098) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk98_2(X4099,X4100),c_Nat_Osize__class_Osize(tc_List_Olist(X4100),X4099))
| c_List_Odistinct(X4100,X4099) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk99_2(X4099,X4100),c_Nat_Osize__class_Osize(tc_List_Olist(X4100),X4099))
| c_List_Odistinct(X4100,X4099) )
& ( esk98_2(X4099,X4100) != esk99_2(X4099,X4100)
| c_List_Odistinct(X4100,X4099) )
& ( c_List_Onth(X4100,X4099,esk98_2(X4099,X4100)) = c_List_Onth(X4100,X4099,esk99_2(X4099,X4100))
| c_List_Odistinct(X4100,X4099) ) ),
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_distinct__conv__nth])])])])])]) ).
fof(i_0_842,plain,
! [X4091,X4092,X4093,X4094] :
( ( c_List_Onth(X4094,X4093,X4092) != c_List_Onth(X4094,X4093,X4091)
| X4092 = X4091
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4091,c_Nat_Osize__class_Osize(tc_List_Olist(X4094),X4093))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4092,c_Nat_Osize__class_Osize(tc_List_Olist(X4094),X4093))
| ~ c_List_Odistinct(X4094,X4093) )
& ( X4092 != X4091
| c_List_Onth(X4094,X4093,X4092) = c_List_Onth(X4094,X4093,X4091)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4091,c_Nat_Osize__class_Osize(tc_List_Olist(X4094),X4093))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4092,c_Nat_Osize__class_Osize(tc_List_Olist(X4094),X4093))
| ~ c_List_Odistinct(X4094,X4093) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq])])]) ).
fof(i_0_843,plain,
! [X3516,X3517,X3518] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3518,X3518),tc_HOL_Obool),X3517,X3516)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3518,X3518),tc_HOL_Obool),X3516,c_Transitive__Closure_Ortrancl(X3518,X3517))
| c_Transitive__Closure_Ortrancl(X3518,X3516) = c_Transitive__Closure_Ortrancl(X3518,X3517) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).
cnf(i_0_844,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_557]) ).
cnf(i_0_845,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_558]) ).
fof(i_0_846,plain,
! [X2347,X2348,X2349,X2350,X2351,X2352] : hAPP(hAPP(c_Product__Type_Ointernal__split(X2352,X2351,X2350),X2349),hAPP(hAPP(c_Product__Type_OPair(X2352,X2351),X2348),X2347)) = hAPP(hAPP(X2349,X2348),X2347),
inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).
fof(i_0_847,plain,
! [X3178,X3179,X3180,X3181,X3182] :
( ~ class_Lattices_Olattice(X3182)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3181,X3182)),X3180),X3179),X3178) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3182),hAPP(X3180,X3178)),hAPP(X3179,X3178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).
fof(i_0_848,plain,
! [X3173,X3174,X3175,X3176,X3177] :
( ~ class_Lattices_Olattice(X3177)
| hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3176,X3177)),X3175),X3174),X3173) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3177),hAPP(X3175,X3173)),hAPP(X3174,X3173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).
fof(i_0_849,plain,
! [X3426,X3427,X3428,X3429,X3430] :
( hBOOL(hAPP(X3430,X3429))
| c_List_OtakeWhile(X3428,X3430,hAPP(hAPP(c_List_Oappend(X3428),X3427),hAPP(hAPP(c_List_Olist_OCons(X3428),X3429),X3426))) = c_List_OtakeWhile(X3428,X3430,X3427) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])]) ).
fof(i_0_850,plain,
! [X3626,X3627,X3628,X3629,X3630] :
( ~ class_Lattices_Osemilattice__inf(X3630)
| ~ c_Orderings_Oord__class_Oless__eq(X3630,X3629,X3628)
| ~ c_Orderings_Oord__class_Oless__eq(X3630,X3627,X3626)
| c_Orderings_Oord__class_Oless__eq(X3630,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3630),X3629),X3627),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3630),X3628),X3626)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).
fof(i_0_851,plain,
! [X3559,X3560,X3561] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3561,X3561),tc_HOL_Obool),X3560,X3559)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3561),tc_List_Olist(X3561)),tc_HOL_Obool),c_List_Olistrel1(X3561,X3560),c_List_Olistrel1(X3561,X3559)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).
fof(i_0_852,plain,
! [X3556,X3557,X3558] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3558,X3558),tc_HOL_Obool),X3557,X3556)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3558),tc_List_Olist(X3558)),tc_HOL_Obool),c_List_Olistrel(X3558,X3557),c_List_Olistrel(X3558,X3556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).
fof(i_0_853,plain,
! [X3519,X3520,X3521] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3521,X3521),tc_HOL_Obool),X3520,c_Transitive__Closure_Ortrancl(X3521,X3519))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3521,X3521),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3521,X3520),c_Transitive__Closure_Ortrancl(X3521,X3519)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).
fof(i_0_854,plain,
! [X3280,X3281,X3282,X3283] :
( ~ class_Lattices_Osemilattice__inf(X3283)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3283),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3283),X3282),X3281)),X3280) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3283),X3282),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3283),X3281),X3280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).
fof(i_0_855,plain,
! [X3272,X3273,X3274,X3275] :
( ~ class_Lattices_Osemilattice__inf(X3275)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3275),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3275),X3274),X3273)),X3272) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3275),X3274),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3275),X3273),X3272)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).
fof(i_0_856,plain,
! [X3276,X3277,X3278,X3279] :
( ~ class_Lattices_Olattice(X3279)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3279),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3279),X3278),X3277)),X3276) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3279),X3278),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3279),X3277),X3276)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).
fof(i_0_857,plain,
! [X2482,X2483,X2484,X2485] : hAPP(hAPP(c_List_Oappend(X2485),hAPP(hAPP(c_List_Oappend(X2485),X2484),X2483)),X2482) = hAPP(hAPP(c_List_Oappend(X2485),X2484),hAPP(hAPP(c_List_Oappend(X2485),X2483),X2482)),
inference(variable_rename,[status(thm)],[fact_append__assoc]) ).
fof(i_0_858,plain,
! [X2486,X2487,X2488,X2489] : hAPP(hAPP(c_List_Oappend(X2489),hAPP(hAPP(c_List_Olist_OCons(X2489),X2488),X2487)),X2486) = hAPP(hAPP(c_List_Olist_OCons(X2489),X2488),hAPP(hAPP(c_List_Oappend(X2489),X2487),X2486)),
inference(variable_rename,[status(thm)],[fact_append__Cons]) ).
fof(i_0_859,plain,
! [X3802,X3803,X3804,X3805,X3806,X3807] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3807,tc_fun(X3806,tc_HOL_Obool)),X3805,X3804)
| ~ hBOOL(hAPP(hAPP(X3805,X3803),X3802))
| hBOOL(hAPP(hAPP(X3804,X3803),X3802)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_860,plain,
! [X3796,X3797,X3798,X3799,X3800,X3801] :
( ~ hBOOL(hAPP(hAPP(X3801,X3800),X3799))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3798,tc_fun(X3797,tc_HOL_Obool)),X3801,X3796)
| hBOOL(hAPP(hAPP(X3796,X3800),X3799)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_861,plain,
! [X4087,X4088,X4089,X4090] : c_List_Onth(X4090,hAPP(hAPP(c_List_Oappend(X4090),X4089),hAPP(hAPP(c_List_Olist_OCons(X4090),X4088),X4087)),c_Nat_Osize__class_Osize(tc_List_Olist(X4090),X4089)) = X4088,
inference(variable_rename,[status(thm)],[fact_nth__append__length]) ).
fof(i_0_862,plain,
! [X3570,X3571,X3572,X3573] :
( ~ hBOOL(hAPP(hAPP(c_member(X3573),X3572),X3571))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3573,tc_HOL_Obool),X3571,X3570)
| hBOOL(hAPP(hAPP(c_member(X3573),X3572),X3570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_863,plain,
! [X3995,X3996,X3997,X3998] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X3998,tc_HOL_Obool),X3997,X3996)
| ~ hBOOL(hAPP(hAPP(c_member(X3998),X3995),X3997))
| hBOOL(hAPP(hAPP(c_member(X3998),X3995),X3996)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_864,plain,
! [X3574,X3575,X3576,X3577] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3577,tc_HOL_Obool),X3576,X3575)
| ~ hBOOL(hAPP(hAPP(c_member(X3577),X3574),X3576))
| hBOOL(hAPP(hAPP(c_member(X3577),X3574),X3575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_865,plain,
! [X3566,X3567,X3568,X3569] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3569,tc_HOL_Obool),X3568,X3567)
| ~ hBOOL(hAPP(hAPP(c_member(X3569),X3566),X3568))
| hBOOL(hAPP(hAPP(c_member(X3569),X3566),X3567)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_866,plain,
! [X3495,X3496,X3497,X3498] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3498,tc_HOL_Obool),X3497,X3496)
| ~ hBOOL(hAPP(hAPP(c_member(X3498),X3495),X3497))
| hBOOL(hAPP(hAPP(c_member(X3498),X3495),X3496)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_867,plain,
! [X3513,X3514,X3515] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3515,X3515),tc_HOL_Obool),X3514,X3513)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3515,X3515),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X3515,X3514),c_Transitive__Closure_Ortrancl(X3515,X3513)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).
fof(i_0_868,plain,
! [X2901,X2902,X2903,X2904,X2905] :
( ~ hBOOL(hAPP(hAPP(X2905,X2904),X2903))
| c_Predicate_ODomainP(X2902,X2901,X2905,X2904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).
fof(i_0_869,plain,
! [X2896,X2897,X2898,X2899,X2900] :
( ~ hBOOL(hAPP(hAPP(X2900,X2899),X2898))
| c_Predicate_ORangeP(X2897,X2896,X2900,X2898) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).
fof(i_0_870,plain,
! [X3468,X3469,X3470] : hAPP(hAPP(c_List_Oappend(X3470),c_List_OtakeWhile(X3470,X3469,X3468)),c_List_OdropWhile(X3470,X3469,X3468)) = X3468,
inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id]) ).
fof(i_0_871,plain,
! [X3422,X3423,X3424,X3425] :
( ( ~ hBOOL(hAPP(X3425,X3424))
| c_List_OtakeWhile(X3423,X3425,hAPP(hAPP(c_List_Olist_OCons(X3423),X3424),X3422)) = hAPP(hAPP(c_List_Olist_OCons(X3423),X3424),c_List_OtakeWhile(X3423,X3425,X3422)) )
& ( hBOOL(hAPP(X3425,X3424))
| c_List_OtakeWhile(X3423,X3425,hAPP(hAPP(c_List_Olist_OCons(X3423),X3424),X3422)) = c_List_Olist_ONil(X3423) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])]) ).
fof(i_0_872,plain,
! [X3601,X3602,X3603] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3603,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3603,tc_HOL_Obool)),X3602),X3601),X3602),
inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).
fof(i_0_873,plain,
! [X3604,X3605,X3606] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3606,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3606,tc_HOL_Obool)),X3605),X3604),X3604),
inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).
fof(i_0_874,plain,
! [X3698,X3699] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3699),tc_List_Olist(X3699)),tc_HOL_Obool),c_List_Olistrel1(X3699,c_Transitive__Closure_Ortrancl(X3699,X3698)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X3699),c_List_Olistrel1(X3699,X3698))),
inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).
fof(i_0_875,plain,
! [X3398,X3399,X3400] : c_List_Obutlast(X3400,hAPP(hAPP(c_List_Oappend(X3400),X3399),hAPP(hAPP(c_List_Olist_OCons(X3400),X3398),c_List_Olist_ONil(X3400)))) = X3399,
inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).
fof(i_0_876,plain,
! [X3320,X3321,X3322] : c_List_Olast(X3322,hAPP(hAPP(c_List_Oappend(X3322),X3321),hAPP(hAPP(c_List_Olist_OCons(X3322),X3320),c_List_Olist_ONil(X3322)))) = X3320,
inference(variable_rename,[status(thm)],[fact_last__snoc]) ).
fof(i_0_877,plain,
! [X3506,X3507,X3508,X3509] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3509,X3508),tc_HOL_Obool),X3507,X3506)
| ~ c_Relation_Osingle__valued(X3509,X3508,X3506)
| c_Relation_Osingle__valued(X3509,X3508,X3507) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).
fof(i_0_878,plain,
! [X3723,X3724,X3725] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3725),c_List_OdropWhile(X3725,X3724,X3723)),c_Nat_Osize__class_Osize(tc_List_Olist(X3725),X3723)),
inference(variable_rename,[status(thm)],[fact_length__dropWhile__le]) ).
fof(i_0_879,plain,
! [X3720,X3721,X3722] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3722),c_List_OtakeWhile(X3722,X3721,X3720)),c_Nat_Osize__class_Osize(tc_List_Olist(X3722),X3720)),
inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).
fof(i_0_880,plain,
! [X2922,X2923,X2924,X2925] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2925,X2924),X2923))
| ~ hBOOL(hAPP(hAPP(X2924,X2922),X2923))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2925,X2924),X2922)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).
fof(i_0_881,plain,
! [X3653,X3654,X3655,X3656] :
( ( c_Orderings_Oord__class_Oless__eq(X3656,X3655,X3654)
| ~ c_Orderings_Oord__class_Oless__eq(X3656,X3655,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3656),X3654),X3653))
| ~ class_Lattices_Osemilattice__inf(X3656) )
& ( c_Orderings_Oord__class_Oless__eq(X3656,X3655,X3653)
| ~ c_Orderings_Oord__class_Oless__eq(X3656,X3655,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3656),X3654),X3653))
| ~ class_Lattices_Osemilattice__inf(X3656) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3656,X3655,X3654)
| ~ c_Orderings_Oord__class_Oless__eq(X3656,X3655,X3653)
| c_Orderings_Oord__class_Oless__eq(X3656,X3655,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3656),X3654),X3653))
| ~ class_Lattices_Osemilattice__inf(X3656) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).
fof(i_0_882,plain,
! [X3635,X3636,X3637,X3638] :
( ~ class_Lattices_Osemilattice__inf(X3638)
| ~ c_Orderings_Oord__class_Oless__eq(X3638,X3637,X3636)
| ~ c_Orderings_Oord__class_Oless__eq(X3638,X3637,X3635)
| c_Orderings_Oord__class_Oless__eq(X3638,X3637,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3638),X3636),X3635)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).
fof(i_0_883,plain,
! [X3631,X3632,X3633,X3634] :
( ~ class_Lattices_Osemilattice__inf(X3634)
| ~ c_Orderings_Oord__class_Oless__eq(X3634,X3633,X3632)
| ~ c_Orderings_Oord__class_Oless__eq(X3634,X3633,X3631)
| c_Orderings_Oord__class_Oless__eq(X3634,X3633,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3634),X3632),X3631)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).
fof(i_0_884,plain,
! [X3522,X3523,X3524] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3524,X3524),tc_HOL_Obool),X3523,X3522)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3524,tc_HOL_Obool),c_Wellfounded_Oacc(X3524,X3522),c_Wellfounded_Oacc(X3524,X3523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).
fof(i_0_885,plain,
! [X3379,X3380] :
( X3380 = c_List_Olist_ONil(X3379)
| hAPP(hAPP(c_List_Oappend(X3379),c_List_Obutlast(X3379,X3380)),hAPP(hAPP(c_List_Olist_OCons(X3379),c_List_Olast(X3379,X3380)),c_List_Olist_ONil(X3379))) = X3380 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).
fof(i_0_886,plain,
! [X3713,X3714,X3715] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3715,tc_fun(X3715,tc_HOL_Obool)),X3714,X3713)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3715,tc_HOL_Obool),c_Wellfounded_Oaccp(X3715,X3713),c_Wellfounded_Oaccp(X3715,X3714)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).
fof(i_0_887,plain,
! [X4051,X4052,X4053,X4054] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X4054,tc_HOL_Obool),X4053,X4052)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4054,tc_HOL_Obool),X4052,X4051)
| c_Orderings_Oord__class_Oless(tc_fun(X4054,tc_HOL_Obool),X4053,X4051) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_888,plain,
! [X3978,X3979,X3980,X3981] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3981,tc_HOL_Obool),X3980,X3979)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3981,tc_HOL_Obool),X3979,X3978)
| c_Orderings_Oord__class_Oless(tc_fun(X3981,tc_HOL_Obool),X3980,X3978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_889,plain,
! [X3982,X3983,X3984,X3985] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X3985,tc_HOL_Obool),X3984,X3983)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3985,tc_HOL_Obool),X3983,X3982)
| c_Orderings_Oord__class_Oless(tc_fun(X3985,tc_HOL_Obool),X3984,X3982) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_890,plain,
! [X3536,X3537,X3538,X3539] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3539,tc_HOL_Obool),X3538,X3537)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3539,tc_HOL_Obool),X3537,X3536)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3539,tc_HOL_Obool),X3538,X3536) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_891,plain,
! [X3292,X3293,X3294,X3295] :
( ~ class_Lattices_Osemilattice__inf(X3295)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3295),X3294),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3295),X3293),X3292)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3295),X3293),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3295),X3294),X3292)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).
fof(i_0_892,plain,
! [X3284,X3285,X3286,X3287] :
( ~ class_Lattices_Osemilattice__inf(X3287)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3287),X3286),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3287),X3285),X3284)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3287),X3285),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3287),X3286),X3284)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).
fof(i_0_893,plain,
! [X3288,X3289,X3290,X3291] :
( ~ class_Lattices_Olattice(X3291)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3291),X3290),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3291),X3289),X3288)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3291),X3289),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3291),X3290),X3288)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).
fof(i_0_894,plain,
! [X3622,X3623,X3624,X3625] :
( ( c_Orderings_Oord__class_Oless__eq(X3625,X3624,X3623)
| ~ c_Orderings_Oord__class_Oless__eq(X3625,X3624,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3625),X3623),X3622))
| ~ class_Lattices_Osemilattice__inf(X3625) )
& ( c_Orderings_Oord__class_Oless__eq(X3625,X3624,X3622)
| ~ c_Orderings_Oord__class_Oless__eq(X3625,X3624,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3625),X3623),X3622))
| ~ class_Lattices_Osemilattice__inf(X3625) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])]) ).
fof(i_0_895,plain,
! [X3974,X3975,X3976,X3977] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3976,X3977),X3975,X3974)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3976,X3977),X3975,X3974)
| ~ class_Orderings_Oord(X3977) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3976,X3977),X3974,X3975)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3976,X3977),X3975,X3974)
| ~ class_Orderings_Oord(X3977) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3976,X3977),X3975,X3974)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3976,X3977),X3974,X3975)
| c_Orderings_Oord__class_Oless(tc_fun(X3976,X3977),X3975,X3974)
| ~ class_Orderings_Oord(X3977) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])])]) ).
fof(i_0_896,plain,
! [X3490,X3491] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X3491),tc_List_Olist(X3491)),tc_HOL_Obool),c_List_Olistrel(X3491,X3490),c_Transitive__Closure_Ortrancl(tc_List_Olist(X3491),c_List_Olistrel1(X3491,X3490))),
inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).
fof(i_0_897,plain,
! [X2157,X2158,X2159,X2160,X2161,X2162] :
( ( X2160 = X2158
| hAPP(hAPP(c_Product__Type_OPair(X2162,X2161),X2160),X2159) != hAPP(hAPP(c_Product__Type_OPair(X2162,X2161),X2158),X2157) )
& ( X2159 = X2157
| hAPP(hAPP(c_Product__Type_OPair(X2162,X2161),X2160),X2159) != hAPP(hAPP(c_Product__Type_OPair(X2162,X2161),X2158),X2157) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).
fof(i_0_898,plain,
! [X2151,X2152,X2153,X2154,X2155,X2156] :
( ( X2154 = X2152
| hAPP(hAPP(c_Product__Type_OPair(X2156,X2155),X2154),X2153) != hAPP(hAPP(c_Product__Type_OPair(X2156,X2155),X2152),X2151) )
& ( X2153 = X2151
| hAPP(hAPP(c_Product__Type_OPair(X2156,X2155),X2154),X2153) != hAPP(hAPP(c_Product__Type_OPair(X2156,X2155),X2152),X2151) )
& ( X2154 != X2152
| X2153 != X2151
| hAPP(hAPP(c_Product__Type_OPair(X2156,X2155),X2154),X2153) = hAPP(hAPP(c_Product__Type_OPair(X2156,X2155),X2152),X2151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).
fof(i_0_899,plain,
! [X3716,X3717,X3718,X3719] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(X3719),X3718),c_Nat_Osize__class_Osize(tc_List_Olist(X3719),X3717))
| X3718 != hAPP(hAPP(c_List_Olist_OCons(X3719),X3716),X3717) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).
fof(i_0_900,plain,
! [X3127,X3128,X3129] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3129,tc_HOL_Obool)),X3128),X3127) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3129,tc_HOL_Obool)),X3127),X3128),
inference(variable_rename,[status(thm)],[fact_Int__commute]) ).
fof(i_0_901,plain,
! [X2676,X2677,X2678,X2679] :
( c_List_Orotate1(X2679,c_List_Olist_ONil(X2679)) = c_List_Olist_ONil(X2679)
& c_List_Orotate1(X2678,hAPP(hAPP(c_List_Olist_OCons(X2678),X2677),X2676)) = hAPP(hAPP(c_List_Oappend(X2678),X2676),hAPP(hAPP(c_List_Olist_OCons(X2678),X2677),c_List_Olist_ONil(X2678))) ),
inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).
fof(i_0_902,plain,
! [X3375,X3376,X3377,X3378] :
( ( X3375 != c_List_Olist_ONil(X3378)
| hAPP(hAPP(c_List_Oappend(X3378),X3377),hAPP(hAPP(c_List_Olist_OCons(X3378),X3376),c_List_Olist_ONil(X3378))) != X3375 )
& ( c_List_Obutlast(X3378,X3375) = X3377
| hAPP(hAPP(c_List_Oappend(X3378),X3377),hAPP(hAPP(c_List_Olist_OCons(X3378),X3376),c_List_Olist_ONil(X3378))) != X3375 )
& ( c_List_Olast(X3378,X3375) = X3376
| hAPP(hAPP(c_List_Oappend(X3378),X3377),hAPP(hAPP(c_List_Olist_OCons(X3378),X3376),c_List_Olist_ONil(X3378))) != X3375 )
& ( X3375 = c_List_Olist_ONil(X3378)
| c_List_Obutlast(X3378,X3375) != X3377
| c_List_Olast(X3378,X3375) != X3376
| hAPP(hAPP(c_List_Oappend(X3378),X3377),hAPP(hAPP(c_List_Olist_OCons(X3378),X3376),c_List_Olist_ONil(X3378))) = X3375 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).
fof(i_0_903,plain,
! [X2454,X2455,X2456,X2457,X2458,X2459] :
( hAPP(hAPP(c_List_Oappend(X2459),X2458),X2457) != X2456
| X2455 != hAPP(hAPP(c_List_Oappend(X2459),X2457),X2454)
| hAPP(hAPP(c_List_Oappend(X2459),X2458),X2455) = hAPP(hAPP(c_List_Oappend(X2459),X2456),X2454) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).
fof(i_0_904,plain,
! [X2490,X2491,X2492,X2493,X2494,X2495] :
( hAPP(hAPP(c_List_Olist_OCons(X2495),X2494),X2493) != X2492
| X2491 != hAPP(hAPP(c_List_Oappend(X2495),X2493),X2490)
| hAPP(hAPP(c_List_Olist_OCons(X2495),X2494),X2491) = hAPP(hAPP(c_List_Oappend(X2495),X2492),X2490) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).
fof(i_0_905,plain,
! [X3607,X3608,X3609] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3609,tc_HOL_Obool),X3608,X3607)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3609,tc_HOL_Obool)),X3608),X3607) = X3608 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).
fof(i_0_906,plain,
! [X3610,X3611,X3612] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3612,tc_HOL_Obool),X3611,X3610)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3612,tc_HOL_Obool)),X3610),X3611) = X3611 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).
fof(i_0_907,plain,
! [X3510,X3511,X3512] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3512,tc_HOL_Obool),X3511,X3510)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X3512),tc_HOL_Obool),c_List_Olistsp(X3512,X3511),c_List_Olistsp(X3512,X3510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])]) ).
fof(i_0_908,plain,
! [X3578,X3579,X3580] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3580,tc_HOL_Obool),X3579,X3578)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X3580),tc_HOL_Obool),c_List_Olists(X3580,X3579),c_List_Olists(X3580,X3578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).
fof(i_0_909,plain,
! [X2662,X2663] : c_List_Olistrelp(X2663,X2662,c_List_Olist_ONil(X2663),c_List_Olist_ONil(X2663)),
inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).
fof(i_0_910,plain,
! [X2660,X2661] : c_List_Olistrelp(X2661,X2660,c_List_Olist_ONil(X2661),c_List_Olist_ONil(X2661)),
inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).
fof(i_0_911,plain,
! [X3447,X3448,X3449,X3450] :
( ( ~ hBOOL(hAPP(X3450,X3449))
| c_List_OdropWhile(X3448,X3450,hAPP(hAPP(c_List_Olist_OCons(X3448),X3449),X3447)) = c_List_OdropWhile(X3448,X3450,X3447) )
& ( hBOOL(hAPP(X3450,X3449))
| c_List_OdropWhile(X3448,X3450,hAPP(hAPP(c_List_Olist_OCons(X3448),X3449),X3447)) = hAPP(hAPP(c_List_Olist_OCons(X3448),X3449),X3447) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_912,plain,
! [X2731,X2732,X2733] : c_List_Omaps(X2733,X2732,X2731,c_List_Olist_ONil(X2733)) = c_List_Olist_ONil(X2732),
inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J]) ).
fof(i_0_913,plain,
! [X3318,X3319] : c_Set_Oimage(X3319,X3319,c_COMBI(X3319),X3318) = X3318,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_914,plain,
! [X3887,X3888,X3889,X3890] :
( ~ class_Lattices_Osemilattice__inf(X3890)
| ~ c_Orderings_Oord__class_Oless(X3890,X3889,X3888)
| c_Orderings_Oord__class_Oless(X3890,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3890),X3889),X3887),X3888) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).
fof(i_0_915,plain,
! [X3891,X3892,X3893,X3894] :
( ~ class_Lattices_Osemilattice__inf(X3894)
| ~ c_Orderings_Oord__class_Oless(X3894,X3893,X3892)
| c_Orderings_Oord__class_Oless(X3894,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3894),X3891),X3893),X3892) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).
fof(i_0_916,plain,
! [X3649,X3650,X3651,X3652] :
( ~ class_Lattices_Osemilattice__inf(X3652)
| ~ c_Orderings_Oord__class_Oless__eq(X3652,X3651,X3650)
| c_Orderings_Oord__class_Oless__eq(X3652,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3652),X3651),X3649),X3650) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).
fof(i_0_917,plain,
! [X3645,X3646,X3647,X3648] :
( ~ class_Lattices_Osemilattice__inf(X3648)
| ~ c_Orderings_Oord__class_Oless__eq(X3648,X3647,X3646)
| c_Orderings_Oord__class_Oless__eq(X3648,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3648),X3645),X3647),X3646) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).
fof(i_0_918,plain,
! [X3546,X3547,X3548] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3546,tc_HOL_Obool),X3548,X3547)
| X3548 != X3547 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3546,tc_HOL_Obool),X3547,X3548)
| X3548 != X3547 )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3546,tc_HOL_Obool),X3548,X3547)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3546,tc_HOL_Obool),X3547,X3548)
| X3548 = X3547 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_919,plain,
! [X3492,X3493,X3494] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3494,tc_HOL_Obool),X3493,X3492)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3494,tc_HOL_Obool),X3492,X3493)
| X3493 = X3492 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_920,plain,
! [X2240,X2241,X2242] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2242),X2241),hAPP(c_fequal,X2240)))
| X2241 = X2240 )
& ( X2241 != X2240
| hBOOL(hAPP(hAPP(c_member(X2242),X2241),hAPP(c_fequal,X2240))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_921,plain,
! [X3780,X3781,X3782,X3783,X3784] :
( ~ class_Orderings_Oord(X3784)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3783,X3784),X3782,X3781)
| c_Orderings_Oord__class_Oless__eq(X3784,hAPP(X3782,X3780),hAPP(X3781,X3780)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_922,plain,
! [X3708,X3709,X3710,X3711,X3712] :
( ~ class_Orderings_Oord(X3712)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3711,X3712),X3710,X3709)
| c_Orderings_Oord__class_Oless__eq(X3712,hAPP(X3710,X3708),hAPP(X3709,X3708)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_923,plain,
! [X3949,X3950,X3951,X3952] :
( ~ class_Orderings_Opreorder(X3952)
| ~ c_Orderings_Oord__class_Oless(X3952,X3951,X3950)
| ~ c_Orderings_Oord__class_Oless(X3952,X3950,X3949)
| c_Orderings_Oord__class_Oless(X3952,X3951,X3949) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_924,plain,
! [X3877,X3878,X3879,X3880] :
( ~ class_Orderings_Opreorder(X3880)
| ~ c_Orderings_Oord__class_Oless__eq(X3880,X3879,X3878)
| ~ c_Orderings_Oord__class_Oless(X3880,X3878,X3877)
| c_Orderings_Oord__class_Oless(X3880,X3879,X3877) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_925,plain,
! [X3869,X3870,X3871,X3872] :
( ~ class_Orderings_Opreorder(X3872)
| ~ c_Orderings_Oord__class_Oless(X3872,X3871,X3870)
| ~ c_Orderings_Oord__class_Oless__eq(X3872,X3870,X3869)
| c_Orderings_Oord__class_Oless(X3872,X3871,X3869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_926,plain,
! [X3953,X3954,X3955,X3956] :
( ~ class_Orderings_Oorder(X3956)
| ~ c_Orderings_Oord__class_Oless(X3956,X3955,X3954)
| ~ c_Orderings_Oord__class_Oless(X3956,X3953,X3955)
| c_Orderings_Oord__class_Oless(X3956,X3953,X3954) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_927,plain,
! [X3881,X3882,X3883,X3884] :
( ~ class_Orderings_Oorder(X3884)
| ~ c_Orderings_Oord__class_Oless__eq(X3884,X3883,X3882)
| ~ c_Orderings_Oord__class_Oless(X3884,X3881,X3883)
| c_Orderings_Oord__class_Oless(X3884,X3881,X3882) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_928,plain,
! [X3873,X3874,X3875,X3876] :
( ~ class_Orderings_Oorder(X3876)
| ~ c_Orderings_Oord__class_Oless(X3876,X3875,X3874)
| ~ c_Orderings_Oord__class_Oless__eq(X3876,X3873,X3875)
| c_Orderings_Oord__class_Oless(X3876,X3873,X3874) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_929,plain,
! [X3736,X3737,X3738,X3739] :
( ~ class_Orderings_Opreorder(X3739)
| ~ c_Orderings_Oord__class_Oless__eq(X3739,X3738,X3737)
| ~ c_Orderings_Oord__class_Oless__eq(X3739,X3737,X3736)
| c_Orderings_Oord__class_Oless__eq(X3739,X3738,X3736) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_930,plain,
! [X3729,X3730,X3731,X3732] :
( ~ class_Orderings_Oorder(X3732)
| ~ c_Orderings_Oord__class_Oless__eq(X3732,X3731,X3730)
| ~ c_Orderings_Oord__class_Oless__eq(X3732,X3729,X3731)
| c_Orderings_Oord__class_Oless__eq(X3732,X3729,X3730) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_931,plain,
! [X2954,X2955] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2955)),c_List_Olist_ONil(X2955)),c_List_Olists(X2955,X2954))),
inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).
fof(i_0_932,plain,
! [X4017,X4018,X4019] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4019,X4018)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4018,X4017)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4019,X4017) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_933,plain,
! [X2690,X2691] : c_List_Opartition(X2691,X2690,c_List_Olist_ONil(X2691)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X2691),tc_List_Olist(X2691)),c_List_Olist_ONil(X2691)),c_List_Olist_ONil(X2691)),
inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).
fof(i_0_934,plain,
! [X2316,X2317,X2318] : c_List_Osplice(X2318,hAPP(hAPP(c_List_Olist_OCons(X2318),X2317),X2316),c_List_Olist_ONil(X2318)) = hAPP(hAPP(c_List_Olist_OCons(X2318),X2317),X2316),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).
fof(i_0_935,plain,
! [X3302,X3303,X3304] :
( ~ class_Lattices_Osemilattice__inf(X3304)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3304),X3303),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3304),X3303),X3302)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3304),X3303),X3302) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).
fof(i_0_936,plain,
! [X3296,X3297,X3298] :
( ~ class_Lattices_Osemilattice__inf(X3298)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3298),X3297),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3298),X3297),X3296)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3298),X3297),X3296) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).
fof(i_0_937,plain,
! [X3299,X3300,X3301] :
( ~ class_Lattices_Olattice(X3301)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3301),X3300),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3301),X3300),X3299)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3301),X3300),X3299) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).
fof(i_0_938,plain,
! [X3830,X3831,X3832] :
( ( c_Orderings_Oord__class_Oless__eq(X3832,X3831,X3830)
| ~ c_Orderings_Oord__class_Oless(X3832,X3831,X3830)
| ~ class_Orderings_Opreorder(X3832) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3832,X3830,X3831)
| ~ c_Orderings_Oord__class_Oless(X3832,X3831,X3830)
| ~ class_Orderings_Opreorder(X3832) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3832,X3831,X3830)
| c_Orderings_Oord__class_Oless__eq(X3832,X3830,X3831)
| c_Orderings_Oord__class_Oless(X3832,X3831,X3830)
| ~ class_Orderings_Opreorder(X3832) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])])]) ).
fof(i_0_939,plain,
! [X3992,X3993,X3994] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3994,tc_HOL_Obool),X3993,X3992)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3994,tc_HOL_Obool),X3993,X3992) )
& ( X3993 != X3992
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3994,tc_HOL_Obool),X3993,X3992) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3994,tc_HOL_Obool),X3993,X3992)
| X3993 = X3992
| c_Orderings_Oord__class_Oless(tc_fun(X3994,tc_HOL_Obool),X3993,X3992) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_940,plain,
! [X3989,X3990,X3991] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3991,tc_HOL_Obool),X3990,X3989)
| c_Orderings_Oord__class_Oless(tc_fun(X3991,tc_HOL_Obool),X3990,X3989)
| X3990 = X3989 )
& ( ~ c_Orderings_Oord__class_Oless(tc_fun(X3991,tc_HOL_Obool),X3990,X3989)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3991,tc_HOL_Obool),X3990,X3989) )
& ( X3990 != X3989
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3991,tc_HOL_Obool),X3990,X3989) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_941,plain,
! [X3525,X3526,X3527,X3528] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3528,tc_HOL_Obool),X3527,X3526)
| ~ hBOOL(hAPP(X3527,X3525))
| hBOOL(hAPP(X3526,X3525)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_942,plain,
! [X3529,X3530,X3531,X3532] :
( ~ hBOOL(hAPP(X3532,X3531))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3530,tc_HOL_Obool),X3532,X3529)
| hBOOL(hAPP(X3529,X3531)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_943,plain,
! [X3986,X3987,X3988] :
( ~ c_Orderings_Oord__class_Oless(tc_fun(X3988,tc_HOL_Obool),X3987,X3986)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3988,tc_HOL_Obool),X3987,X3986) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_944,plain,
! [X3393,X3394,X3395] :
( ( X3395 != c_List_Olist_ONil(X3394)
| c_List_Obutlast(X3394,hAPP(hAPP(c_List_Oappend(X3394),X3393),X3395)) = c_List_Obutlast(X3394,X3393) )
& ( X3395 = c_List_Olist_ONil(X3394)
| c_List_Obutlast(X3394,hAPP(hAPP(c_List_Oappend(X3394),X3393),X3395)) = hAPP(hAPP(c_List_Oappend(X3394),X3393),c_List_Obutlast(X3394,X3395)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).
fof(i_0_945,plain,
! [X3390,X3391,X3392] :
( ( X3392 != c_List_Olist_ONil(X3391)
| c_List_Obutlast(X3391,hAPP(hAPP(c_List_Olist_OCons(X3391),X3390),X3392)) = c_List_Olist_ONil(X3391) )
& ( X3392 = c_List_Olist_ONil(X3391)
| c_List_Obutlast(X3391,hAPP(hAPP(c_List_Olist_OCons(X3391),X3390),X3392)) = hAPP(hAPP(c_List_Olist_OCons(X3391),X3390),c_List_Obutlast(X3391,X3392)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).
fof(i_0_946,plain,
! [X2175,X2176,X2177] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2177),X2176),X2175))
| hBOOL(hAPP(X2175,X2176)) )
& ( ~ hBOOL(hAPP(X2175,X2176))
| hBOOL(hAPP(hAPP(c_member(X2177),X2176),X2175)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_947,plain,
! [X4009,X4010,X4011] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4010,X4011)
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| X4011 = X4010
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4011,X4010) )
& ( ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| X4011 = X4010
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4011,X4010) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4010,X4011)
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4011,X4010) )
& ( ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4011,X4010) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4010,X4011)
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| X4011 = X4010
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011)) )
& ( ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| X4011 = X4010
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4010,X4011)
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011)) )
& ( ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011))
| ~ hBOOL(hAPP(hAPP(X4009,X4010),X4011)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_948,plain,
! [X3857,X3858,X3859] :
( ( c_Orderings_Oord__class_Oless(X3859,X3858,X3857)
| X3858 = X3857
| ~ c_Orderings_Oord__class_Oless__eq(X3859,X3858,X3857)
| ~ class_Orderings_Olinorder(X3859) )
& ( X3858 != X3857
| ~ c_Orderings_Oord__class_Oless(X3859,X3858,X3857)
| ~ c_Orderings_Oord__class_Oless__eq(X3859,X3858,X3857)
| ~ class_Orderings_Olinorder(X3859) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])])]) ).
fof(i_0_949,plain,
! [X3765,X3766,X3767] :
( ( c_Orderings_Oord__class_Oless__eq(X3767,X3766,X3765)
| X3766 != X3765
| ~ class_Orderings_Oorder(X3767) )
& ( c_Orderings_Oord__class_Oless__eq(X3767,X3765,X3766)
| X3766 != X3765
| ~ class_Orderings_Oorder(X3767) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3767,X3766,X3765)
| ~ c_Orderings_Oord__class_Oless__eq(X3767,X3765,X3766)
| X3766 = X3765
| ~ class_Orderings_Oorder(X3767) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_950,plain,
! [X3759,X3760,X3761] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3761,X3759,X3760)
| X3759 = X3760
| ~ c_Orderings_Oord__class_Oless__eq(X3761,X3760,X3759)
| ~ class_Orderings_Oorder(X3761) )
& ( X3759 != X3760
| c_Orderings_Oord__class_Oless__eq(X3761,X3759,X3760)
| ~ c_Orderings_Oord__class_Oless__eq(X3761,X3760,X3759)
| ~ class_Orderings_Oorder(X3761) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_951,plain,
! [X3740,X3741,X3742] :
( ~ class_Orderings_Oorder(X3742)
| ~ c_Orderings_Oord__class_Oless__eq(X3742,X3741,X3740)
| ~ c_Orderings_Oord__class_Oless__eq(X3742,X3740,X3741)
| X3741 = X3740 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_952,plain,
! [X3733,X3734,X3735] :
( ~ class_Orderings_Oorder(X3735)
| ~ c_Orderings_Oord__class_Oless__eq(X3735,X3734,X3733)
| ~ c_Orderings_Oord__class_Oless__eq(X3735,X3733,X3734)
| X3733 = X3734 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_953,plain,
! [X3930,X3931,X3932] :
( ~ class_Orderings_Oorder(X3932)
| ~ c_Orderings_Oord__class_Oless(X3932,X3931,X3930)
| ~ c_Orderings_Oord__class_Oless(X3932,X3930,X3931) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).
fof(i_0_954,plain,
! [X3900,X3901,X3902] :
( ( c_Orderings_Oord__class_Oless(X3902,X3901,X3900)
| c_Orderings_Oord__class_Oless(X3902,X3900,X3901)
| X3901 = X3900
| ~ class_Orderings_Olinorder(X3902) )
& ( ~ c_Orderings_Oord__class_Oless(X3902,X3900,X3901)
| ~ c_Orderings_Oord__class_Oless(X3902,X3901,X3900)
| ~ class_Orderings_Olinorder(X3902) )
& ( X3901 != X3900
| ~ c_Orderings_Oord__class_Oless(X3902,X3901,X3900)
| ~ class_Orderings_Olinorder(X3902) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])])]) ).
fof(i_0_955,plain,
! [X3851,X3852,X3853] :
( ~ class_Orderings_Olinorder(X3853)
| ~ c_Orderings_Oord__class_Oless__eq(X3853,X3852,X3851)
| ~ c_Orderings_Oord__class_Oless(X3853,X3851,X3852) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_956,plain,
! [X3818,X3819,X3820] :
( ( c_Orderings_Oord__class_Oless(X3820,X3819,X3818)
| c_Orderings_Oord__class_Oless__eq(X3820,X3818,X3819)
| ~ class_Orderings_Olinorder(X3820) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3820,X3818,X3819)
| ~ c_Orderings_Oord__class_Oless(X3820,X3819,X3818)
| ~ class_Orderings_Olinorder(X3820) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])])]) ).
fof(i_0_957,plain,
! [X3821,X3822,X3823] :
( ( c_Orderings_Oord__class_Oless__eq(X3823,X3822,X3821)
| c_Orderings_Oord__class_Oless(X3823,X3821,X3822)
| ~ class_Orderings_Olinorder(X3823) )
& ( ~ c_Orderings_Oord__class_Oless(X3823,X3821,X3822)
| ~ c_Orderings_Oord__class_Oless__eq(X3823,X3822,X3821)
| ~ class_Orderings_Olinorder(X3823) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])])]) ).
fof(i_0_958,plain,
! [X3957,X3958,X3959] :
( ~ class_Orderings_Opreorder(X3959)
| ~ c_Orderings_Oord__class_Oless(X3959,X3958,X3957)
| ~ c_Orderings_Oord__class_Oless(X3959,X3957,X3958) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])]) ).
fof(i_0_959,plain,
! [X3927,X3928,X3929] :
( ~ class_Orderings_Opreorder(X3929)
| ~ c_Orderings_Oord__class_Oless(X3929,X3928,X3927)
| ~ c_Orderings_Oord__class_Oless(X3929,X3927,X3928) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_960,plain,
! [X3918,X3919,X3920] :
( ~ class_Orderings_Opreorder(X3920)
| ~ c_Orderings_Oord__class_Oless(X3920,X3919,X3918)
| ~ c_Orderings_Oord__class_Oless(X3920,X3918,X3919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])]) ).
fof(i_0_961,plain,
! [X3915,X3916,X3917] :
( ~ class_Orderings_Opreorder(X3917)
| ~ c_Orderings_Oord__class_Oless(X3917,X3916,X3915)
| ~ c_Orderings_Oord__class_Oless(X3917,X3915,X3916) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).
fof(i_0_962,plain,
! [X4020,X4021] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4021,X4020)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4020,X4021)
| X4021 = X4020 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_963,plain,
! [X2243,X2244,X2245,X2246,X2247] :
( ( X2246 = X2244
| hAPP(hAPP(c_List_Olist_OCons(X2247),X2246),X2245) != hAPP(hAPP(c_List_Olist_OCons(X2247),X2244),X2243) )
& ( X2245 = X2243
| hAPP(hAPP(c_List_Olist_OCons(X2247),X2246),X2245) != hAPP(hAPP(c_List_Olist_OCons(X2247),X2244),X2243) )
& ( X2246 != X2244
| X2245 != X2243
| hAPP(hAPP(c_List_Olist_OCons(X2247),X2246),X2245) = hAPP(hAPP(c_List_Olist_OCons(X2247),X2244),X2243) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).
fof(i_0_964,plain,
! [X2460,X2461,X2462,X2463] :
( ( hAPP(hAPP(c_List_Oappend(X2463),X2462),X2461) != hAPP(hAPP(c_List_Oappend(X2463),X2460),X2461)
| X2462 = X2460 )
& ( X2462 != X2460
| hAPP(hAPP(c_List_Oappend(X2463),X2462),X2461) = hAPP(hAPP(c_List_Oappend(X2463),X2460),X2461) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).
fof(i_0_965,plain,
! [X2464,X2465,X2466,X2467] :
( ( hAPP(hAPP(c_List_Oappend(X2467),X2466),X2465) != hAPP(hAPP(c_List_Oappend(X2467),X2466),X2464)
| X2465 = X2464 )
& ( X2465 != X2464
| hAPP(hAPP(c_List_Oappend(X2467),X2466),X2465) = hAPP(hAPP(c_List_Oappend(X2467),X2466),X2464) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).
fof(i_0_966,plain,
! [X3666,X3667,X3668] :
( ~ class_Lattices_Osemilattice__inf(X3668)
| c_Orderings_Oord__class_Oless__eq(X3668,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3668),X3667),X3666),X3667) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).
fof(i_0_967,plain,
! [X3669,X3670,X3671] :
( ~ class_Lattices_Olattice(X3671)
| c_Orderings_Oord__class_Oless__eq(X3671,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3671),X3670),X3669),X3670) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).
fof(i_0_968,plain,
! [X3660,X3661,X3662] :
( ~ class_Lattices_Osemilattice__inf(X3662)
| c_Orderings_Oord__class_Oless__eq(X3662,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3662),X3661),X3660),X3660) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).
fof(i_0_969,plain,
! [X3663,X3664,X3665] :
( ~ class_Lattices_Olattice(X3665)
| c_Orderings_Oord__class_Oless__eq(X3665,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3665),X3664),X3663),X3663) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).
fof(i_0_970,plain,
! [X3866,X3867,X3868] :
( ~ class_Orderings_Oorder(X3868)
| ~ c_Orderings_Oord__class_Oless__eq(X3868,X3867,X3866)
| X3866 = X3867
| c_Orderings_Oord__class_Oless(X3868,X3867,X3866) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_971,plain,
! [X3863,X3864,X3865] :
( ~ class_Orderings_Oorder(X3865)
| ~ c_Orderings_Oord__class_Oless__eq(X3865,X3864,X3863)
| X3864 = X3863
| c_Orderings_Oord__class_Oless(X3865,X3864,X3863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_972,plain,
! [X3860,X3861,X3862] :
( ~ class_Orderings_Oorder(X3862)
| ~ c_Orderings_Oord__class_Oless__eq(X3862,X3861,X3860)
| c_Orderings_Oord__class_Oless(X3862,X3861,X3860)
| X3861 = X3860 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_973,plain,
! [X3845,X3846,X3847] :
( ~ class_Orderings_Oorder(X3847)
| X3846 = X3845
| ~ c_Orderings_Oord__class_Oless__eq(X3847,X3846,X3845)
| c_Orderings_Oord__class_Oless(X3847,X3846,X3845) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_974,plain,
! [X3833,X3834,X3835] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3835,X3834,X3833)
| c_Orderings_Oord__class_Oless(X3835,X3834,X3833)
| X3834 = X3833
| ~ class_Orderings_Oorder(X3835) )
& ( ~ c_Orderings_Oord__class_Oless(X3835,X3834,X3833)
| c_Orderings_Oord__class_Oless__eq(X3835,X3834,X3833)
| ~ class_Orderings_Oorder(X3835) )
& ( X3834 != X3833
| c_Orderings_Oord__class_Oless__eq(X3835,X3834,X3833)
| ~ class_Orderings_Oorder(X3835) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_975,plain,
! [X3827,X3828,X3829] :
( ( c_Orderings_Oord__class_Oless__eq(X3829,X3828,X3827)
| ~ c_Orderings_Oord__class_Oless(X3829,X3828,X3827)
| ~ class_Orderings_Oorder(X3829) )
& ( X3828 != X3827
| ~ c_Orderings_Oord__class_Oless(X3829,X3828,X3827)
| ~ class_Orderings_Oorder(X3829) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3829,X3828,X3827)
| X3828 = X3827
| c_Orderings_Oord__class_Oless(X3829,X3828,X3827)
| ~ class_Orderings_Oorder(X3829) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_976,plain,
! [X3842,X3843,X3844] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3844,X3843,X3842)
| X3843 = X3842
| c_Orderings_Oord__class_Oless(X3844,X3843,X3842)
| ~ class_Orderings_Olinorder(X3844) )
& ( X3843 != X3842
| c_Orderings_Oord__class_Oless__eq(X3844,X3843,X3842)
| c_Orderings_Oord__class_Oless(X3844,X3843,X3842)
| ~ class_Orderings_Olinorder(X3844) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])])]) ).
fof(i_0_977,plain,
! [X3848,X3849,X3850] :
( ~ class_Orderings_Oorder(X3850)
| X3849 = X3848
| ~ c_Orderings_Oord__class_Oless__eq(X3850,X3848,X3849)
| c_Orderings_Oord__class_Oless(X3850,X3848,X3849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_978,plain,
! [X3854,X3855,X3856] :
( ~ class_Orderings_Opreorder(X3856)
| ~ c_Orderings_Oord__class_Oless(X3856,X3855,X3854)
| c_Orderings_Oord__class_Oless__eq(X3856,X3855,X3854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_979,plain,
! [X3657,X3658,X3659] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3659,X3658,X3657)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3659),X3658),X3657) = X3658
| ~ class_Lattices_Osemilattice__inf(X3659) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3659),X3658),X3657) != X3658
| c_Orderings_Oord__class_Oless__eq(X3659,X3658,X3657)
| ~ class_Lattices_Osemilattice__inf(X3659) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).
fof(i_0_980,plain,
! [X3642,X3643,X3644] :
( ~ class_Lattices_Osemilattice__inf(X3644)
| ~ c_Orderings_Oord__class_Oless__eq(X3644,X3643,X3642)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3644),X3643),X3642) = X3643 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).
fof(i_0_981,plain,
! [X3639,X3640,X3641] :
( ~ class_Lattices_Osemilattice__inf(X3641)
| ~ c_Orderings_Oord__class_Oless__eq(X3641,X3640,X3639)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3641),X3639),X3640) = X3640 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).
fof(i_0_982,plain,
! [X3130,X3131] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3131,tc_HOL_Obool)),X3130),X3130) = X3130,
inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).
fof(i_0_983,plain,
! [X3453,X3454,X3455] :
( ~ c_List_Odistinct(X3455,X3454)
| c_List_Odistinct(X3455,c_List_OdropWhile(X3455,X3453,X3454)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile])]) ).
fof(i_0_984,plain,
! [X3417,X3418,X3419] :
( ~ c_List_Odistinct(X3419,X3418)
| c_List_Odistinct(X3419,c_List_OtakeWhile(X3419,X3417,X3418)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).
fof(i_0_985,plain,
! [X2394,X2395,X2396] :
( ~ c_List_Odistinct(X2396,X2395)
| c_List_Odistinct(X2396,c_List_Oinsert(X2396,X2394,X2395)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])]) ).
fof(i_0_986,plain,
! [X4028,X4029] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4029,X4028)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4029,X4028)
| X4029 = X4028 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4029,X4028)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4029,X4028) )
& ( X4029 != X4028
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4029,X4028) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_987,plain,
! [X4024,X4025] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4025,X4024)
| X4025 = X4024
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4025,X4024) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_988,plain,
! [X3972,X3973] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3973,X3972)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3973,X3972) )
& ( X3973 != X3972
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3973,X3972) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3973,X3972)
| X3973 = X3972
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3973,X3972) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_989,plain,
! [X3372,X3373,X3374] :
( X3374 != c_List_Olist_ONil(X3373)
| c_List_Olast(X3373,hAPP(hAPP(c_List_Oappend(X3373),X3372),X3374)) = c_List_Olast(X3373,X3372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).
fof(i_0_990,plain,
! [X3366,X3367,X3368] :
( ( X3368 != c_List_Olist_ONil(X3367)
| c_List_Olast(X3367,hAPP(hAPP(c_List_Oappend(X3367),X3366),X3368)) = c_List_Olast(X3367,X3366) )
& ( X3368 = c_List_Olist_ONil(X3367)
| c_List_Olast(X3367,hAPP(hAPP(c_List_Oappend(X3367),X3366),X3368)) = c_List_Olast(X3367,X3368) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).
fof(i_0_991,plain,
! [X4026,X4027] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4027,X4026)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4027,X4026) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_992,plain,
! [X4022,X4023] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4023,X4022)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4023,X4022) )
& ( X4023 != X4022
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4023,X4022) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_993,plain,
! [X3885,X3886] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3886,X3885)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3886,X3885) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_994,plain,
! [X3369,X3370,X3371] :
( X3371 = c_List_Olist_ONil(X3370)
| c_List_Olast(X3370,hAPP(hAPP(c_List_Oappend(X3370),X3369),X3371)) = c_List_Olast(X3370,X3371) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).
fof(i_0_995,plain,
! [X3360,X3361,X3362] :
( X3362 = c_List_Olist_ONil(X3361)
| c_List_Olast(X3361,hAPP(hAPP(c_List_Olist_OCons(X3361),X3360),X3362)) = c_List_Olast(X3361,X3362) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).
fof(i_0_996,plain,
! [X3357,X3358,X3359] :
( ( X3359 != c_List_Olist_ONil(X3358)
| c_List_Olast(X3358,hAPP(hAPP(c_List_Olist_OCons(X3358),X3357),X3359)) = X3357 )
& ( X3359 = c_List_Olist_ONil(X3358)
| c_List_Olast(X3358,hAPP(hAPP(c_List_Olist_OCons(X3358),X3357),X3359)) = c_List_Olast(X3358,X3359) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).
fof(i_0_997,plain,
! [X2104,X2105] :
( hAPP(X2105,esk1_2(X2104,X2105)) != hAPP(X2104,esk1_2(X2104,X2105))
| X2105 = X2104 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_998,plain,
! [X3363,X3364,X3365] :
( X3365 != c_List_Olist_ONil(X3364)
| c_List_Olast(X3364,hAPP(hAPP(c_List_Olist_OCons(X3364),X3363),X3365)) = X3363 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).
fof(i_0_999,plain,
! [X4214,X4215] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4215),X4214))
| hBOOL(X4215) ),
inference(variable_rename,[status(thm)],[i_0_576]) ).
fof(i_0_1000,plain,
! [X4216,X4217] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X4217),X4216))
| hBOOL(X4216) ),
inference(variable_rename,[status(thm)],[i_0_577]) ).
fof(i_0_1001,plain,
! [X4206,X4207] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4207),X4206))
| X4207 = X4206 ),
inference(variable_rename,[status(thm)],[i_0_578]) ).
fof(i_0_1002,plain,
! [X4184,X4185,X4186,X4187] : hAPP(c_COMBK(X4187,X4186,X4185),X4184) = X4185,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1003,plain,
! [X3897,X3898,X3899] :
( ( X3898 = X3897
| c_Orderings_Oord__class_Oless(X3899,X3898,X3897)
| c_Orderings_Oord__class_Oless(X3899,X3897,X3898)
| ~ class_Orderings_Olinorder(X3899) )
& ( ~ c_Orderings_Oord__class_Oless(X3899,X3898,X3897)
| X3898 != X3897
| ~ class_Orderings_Olinorder(X3899) )
& ( ~ c_Orderings_Oord__class_Oless(X3899,X3897,X3898)
| X3898 != X3897
| ~ class_Orderings_Olinorder(X3899) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_1004,plain,
! [X3960,X3961,X3962] :
( ~ class_Orderings_Olinorder(X3962)
| c_Orderings_Oord__class_Oless(X3962,X3961,X3960)
| X3961 = X3960
| c_Orderings_Oord__class_Oless(X3962,X3960,X3961) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])]) ).
fof(i_0_1005,plain,
! [X3909,X3910,X3911] :
( ~ class_Orderings_Olinorder(X3911)
| X3910 = X3909
| c_Orderings_Oord__class_Oless(X3911,X3910,X3909)
| c_Orderings_Oord__class_Oless(X3911,X3909,X3910) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])]) ).
fof(i_0_1006,plain,
! [X3906,X3907,X3908] :
( ( c_Orderings_Oord__class_Oless(X3908,X3906,X3907)
| X3906 = X3907
| c_Orderings_Oord__class_Oless(X3908,X3907,X3906)
| ~ class_Orderings_Olinorder(X3908) )
& ( X3906 != X3907
| ~ c_Orderings_Oord__class_Oless(X3908,X3906,X3907)
| c_Orderings_Oord__class_Oless(X3908,X3907,X3906)
| ~ class_Orderings_Olinorder(X3908) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_581])])]) ).
fof(i_0_1007,plain,
! [X3903,X3904,X3905] :
( ~ class_Orderings_Olinorder(X3905)
| c_Orderings_Oord__class_Oless(X3905,X3904,X3903)
| X3904 = X3903
| c_Orderings_Oord__class_Oless(X3905,X3903,X3904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_1008,plain,
! [X2374,X2375] : c_List_Oinsert(X2375,X2374,c_List_Olist_ONil(X2375)) = hAPP(hAPP(c_List_Olist_OCons(X2375),X2374),c_List_Olist_ONil(X2375)),
inference(variable_rename,[status(thm)],[fact_insert__Nil]) ).
fof(i_0_1009,plain,
! [X3839,X3840,X3841] :
( ~ class_Orderings_Olinorder(X3841)
| c_Orderings_Oord__class_Oless__eq(X3841,X3840,X3839)
| c_Orderings_Oord__class_Oless(X3841,X3839,X3840) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_582])]) ).
fof(i_0_1010,plain,
! [X3824,X3825,X3826] :
( ~ class_Orderings_Olinorder(X3826)
| c_Orderings_Oord__class_Oless__eq(X3826,X3825,X3824)
| c_Orderings_Oord__class_Oless(X3826,X3824,X3825) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_1011,plain,
! [X3836,X3837,X3838] :
( ~ class_Orderings_Olinorder(X3838)
| c_Orderings_Oord__class_Oless(X3838,X3837,X3836)
| c_Orderings_Oord__class_Oless__eq(X3838,X3836,X3837) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_583])]) ).
fof(i_0_1012,plain,
! [X3768,X3769,X3770] :
( ~ class_Orderings_Olinorder(X3770)
| c_Orderings_Oord__class_Oless__eq(X3770,X3769,X3768)
| c_Orderings_Oord__class_Oless__eq(X3770,X3768,X3769) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_1013,plain,
! [X3726,X3727,X3728] :
( ~ class_Orderings_Olinorder(X3728)
| c_Orderings_Oord__class_Oless__eq(X3728,X3727,X3726)
| c_Orderings_Oord__class_Oless__eq(X3728,X3726,X3727) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_584])]) ).
fof(i_0_1014,plain,
! [X3311,X3312,X3313] :
( ~ class_Lattices_Osemilattice__inf(X3313)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3313),X3312),X3311) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3313),X3311),X3312) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).
fof(i_0_1015,plain,
! [X3305,X3306,X3307] :
( ~ class_Lattices_Osemilattice__inf(X3307)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3307),X3306),X3305) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3307),X3305),X3306) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).
fof(i_0_1016,plain,
! [X3308,X3309,X3310] :
( ~ class_Lattices_Olattice(X3310)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3310),X3309),X3308) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3310),X3308),X3309) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).
fof(i_0_1017,plain,
! [X4002,X4003] :
( X4003 = X4002
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4003,X4002)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4002,X4003) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_585])]) ).
fof(i_0_1018,plain,
! [X4000,X4001] :
( ( X4001 = X4000
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4001,X4000)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4000,X4001) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4001,X4000)
| X4001 != X4000 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4000,X4001)
| X4001 != X4000 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_1019,plain,
! [X4013,X4014] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4014,X4013)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4013,X4014) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_1020,plain,
! [X4170,X4171] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4171,X4170) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4170,X4171),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_1021,plain,
! [X3924,X3925,X3926] :
( ~ class_Orderings_Oorder(X3926)
| ~ c_Orderings_Oord__class_Oless(X3926,X3925,X3924)
| X3924 != X3925 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_1022,plain,
! [X3921,X3922,X3923] :
( ~ class_Orderings_Oorder(X3923)
| ~ c_Orderings_Oord__class_Oless(X3923,X3922,X3921)
| X3922 != X3921 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_1023,plain,
! [X3912,X3913,X3914] :
( ~ class_Orderings_Oorder(X3914)
| ~ c_Orderings_Oord__class_Oless(X3914,X3913,X3912)
| X3913 != X3912 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_1024,plain,
! [X3027,X3028] : hBOOL(hAPP(c_List_Olistsp(X3028,X3027),c_List_Olist_ONil(X3028))),
inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J]) ).
fof(i_0_1025,plain,
! [X3017,X3018] : hBOOL(hAPP(c_List_Olistsp(X3018,X3017),c_List_Olist_ONil(X3018))),
inference(variable_rename,[status(thm)],[fact_listsp_ONil]) ).
fof(i_0_1026,plain,
! [X2509,X2510,X2511] :
( ( X2510 = c_List_Olist_ONil(X2511)
| hAPP(hAPP(c_List_Oappend(X2511),X2510),X2509) != c_List_Olist_ONil(X2511) )
& ( X2509 = c_List_Olist_ONil(X2511)
| hAPP(hAPP(c_List_Oappend(X2511),X2510),X2509) != c_List_Olist_ONil(X2511) )
& ( X2510 != c_List_Olist_ONil(X2511)
| X2509 != c_List_Olist_ONil(X2511)
| hAPP(hAPP(c_List_Oappend(X2511),X2510),X2509) = c_List_Olist_ONil(X2511) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).
fof(i_0_1027,plain,
! [X2498,X2499,X2500] :
( ( X2499 = c_List_Olist_ONil(X2500)
| c_List_Olist_ONil(X2500) != hAPP(hAPP(c_List_Oappend(X2500),X2499),X2498) )
& ( X2498 = c_List_Olist_ONil(X2500)
| c_List_Olist_ONil(X2500) != hAPP(hAPP(c_List_Oappend(X2500),X2499),X2498) )
& ( X2499 != c_List_Olist_ONil(X2500)
| X2498 != c_List_Olist_ONil(X2500)
| c_List_Olist_ONil(X2500) = hAPP(hAPP(c_List_Oappend(X2500),X2499),X2498) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).
fof(i_0_1028,plain,
! [X3895,X3896] :
( ~ class_Orderings_Opreorder(X3896)
| ~ c_Orderings_Oord__class_Oless(X3896,X3895,X3895) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_586])]) ).
fof(i_0_1029,plain,
! [X4212,X4213] :
( ~ hBOOL(X4213)
| ~ hBOOL(X4212)
| hBOOL(hAPP(hAPP(c_fconj,X4213),X4212)) ),
inference(variable_rename,[status(thm)],[i_0_587]) ).
fof(i_0_1030,plain,
! [X2515,X2516,X2517] :
( ( hAPP(hAPP(c_List_Oappend(X2517),X2516),X2515) != X2515
| X2516 = c_List_Olist_ONil(X2517) )
& ( X2516 != c_List_Olist_ONil(X2517)
| hAPP(hAPP(c_List_Oappend(X2517),X2516),X2515) = X2515 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).
fof(i_0_1031,plain,
! [X2512,X2513,X2514] :
( ( hAPP(hAPP(c_List_Oappend(X2514),X2513),X2512) != X2513
| X2512 = c_List_Olist_ONil(X2514) )
& ( X2512 != c_List_Olist_ONil(X2514)
| hAPP(hAPP(c_List_Oappend(X2514),X2513),X2512) = X2513 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).
fof(i_0_1032,plain,
! [X2503,X2504,X2505] :
( ( X2505 != hAPP(hAPP(c_List_Oappend(X2504),X2505),X2503)
| X2503 = c_List_Olist_ONil(X2504) )
& ( X2503 != c_List_Olist_ONil(X2504)
| X2505 = hAPP(hAPP(c_List_Oappend(X2504),X2505),X2503) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).
fof(i_0_1033,plain,
! [X2506,X2507,X2508] :
( ( X2508 != hAPP(hAPP(c_List_Oappend(X2507),X2506),X2508)
| X2506 = c_List_Olist_ONil(X2507) )
& ( X2506 != c_List_Olist_ONil(X2507)
| X2508 = hAPP(hAPP(c_List_Oappend(X2507),X2506),X2508) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).
fof(i_0_1034,plain,
! [X2207,X2208,X2209] : hAPP(hAPP(c_List_Olist_OCons(X2209),X2208),X2207) != c_List_Olist_ONil(X2209),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).
fof(i_0_1035,plain,
! [X2204,X2205,X2206] : c_List_Olist_ONil(X2206) != hAPP(hAPP(c_List_Olist_OCons(X2206),X2205),X2204),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
fof(i_0_1036,plain,
! [X4007,X4008] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4008,X4007)
| X4008 != X4007 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_1037,plain,
! [X4005,X4006] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4006,X4005)
| X4005 != X4006 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_1038,plain,
! [X2723,X2724] : c_List_Olistrel(X2724,c_Transitive__Closure_Ortrancl(X2724,X2723)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X2724),c_List_Olistrel1(X2724,X2723)),
inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).
fof(i_0_1039,plain,
! [X2248,X2249,X2250] : hAPP(hAPP(c_List_Olist_OCons(X2250),X2249),X2248) != X2248,
inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).
fof(i_0_1040,plain,
! [X2251,X2252,X2253] : X2253 != hAPP(hAPP(c_List_Olist_OCons(X2252),X2251),X2253),
inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).
fof(i_0_1041,plain,
! [X4004] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4004,X4004),
inference(variable_rename,[status(thm)],[i_0_588]) ).
fof(i_0_1042,plain,
! [X3999] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3999,X3999),
inference(variable_rename,[status(thm)],[i_0_589]) ).
fof(i_0_1043,plain,
! [X2960,X2961] : c_Relation_ORange(X2961,X2961,c_Relation_OId__on(X2961,X2960)) = X2960,
inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).
fof(i_0_1044,plain,
! [X2956,X2957] : c_Relation_ODomain(X2957,X2957,c_Relation_OId__on(X2957,X2956)) = X2956,
inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).
fof(i_0_1045,plain,
! [X3533,X3534,X3535] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3533,tc_HOL_Obool),X3535,X3534)
| X3535 != X3534 )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3533,tc_HOL_Obool),X3534,X3535)
| X3535 != X3534 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_590])])]) ).
fof(i_0_1046,plain,
! [X3543,X3544,X3545] :
( X3545 != X3544
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3543,tc_HOL_Obool),X3545,X3544) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_1047,plain,
! [X3540,X3541,X3542] :
( X3542 != X3541
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3540,tc_HOL_Obool),X3541,X3542) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_1048,plain,
! [X2962,X2963] : c_Relation_Osingle__valued(X2963,X2963,c_Relation_OId__on(X2963,X2962)),
inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).
fof(i_0_1049,plain,
! [X4208,X4209] :
( X4209 != X4208
| hBOOL(hAPP(hAPP(c_fequal,X4209),X4208)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1050,plain,
! [X2646,X2647] :
( ( ~ c_List_Odistinct(X2647,c_List_Orotate1(X2647,X2646))
| c_List_Odistinct(X2647,X2646) )
& ( ~ c_List_Odistinct(X2647,X2646)
| c_List_Odistinct(X2647,c_List_Orotate1(X2647,X2646)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).
fof(i_0_1051,plain,
! [X3549,X3550] : c_Orderings_Oord__class_Oless__eq(tc_fun(X3550,tc_HOL_Obool),X3549,X3549),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_1052,plain,
! [X2719,X2720] :
( ~ c_Relation_Otrans(X2720,X2719)
| c_Relation_Otrans(tc_List_Olist(X2720),c_List_Olistrel(X2720,X2719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__trans])]) ).
fof(i_0_1053,plain,
! [X2721,X2722] :
( ~ c_Relation_Otrans(X2722,X2721)
| c_Relation_Otrans(tc_List_Olist(X2722),c_List_Olexord(X2722,X2721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__transI])]) ).
fof(i_0_1054,plain,
! [X2518,X2519,X2520] :
( X2520 != X2519
| X2520 = hAPP(hAPP(c_List_Oappend(X2518),c_List_Olist_ONil(X2518)),X2519) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).
fof(i_0_1055,plain,
! [X3396,X3397] :
( X3397 = c_List_Olist_ONil(X3396)
| ~ c_List_Odistinct(X3396,X3397)
| c_List_Odistinct(X3396,c_List_Obutlast(X3396,X3397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).
fof(i_0_1056,plain,
! [X2639,X2640] : c_Nat_Osize__class_Osize(tc_List_Olist(X2640),c_List_Orotate1(X2640,X2639)) = c_Nat_Osize__class_Osize(tc_List_Olist(X2640),X2639),
inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).
fof(i_0_1057,plain,
! [X3762,X3763,X3764] :
( ~ class_Orderings_Opreorder(X3764)
| X3763 != X3762
| c_Orderings_Oord__class_Oless__eq(X3764,X3763,X3762) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1058,plain,
! [X2496,X2497] : hAPP(hAPP(c_List_Oappend(X2497),c_List_Olist_ONil(X2497)),X2496) = X2496,
inference(variable_rename,[status(thm)],[fact_append__Nil]) ).
fof(i_0_1059,plain,
! [X3451,X3452] : c_List_OdropWhile(X3452,X3451,c_List_Olist_ONil(X3452)) = c_List_Olist_ONil(X3452),
inference(variable_rename,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).
fof(i_0_1060,plain,
! [X3420,X3421] : c_List_OtakeWhile(X3421,X3420,c_List_Olist_ONil(X3421)) = c_List_Olist_ONil(X3421),
inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).
fof(i_0_1061,plain,
! [X3700,X3701] :
( ~ class_Orderings_Opreorder(X3701)
| c_Orderings_Oord__class_Oless__eq(X3701,X3700,X3700) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1062,plain,
! [X2324,X2325] : c_List_Osplice(X2325,c_List_Olist_ONil(X2325),X2324) = X2324,
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).
fof(i_0_1063,plain,
! [X2326,X2327] : c_List_Osplice(X2327,X2326,c_List_Olist_ONil(X2327)) = X2326,
inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).
fof(i_0_1064,plain,
! [X3316,X3317] :
( ~ class_Lattices_Osemilattice__inf(X3317)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3317),X3316),X3316) = X3316 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).
fof(i_0_1065,plain,
! [X3314,X3315] :
( ~ class_Lattices_Osemilattice__inf(X3315)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X3315),X3314),X3314) = X3314 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).
fof(i_0_1066,plain,
! [X2501,X2502] : hAPP(hAPP(c_List_Oappend(X2502),X2501),c_List_Olist_ONil(X2502)) = X2501,
inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).
fof(i_0_1067,plain,
! [X4015,X4016] :
( X4016 != X4015
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4016,X4015) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1068,plain,
! [X2779,X2780] : c_Transitive__Closure_Ortrancl(X2780,c_Transitive__Closure_Ortrancl(X2780,X2779)) = c_Transitive__Closure_Ortrancl(X2780,X2779),
inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).
fof(i_0_1069,plain,
! [X4012] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4012,X4012),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1070,plain,
! [X4210] :
( ~ hBOOL(hAPP(c_fNot,X4210))
| ~ hBOOL(X4210) ),
inference(variable_rename,[status(thm)],[i_0_591]) ).
fof(i_0_1071,plain,
! [X2958,X2959] : c_Relation_Otrans(X2959,c_Relation_OId__on(X2959,X2958)),
inference(variable_rename,[status(thm)],[fact_trans__Id__on]) ).
fof(i_0_1072,plain,
! [X2781,X2782] : c_Relation_Otrans(X2782,c_Transitive__Closure_Ortrancl(X2782,X2781)),
inference(variable_rename,[status(thm)],[fact_trans__rtrancl]) ).
fof(i_0_1073,plain,
! [X4178,X4179] :
( ~ class_Orderings_Oorder(X4179)
| class_Orderings_Oorder(tc_fun(X4178,X4179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1074,plain,
! [X4180,X4181] :
( ~ class_Orderings_Oord(X4181)
| class_Orderings_Oord(tc_fun(X4180,X4181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1075,plain,
! [X4174,X4175] :
( ~ class_Orderings_Opreorder(X4175)
| class_Orderings_Opreorder(tc_fun(X4174,X4175)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1076,plain,
! [X4172,X4173] :
( ~ class_Lattices_Olattice(X4173)
| class_Lattices_Osemilattice__inf(tc_fun(X4172,X4173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).
fof(i_0_1077,plain,
! [X4176,X4177] :
( ~ class_Lattices_Olattice(X4177)
| class_Lattices_Olattice(tc_fun(X4176,X4177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).
fof(i_0_1078,plain,
! [X2644,X2645] :
( ( c_List_Orotate1(X2645,X2644) != c_List_Olist_ONil(X2645)
| X2644 = c_List_Olist_ONil(X2645) )
& ( X2644 != c_List_Olist_ONil(X2645)
| c_List_Orotate1(X2645,X2644) = c_List_Olist_ONil(X2645) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).
fof(i_0_1079,plain,
! [X4211] :
( hBOOL(X4211)
| hBOOL(hAPP(c_fNot,X4211)) ),
inference(variable_rename,[status(thm)],[i_0_592]) ).
fof(i_0_1080,plain,
! [X3389] : c_List_Obutlast(X3389,c_List_Olist_ONil(X3389)) = c_List_Olist_ONil(X3389),
inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).
fof(i_0_1081,plain,
! [X4182,X4183] : hAPP(c_COMBI(X4183),X4182) = X4182,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1082,plain,
! [X2203] : c_List_Odistinct(X2203,c_List_Olist_ONil(X2203)),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
cnf(i_0_1083,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_1084,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk66_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk67_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk68_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk69_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_593]),
[final] ).
cnf(i_0_1085,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),esk70_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk71_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk72_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk73_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_594]),
[final] ).
cnf(i_0_1086,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),esk72_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk73_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_594]),
[final] ).
cnf(i_0_1087,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),esk66_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk67_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_593]),
[final] ).
cnf(i_0_1088,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_1089,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),esk74_7(X3,X4,X5,X6,X7,X2,X1)),esk75_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_595]),
[final] ).
cnf(i_0_1090,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(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_596]),
[final] ).
cnf(i_0_1091,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),esk74_7(X5,X6,X7,X4,X3,X2,X1)),esk75_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_595]),
[final] ).
cnf(i_0_1092,plain,
( hBOOL(hAPP(hAPP(X1,X4),X3))
| ~ hBOOL(hAPP(hAPP(X1,esk68_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk69_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_593]),
[final] ).
cnf(i_0_1093,plain,
( hBOOL(hAPP(hAPP(X1,X6),X5))
| ~ hBOOL(hAPP(hAPP(X1,esk70_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk71_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_594]),
[final] ).
cnf(i_0_1094,plain,
( hBOOL(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X6))) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1095,plain,
( hBOOL(hAPP(hAPP(X1,esk66_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk67_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_593]),
[final] ).
cnf(i_0_1096,plain,
( hBOOL(hAPP(hAPP(X1,esk72_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk73_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_594]),
[final] ).
cnf(i_0_1097,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_597]),
[final] ).
cnf(i_0_1098,plain,
c_List_Opartition(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)) = hAPP(hAPP(c_Product__Type_Ointernal__split(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(rw,[status(thm)],[i_0_598,c_0_599]),
[final] ).
cnf(i_0_1099,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_600]),
[final] ).
cnf(i_0_1100,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_597]),
[final] ).
cnf(i_0_1101,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_601]),
[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),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_600]),
[final] ).
cnf(i_0_1103,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_1104,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Ointernal__split(X5,X4,tc_fun(X1,tc_HOL_Obool)),X3),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk87_6(X3,X2,X1,X4,X5,X6)),esk88_6(X3,X2,X1,X4,X5,X6)))) ),
inference(rw,[status(thm)],[i_0_602,c_0_599]),
[final] ).
cnf(i_0_1105,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_601]),
[final] ).
cnf(i_0_1106,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,esk8_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,esk8_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_603]),
[final] ).
cnf(i_0_1107,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,esk8_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,esk8_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_603]),
[final] ).
cnf(i_0_1108,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,esk7_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,esk7_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_604]),
[final] ).
cnf(i_0_1109,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_605]),
[final] ).
cnf(i_0_1110,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_606]),
[final] ).
cnf(i_0_1111,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_607]),
[final] ).
cnf(i_0_1112,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_608]),
[final] ).
cnf(i_0_1113,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk85_6(X4,X3,X5,X6,X2,X1)),esk86_6(X4,X3,X5,X6,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Ointernal__split(X6,X5,tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(rw,[status(thm)],[i_0_609,c_0_599]),
[final] ).
cnf(i_0_1114,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,esk8_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,esk8_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_603]),
[final] ).
cnf(i_0_1115,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,esk8_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,esk8_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_603]),
[final] ).
cnf(i_0_1116,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,esk7_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,esk7_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_604]),
[final] ).
cnf(i_0_1117,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_605]),
[final] ).
cnf(i_0_1118,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_606]),
[final] ).
cnf(i_0_1119,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_607]),
[final] ).
cnf(i_0_1120,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)),esk77_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),esk76_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_610]),
[final] ).
cnf(i_0_1121,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk43_5(X5,X4,X3,X2,X1)),esk43_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_611]),
[final] ).
cnf(i_0_1122,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_612]),
[final] ).
cnf(i_0_1123,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),esk84_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_613]),
[final] ).
cnf(i_0_1124,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X6),c_FuncSet_OPi(X1,X2,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),esk84_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_613]),
[final] ).
cnf(i_0_1125,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)),esk77_5(X2,X3,X4,X5,X1)),X3)),c_List_Olistrel1(X1,X2)))
| X5 = hAPP(hAPP(c_List_Olist_OCons(X1),esk76_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_610]),
[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,esk89_5(X3,X2,X1,X4,X5))),hAPP(X3,esk89_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_1127,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_615]),
[final] ).
cnf(i_0_1128,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),esk45_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),esk44_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_616]),
[final] ).
cnf(i_0_1129,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk77_5(X4,X5,X3,X1,X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk76_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_610]),
[final] ).
cnf(i_0_1130,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_617]),
[final] ).
cnf(i_0_1131,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),X4)),c_List_Olistrel(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),c_List_Onth(X1,X2,esk96_4(X3,X4,X2,X1))),c_List_Onth(X1,X4,esk96_4(X3,X4,X2,X1)))),X3))
| c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) != c_Nat_Osize__class_Osize(tc_List_Olist(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1132,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)),esk38_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_619]),
[final] ).
cnf(i_0_1133,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk37_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_619]),
[final] ).
cnf(i_0_1134,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,esk84_6(X5,X2,X3,X6,X4,X1)) != hAPP(X3,esk84_6(X5,X2,X3,X6,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1135,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,esk84_6(X5,X2,X6,X3,X4,X1)) != hAPP(X6,esk84_6(X5,X2,X6,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1136,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,esk9_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,esk9_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_620]),
[final] ).
cnf(i_0_1137,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,esk9_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,esk9_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_620]),
[final] ).
cnf(i_0_1138,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk85_6(X1,X4,X3,X2,X5,X6)),esk86_6(X1,X4,X3,X2,X5,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Ointernal__split(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
inference(rw,[status(thm)],[i_0_621,c_0_599]),
[final] ).
cnf(i_0_1139,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk87_6(X4,X5,X6,X3,X2,X1)),esk88_6(X4,X5,X6,X3,X2,X1))
| hBOOL(hAPP(hAPP(c_member(X6),X5),hAPP(hAPP(c_Product__Type_Ointernal__split(X2,X3,tc_fun(X6,tc_HOL_Obool)),X4),X1))) ),
inference(rw,[status(thm)],[i_0_622,c_0_599]),
[final] ).
cnf(i_0_1140,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,esk25_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1141,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),esk45_5(X3,X4,X2,X5,X1))),c_List_Olistrel1(X1,X3)))
| X4 = hAPP(hAPP(c_List_Olist_OCons(X1),esk44_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_616]),
[final] ).
cnf(i_0_1142,plain,
c_Relation_OId__on(X1,X2) = hAPP(c_Product__Type_Ointernal__split(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(rw,[status(thm)],[i_0_624,c_0_599]),
[final] ).
cnf(i_0_1143,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk45_5(X4,X1,X5,X3,X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),esk44_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_616]),
[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,esk9_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,esk9_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_620]),
[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,esk9_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,esk9_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_620]),
[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),esk36_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_625]),
[final] ).
cnf(i_0_1147,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk35_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_625]),
[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),esk29_4(X2,X3,X4,X1)),esk28_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[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),esk28_4(X2,X3,X4,X1)),esk29_4(X2,X3,X4,X1))),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1150,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk102_5(X2,X3,X4,X1,X5)),hAPP(X2,esk101_5(X2,X3,X4,X1,X5))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),X4),c_Product__Type_OSigma(X5,X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[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_628]),
[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_628]),
[final] ).
cnf(i_0_1153,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(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(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_629]),
[final] ).
cnf(i_0_1154,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_member(tc_prod(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_630]),
[final] ).
cnf(i_0_1155,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_630]),
[final] ).
cnf(i_0_1156,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,esk95_5(X3,X2,X1,X4,X5)),hAPP(X3,esk95_5(X3,X2,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_631]),
[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))
| 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_630]),
[final] ).
cnf(i_0_1158,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_632]),
[final] ).
cnf(i_0_1159,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),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(X2,esk18_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_633]),
[final] ).
cnf(i_0_1160,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk39_4(X2,X3,X4,X1)),esk40_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_634]),
[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_630]),
[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_632]),
[final] ).
cnf(i_0_1163,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)))
| ~ hBOOL(hAPP(hAPP(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_635]),
[final] ).
cnf(i_0_1164,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),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(esk18_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_633]),
[final] ).
cnf(i_0_1165,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))),esk18_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_633]),
[final] ).
cnf(i_0_1166,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk19_2(X1,X2) != esk20_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_633]),
[final] ).
cnf(i_0_1167,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_636]),
[final] ).
cnf(i_0_1168,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_628]),
[final] ).
cnf(i_0_1169,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk45_5(X4,X1,X5,X3,X2))
| X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk44_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_616]),
[final] ).
cnf(i_0_1170,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk35_5(X3,X1,X4,X5,X2)),esk36_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_625]),
[final] ).
cnf(i_0_1171,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_630]),
[final] ).
cnf(i_0_1172,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_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk104_0)),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____,esk104_0)),v_c____),v_b____)),v_b____),v_a____))) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1173,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_638]),
[final] ).
cnf(i_0_1174,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk101_5(X2,X3,X4,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X5)),X4),c_Product__Type_OSigma(X1,X5,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1175,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk25_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_623]),
[final] ).
cnf(i_0_1176,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_630]),
[final] ).
cnf(i_0_1177,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk77_5(X4,X5,X3,X1,X2))
| X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk76_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_610]),
[final] ).
cnf(i_0_1178,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk37_5(X3,X4,X5,X1,X2)),esk38_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_619]),
[final] ).
cnf(i_0_1179,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk89_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_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_615]),
[final] ).
cnf(i_0_1181,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk95_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_631]),
[final] ).
cnf(i_0_1182,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_639]),
[final] ).
cnf(i_0_1183,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_640]),
[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),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_632]),
[final] ).
cnf(i_0_1185,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_632]),
[final] ).
cnf(i_0_1186,plain,
hAPP(hAPP(c_Product__Type_Ointernal__split(X1,X2,X3),X4),hAPP(hAPP(c_Product__Type_Ointernal__split(X5,X6,tc_prod(X1,X2)),X7),X8)) = hAPP(hAPP(c_Product__Type_Ointernal__split(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_Ointernal__split(X1,X2,X3),X4))),X7)),X8),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_641,c_0_599]),c_0_599]),c_0_599]),c_0_599]),
[final] ).
cnf(i_0_1187,plain,
c_Product__Type_OSigma(X1,X2,X3,hAPP(hAPP(c_COMBS(X1,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4)),X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,X4)),c_Product__Type_OSigma(X1,X2,X3,X5)),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1188,plain,
( hBOOL(hAPP(hAPP(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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_635]),
[final] ).
cnf(i_0_1189,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk32_5(X3,X4,X1,X5,X2)),X3)
| hAPP(hAPP(c_List_Oappend(X2),esk31_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_643]),
[final] ).
cnf(i_0_1190,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk56_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_644]),
[final] ).
cnf(i_0_1191,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk54_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_645]),
[final] ).
cnf(i_0_1192,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk101_5(X4,X5,X1,X3,X2)),esk102_5(X4,X5,X1,X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X3)),X1),c_Product__Type_OSigma(X2,X3,X5,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[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_646]),
[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_647]),
[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_648]),
[final] ).
cnf(i_0_1196,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_649]),
[final] ).
cnf(i_0_1197,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),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_650]),
[final] ).
cnf(i_0_1198,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_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)),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_647]),
[final] ).
cnf(i_0_1200,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_646]),
[final] ).
cnf(i_0_1201,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_a____),v_c____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Obelow,hAPP(v_P____,esk104_0)),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____,esk104_0)),v_c____),v_b____)),v_b____),v_a____))) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1202,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,esk14_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1203,plain,
c_List_Olistsp(X1,hAPP(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))) = hAPP(hAPP(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_652]),
[final] ).
cnf(i_0_1204,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_646]),
[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_Olex(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[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_Olexord(X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1207,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk32_5(X3,X4,X5,X2,X1)) = X4
| hAPP(hAPP(c_List_Oappend(X1),esk31_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_643]),
[final] ).
cnf(i_0_1208,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk32_5(X3,X4,X1,X5,X2)),X3)
| X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk31_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_643]),
[final] ).
cnf(i_0_1209,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_653]),
[final] ).
cnf(i_0_1210,plain,
( c_Relation_Orefl__on(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk103_3(X2,X3,X1)),esk103_3(X2,X3,X1))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_654]),
[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_655]),
[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_656]),
[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_657]),
[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_657]),
[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_646]),
[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_647]),
[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_648]),
[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_658]),
[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_659]),
[final] ).
cnf(i_0_1220,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk41_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk40_4(X3,X1,X4,X2)),esk42_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_634]),
[final] ).
cnf(i_0_1221,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk41_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk39_4(X3,X4,X1,X2)),esk42_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_634]),
[final] ).
cnf(i_0_1222,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_647]),
[final] ).
cnf(i_0_1223,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_646]),
[final] ).
cnf(i_0_1224,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_660]),
[final] ).
cnf(i_0_1225,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),c_List_Onth(X2,X3,X1)),c_List_Onth(X2,X4,X1))),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_List_Olist(X2),X3))
| ~ 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)),X3),X4)),c_List_Olistrel(X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1226,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_661]),
[final] ).
cnf(i_0_1227,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk30_3(X2,X3,X1)),esk30_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_662]),
[final] ).
cnf(i_0_1228,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_663]),
[final] ).
cnf(i_0_1229,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_664]),
[final] ).
cnf(i_0_1230,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_665]),
[final] ).
cnf(i_0_1231,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_664]),
[final] ).
cnf(i_0_1232,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),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_647]),
[final] ).
cnf(i_0_1233,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X5)),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X6))),c_List_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_646]),
[final] ).
cnf(i_0_1234,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_666]),
[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_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_648]),
[final] ).
cnf(i_0_1236,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_667]),
[final] ).
cnf(i_0_1237,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk57_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_1238,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk53_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_1239,plain,
( hAPP(hAPP(c_List_Oappend(X1),X2),esk32_5(X3,X4,X5,X2,X1)) = X4
| X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk31_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_643]),
[final] ).
cnf(i_0_1240,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk34_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_1241,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk33_5(X2,X3,X4,X5,X1)),X4) = X2
| X4 = hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2)
| hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1242,plain,
( hAPP(hAPP(c_List_Oappend(X1),esk33_5(X2,X3,X4,X5,X1)),X4) = X2
| X5 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X5),X4) != hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1243,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X2),esk34_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_1244,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_660]),
[final] ).
cnf(i_0_1245,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_660]),
[final] ).
cnf(i_0_1246,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_660]),
[final] ).
cnf(i_0_1247,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_660]),
[final] ).
cnf(i_0_1248,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_661]),
[final] ).
cnf(i_0_1249,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_661]),
[final] ).
cnf(i_0_1250,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_661]),
[final] ).
cnf(i_0_1251,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_661]),
[final] ).
cnf(i_0_1252,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_672]),
[final] ).
cnf(i_0_1253,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_673]),
[final] ).
cnf(i_0_1254,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_674]),
[final] ).
cnf(i_0_1255,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_675]),
[final] ).
cnf(i_0_1256,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(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_676]),
[final] ).
cnf(i_0_1257,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(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_676]),
[final] ).
cnf(i_0_1258,plain,
( hBOOL(hAPP(hAPP(X3,X5),X6))
| ~ hBOOL(hAPP(hAPP(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_677]),
[final] ).
cnf(i_0_1259,plain,
( hBOOL(hAPP(hAPP(X4,X5),X6))
| ~ hBOOL(hAPP(hAPP(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_678]),
[final] ).
cnf(i_0_1260,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Ortrancl(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),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_679]),
[final] ).
cnf(i_0_1261,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_680]),
[final] ).
cnf(i_0_1262,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_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_681]),
[final] ).
cnf(i_0_1263,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_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_682]),
[final] ).
cnf(i_0_1264,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)),hAPP(hAPP(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_683]),
[final] ).
cnf(i_0_1265,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_684]),
[final] ).
cnf(i_0_1266,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_1267,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_686]),
[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_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_684]),
[final] ).
cnf(i_0_1269,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X2),X1)),c_List_Olexord(X4,X3)))
| X2 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X4),tc_List_Olist(X4))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X4),tc_List_Olist(X4)),X1),X2)),c_List_Olexord(X4,X3)))
| esk28_4(X1,X2,X3,X4) != esk29_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_626]),
[final] ).
cnf(i_0_1270,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_687]),
[final] ).
cnf(i_0_1271,plain,
( hBOOL(hAPP(hAPP(c_member(X6),hAPP(hAPP(X7,X3),X4)),c_Set_Oimage(tc_prod(X1,X2),X6,hAPP(c_Product__Type_Ointernal__split(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(rw,[status(thm)],[i_0_688,c_0_599]),
[final] ).
cnf(i_0_1272,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_674]),
[final] ).
cnf(i_0_1273,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X2),c_List_OtakeWhile(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,c_List_Onth(X2,X3,esk100_4(X3,X2,X1,X4))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1274,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_690]),
[final] ).
cnf(i_0_1275,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_691]),
[final] ).
cnf(i_0_1276,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_660]),
[final] ).
cnf(i_0_1277,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_660]),
[final] ).
cnf(i_0_1278,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_660]),
[final] ).
cnf(i_0_1279,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_692]),
[final] ).
cnf(i_0_1280,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_693]),
[final] ).
cnf(i_0_1281,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk78_3(X3,X2,X1)),esk80_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1282,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk78_3(X3,X2,X1)),esk79_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1283,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk50_3(X3,X2,X1)),esk52_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1284,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk50_3(X3,X2,X1)),esk51_3(X3,X2,X1))),X3))
| c_Relation_Osingle__valued(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1285,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_674]),
[final] ).
cnf(i_0_1286,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_696]),
[final] ).
cnf(i_0_1287,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_697]),
[final] ).
cnf(i_0_1288,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_660]),
[final] ).
cnf(i_0_1289,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_660]),
[final] ).
cnf(i_0_1290,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_660]),
[final] ).
cnf(i_0_1291,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_660]),
[final] ).
cnf(i_0_1292,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_660]),
[final] ).
cnf(i_0_1293,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_661]),
[final] ).
cnf(i_0_1294,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_661]),
[final] ).
cnf(i_0_1295,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_661]),
[final] ).
cnf(i_0_1296,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_698]),
[final] ).
cnf(i_0_1297,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk93_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_699]),
[final] ).
cnf(i_0_1298,plain,
( hBOOL(hAPP(hAPP(hAPP(X4,X5),X6),X7))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Ointernal__split(X1,X2,tc_fun(X3,tc_HOL_Obool)),X4),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),X7)) ),
inference(rw,[status(thm)],[i_0_700,c_0_599]),
[final] ).
cnf(i_0_1299,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),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk10_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),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk11_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1300,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_661]),
[final] ).
cnf(i_0_1301,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_661]),
[final] ).
cnf(i_0_1302,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_661]),
[final] ).
cnf(i_0_1303,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_661]),
[final] ).
cnf(i_0_1304,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_661]),
[final] ).
cnf(i_0_1305,plain,
c_Product__Type_OSigma(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4),c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))),c_Product__Type_OSigma(X1,X2,X4,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X5))),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_1306,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_702]),
[final] ).
cnf(i_0_1307,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk93_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_699]),
[final] ).
cnf(i_0_1308,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_695]),
[final] ).
cnf(i_0_1309,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_703]),
[final] ).
cnf(i_0_1310,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk94_4(X3,X2,X4,X1)),hAPP(X3,esk94_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_704]),
[final] ).
cnf(i_0_1311,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),c_Product__Type_OSigma(X5,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1312,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X1)),hAPP(hAPP(c_Product__Type_OPair(X5,X1),X4),X2)),c_Product__Type_OSigma(X5,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_706]),
[final] ).
cnf(i_0_1313,plain,
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(X6,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Product__Type_OSigma(X1,X2,X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1314,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_708]),
[final] ).
cnf(i_0_1315,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1316,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_706]),
[final] ).
cnf(i_0_1317,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Product__Type_OSigma(X1,X2,X5,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1318,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ 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)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X4,c_Product__Type_OSigma(X1,X1,X5,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_710]),
[final] ).
cnf(i_0_1319,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_673]),
[final] ).
cnf(i_0_1320,plain,
( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk26_3(X3,X2,X1)),esk27_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_711]),
[final] ).
cnf(i_0_1321,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_712]),
[final] ).
cnf(i_0_1322,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_713]),
[final] ).
cnf(i_0_1323,plain,
( hBOOL(hAPP(hAPP(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_714]),
[final] ).
cnf(i_0_1324,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_708]),
[final] ).
cnf(i_0_1325,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)),c_Product__Type_OSigma(X1,X2,X5,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1326,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_716]),
[final] ).
cnf(i_0_1327,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_717]),
[final] ).
cnf(i_0_1328,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_717]),
[final] ).
cnf(i_0_1329,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk62_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_718]),
[final] ).
cnf(i_0_1330,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_719]),
[final] ).
cnf(i_0_1331,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk55_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_720]),
[final] ).
cnf(i_0_1332,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_660]),
[final] ).
cnf(i_0_1333,plain,
hAPP(c_Product__Type_Ointernal__split(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(rw,[status(thm)],[i_0_721,c_0_599]),
[final] ).
cnf(i_0_1334,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_722]),
[final] ).
cnf(i_0_1335,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1)),esk13_1(X1))),hAPP(esk11_1(X1),X2)))
| c_Arrow__Order__Mirabelle_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),esk12_1(X1)),esk13_1(X1))),hAPP(esk10_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[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),esk12_1(X1)),esk13_1(X1))),hAPP(esk10_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),esk12_1(X1)),esk13_1(X1))),hAPP(esk11_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1337,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_716]),
[final] ).
cnf(i_0_1338,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_723]),
[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)),c_List_Olist_ONil(X1)),X2)),c_List_Olistrel1(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_724]),
[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)),c_List_Olist_ONil(X1)),X2)),c_List_Olex(X1,X3))),
inference(split_conjunct,[status(thm)],[i_0_725]),
[final] ).
cnf(i_0_1341,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_692]),
[final] ).
cnf(i_0_1342,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_726]),
[final] ).
cnf(i_0_1343,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_727]),
[final] ).
cnf(i_0_1344,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_728]),
[final] ).
cnf(i_0_1345,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_729]),
[final] ).
cnf(i_0_1346,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_Product__Type_OSigma(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Olists(X1,X3),c_COMBK(tc_fun(tc_List_Olist(X1),tc_HOL_Obool),tc_List_Olist(X1),c_List_Olists(X1,X3))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_730]),
[final] ).
cnf(i_0_1347,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_661]),
[final] ).
cnf(i_0_1348,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_731]),
[final] ).
cnf(i_0_1349,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_618]),
[final] ).
cnf(i_0_1350,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_732]),
[final] ).
cnf(i_0_1351,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_684]),
[final] ).
cnf(i_0_1352,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk34_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_1353,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk33_5(X4,X3,X5,X1,X2))
| X5 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4)
| hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1354,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk4_3(X3,X2,X1)),esk5_3(X3,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1355,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_734]),
[final] ).
cnf(i_0_1356,plain,
c_Set_Oimage(tc_prod(X1,X2),tc_prod(X2,X1),hAPP(c_Product__Type_Ointernal__split(X1,X2,tc_prod(X2,X1)),hAPP(c_COMBC(X2,X1,tc_prod(X2,X1)),c_Product__Type_OPair(X2,X1))),c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4))) = c_Product__Type_OSigma(X2,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X2,X3)),
inference(rw,[status(thm)],[i_0_735,c_0_599]),
[final] ).
cnf(i_0_1357,plain,
( c_Relation_Otrans(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk90_2(X2,X1)),esk92_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1358,plain,
( c_Relation_Otrans(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk46_2(X2,X1)),esk48_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_1359,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_737]),
[final] ).
cnf(i_0_1360,plain,
( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk34_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_1361,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk33_5(X4,X3,X5,X1,X2))
| X1 = c_List_Olist_ONil(X2)
| hAPP(hAPP(c_List_Oappend(X2),X1),X5) != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1362,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Product__Type_Ointernal__split(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(rw,[status(thm)],[i_0_738,c_0_599]),
[final] ).
cnf(i_0_1363,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_739]),
[final] ).
cnf(i_0_1364,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ORange(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X1),tc_HOL_Obool)),X3),X4)),hAPP(hAPP(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_740]),
[final] ).
cnf(i_0_1365,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Relation_ODomain(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X3),X4)),hAPP(hAPP(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_741]),
[final] ).
cnf(i_0_1366,plain,
( ~ c_Orderings_Oord__class_Oless(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))
| ~ hBOOL(hAPP(X2,c_List_Onth(X1,X3,c_Nat_Osize__class_Osize(tc_List_Olist(X1),c_List_OtakeWhile(X1,X2,X3))))) ),
inference(split_conjunct,[status(thm)],[i_0_742]),
[final] ).
cnf(i_0_1367,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_743]),
[final] ).
cnf(i_0_1368,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_744]),
[final] ).
cnf(i_0_1369,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_705]),
[final] ).
cnf(i_0_1370,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X4),X2),X5)),c_Product__Type_OSigma(X1,X4,X3,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_745]),
[final] ).
cnf(i_0_1371,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_746]),
[final] ).
cnf(i_0_1372,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_747]),
[final] ).
cnf(i_0_1373,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_674]),
[final] ).
cnf(i_0_1374,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_748]),
[final] ).
cnf(i_0_1375,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_749]),
[final] ).
cnf(i_0_1376,plain,
c_Product__Type_OSigma(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X2,X3,X5)),c_Product__Type_OSigma(X1,X2,X4,X5)),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_1377,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_749]),
[final] ).
cnf(i_0_1378,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_748]),
[final] ).
cnf(i_0_1379,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_749]),
[final] ).
cnf(i_0_1380,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_748]),
[final] ).
cnf(i_0_1381,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk96_4(X1,X2,X3,X4),c_Nat_Osize__class_Osize(tc_List_Olist(X4),X3))
| 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)),X3),X2)),c_List_Olistrel(X4,X1)))
| c_Nat_Osize__class_Osize(tc_List_Olist(X4),X3) != c_Nat_Osize__class_Osize(tc_List_Olist(X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1382,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_751]),
[final] ).
cnf(i_0_1383,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_751]),
[final] ).
cnf(i_0_1384,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk10_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),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk11_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1385,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_752]),
[final] ).
cnf(i_0_1386,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_691]),
[final] ).
cnf(i_0_1387,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_660]),
[final] ).
cnf(i_0_1388,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_753]),
[final] ).
cnf(i_0_1389,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_754]),
[final] ).
cnf(i_0_1390,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_755]),
[final] ).
cnf(i_0_1391,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_661]),
[final] ).
cnf(i_0_1392,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk103_3(X2,X3,X1)),X3))
| c_Relation_Orefl__on(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_654]),
[final] ).
cnf(i_0_1393,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_720]),
[final] ).
cnf(i_0_1394,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_756]),
[final] ).
cnf(i_0_1395,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_757]),
[final] ).
cnf(i_0_1396,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_758]),
[final] ).
cnf(i_0_1397,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X4),tc_HOL_Obool),c_Product__Type_OSigma(X1,X4,X2,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X5)),c_Product__Type_OSigma(X1,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X5)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X6),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_715]),
[final] ).
cnf(i_0_1398,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_759]),
[final] ).
cnf(i_0_1399,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_1400,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_760]),
[final] ).
cnf(i_0_1401,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_645]),
[final] ).
cnf(i_0_1402,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_761]),
[final] ).
cnf(i_0_1403,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_762]),
[final] ).
cnf(i_0_1404,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_711]),
[final] ).
cnf(i_0_1405,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_763]),
[final] ).
cnf(i_0_1406,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_764]),
[final] ).
cnf(i_0_1407,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_765]),
[final] ).
cnf(i_0_1408,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_766]),
[final] ).
cnf(i_0_1409,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),esk16_1(X1)),esk17_1(X1))),hAPP(X1,esk15_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1410,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_764]),
[final] ).
cnf(i_0_1411,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk49_2(X2,X1)),esk49_2(X2,X1))),X2))
| c_Relation_Oirrefl(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_767]),
[final] ).
cnf(i_0_1412,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk91_2(X2,X1)),esk92_2(X2,X1))),X2))
| c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1413,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk90_2(X2,X1)),esk91_2(X2,X1))),X2))
| c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1414,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk47_2(X2,X1)),esk48_2(X2,X1))),X2))
| c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_1415,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_685]),
[final] ).
cnf(i_0_1416,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_767]),
[final] ).
cnf(i_0_1417,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_768]),
[final] ).
cnf(i_0_1418,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_769]),
[final] ).
cnf(i_0_1419,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_770]),
[final] ).
cnf(i_0_1420,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_746]),
[final] ).
cnf(i_0_1421,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_771]),
[final] ).
cnf(i_0_1422,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_748]),
[final] ).
cnf(i_0_1423,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_749]),
[final] ).
cnf(i_0_1424,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_772]),
[final] ).
cnf(i_0_1425,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_749]),
[final] ).
cnf(i_0_1426,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_748]),
[final] ).
cnf(i_0_1427,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,hAPP(hAPP(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_773]),
[final] ).
cnf(i_0_1428,plain,
( hBOOL(hAPP(hAPP(X3,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ointernal__split(X1,X2,tc_HOL_Obool),X3),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5))) ),
inference(rw,[status(thm)],[i_0_774,c_0_599]),
[final] ).
cnf(i_0_1429,plain,
( X3 = X5
| c_Product__Type_OSigma(X1,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4)) != c_Product__Type_OSigma(X1,X2,X5,c_COMBK(tc_fun(X2,tc_HOL_Obool),X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_775]),
[final] ).
cnf(i_0_1430,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_776]),
[final] ).
cnf(i_0_1431,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_777]),
[final] ).
cnf(i_0_1432,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_758]),
[final] ).
cnf(i_0_1433,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))),esk22_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_755]),
[final] ).
cnf(i_0_1434,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_778]),
[final] ).
cnf(i_0_1435,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_779]),
[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))),esk15_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1437,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk11_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1438,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))),esk10_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1439,plain,
( c_List_Onth(X2,c_List_OdropWhile(X2,X3,X4),X1) = c_List_Onth(X2,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_List_Olist(X2),c_List_OtakeWhile(X2,X3,X4))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_List_Olist(X2),c_List_OdropWhile(X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1440,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Relation_Orefl__on(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_654]),
[final] ).
cnf(i_0_1441,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_781]),
[final] ).
cnf(i_0_1442,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_782]),
[final] ).
cnf(i_0_1443,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_691]),
[final] ).
cnf(i_0_1444,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_1445,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_1446,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_783]),
[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_784]),
[final] ).
cnf(i_0_1448,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_764]),
[final] ).
cnf(i_0_1449,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_765]),
[final] ).
cnf(i_0_1450,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_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,
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_787]),
[final] ).
cnf(i_0_1453,plain,
c_List_Olist_Olist__case(X1,X2,X3,X4,c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_1454,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_789]),
[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),X2),X4)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_783]),
[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_Oappend(X1),X4),X2)),c_List_Olists(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_783]),
[final] ).
cnf(i_0_1457,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_790]),
[final] ).
cnf(i_0_1458,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_791]),
[final] ).
cnf(i_0_1459,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1460,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1461,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1462,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_793]),
[final] ).
cnf(i_0_1463,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_794]),
[final] ).
cnf(i_0_1464,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1465,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_1(X1)),esk17_1(X1))),hAPP(esk15_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1466,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_790]),
[final] ).
cnf(i_0_1467,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk65_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_796]),
[final] ).
cnf(i_0_1468,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_797]),
[final] ).
cnf(i_0_1469,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_798]),
[final] ).
cnf(i_0_1470,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),esk21_2(X2,X1)),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
inference(split_conjunct,[status(thm)],[i_0_799]),
[final] ).
cnf(i_0_1471,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_699]),
[final] ).
cnf(i_0_1472,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk62_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_718]),
[final] ).
cnf(i_0_1473,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_719]),
[final] ).
cnf(i_0_1474,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),esk55_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_720]),
[final] ).
cnf(i_0_1475,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_790]),
[final] ).
cnf(i_0_1476,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_737]),
[final] ).
cnf(i_0_1477,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X2,c_Product__Type_OSigma(X1,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X3)))
| ~ c_Relation_Orefl__on(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_654]),
[final] ).
cnf(i_0_1478,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(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_792]),
[final] ).
cnf(i_0_1479,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(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_800]),
[final] ).
cnf(i_0_1480,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk100_4(X1,X2,X3,X4),X4)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X2),c_List_OtakeWhile(X2,X3,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1481,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Ointernal__split(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(rw,[status(thm)],[i_0_801,c_0_599]),
[final] ).
cnf(i_0_1482,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Ointernal__split(X4,X5,tc_HOL_Obool),X1),hAPP(hAPP(c_Product__Type_OPair(X4,X5),X2),X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(rw,[status(thm)],[i_0_802,c_0_599]),
[final] ).
cnf(i_0_1483,plain,
( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk65_3(X3,X1,X2)),esk65_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_796]),
[final] ).
cnf(i_0_1484,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1485,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1486,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1487,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_805]),
[final] ).
cnf(i_0_1488,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_806]),
[final] ).
cnf(i_0_1489,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_807]),
[final] ).
cnf(i_0_1490,plain,
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk64_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_808]),
[final] ).
cnf(i_0_1491,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_806]),
[final] ).
cnf(i_0_1492,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_748]),
[final] ).
cnf(i_0_1493,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_749]),
[final] ).
cnf(i_0_1494,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Relation_OId__on(X1,X2),c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1495,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)),esk24_2(X2,X1)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1496,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_811]),
[final] ).
cnf(i_0_1497,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4),hAPP(hAPP(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_812]),
[final] ).
cnf(i_0_1498,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk63_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_808]),
[final] ).
cnf(i_0_1499,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_813]),
[final] ).
cnf(i_0_1500,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X4)),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1501,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_815]),
[final] ).
cnf(i_0_1502,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_816]),
[final] ).
cnf(i_0_1503,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_806]),
[final] ).
cnf(i_0_1504,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_808]),
[final] ).
cnf(i_0_1505,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
| ~ hBOOL(hAPP(X1,esk3_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_733]),
[final] ).
cnf(i_0_1506,plain,
( c_Relation_Otrans(X1,hAPP(hAPP(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_817]),
[final] ).
cnf(i_0_1507,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_818]),
[final] ).
cnf(i_0_1508,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk24_2(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1509,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk63_3(X3,X1,X2)),esk64_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_808]),
[final] ).
cnf(i_0_1510,plain,
( hBOOL(hAPP(hAPP(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_819]),
[final] ).
cnf(i_0_1511,plain,
( c_List_Onth(X2,c_List_OtakeWhile(X2,X3,X4),X1) = c_List_Onth(X2,X4,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_List_Olist(X2),c_List_OtakeWhile(X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_820]),
[final] ).
cnf(i_0_1512,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_821]),
[final] ).
cnf(i_0_1513,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),esk6_0),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(split_conjunct,[status(thm)],[i_0_822]),
[final] ).
cnf(i_0_1514,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_1515,plain,
hAPP(c_Product__Type_Ointernal__split(X1,X2,X3),c_Product__Type_Ocurry(X1,X2,X3,X4)) = X4,
inference(rw,[status(thm)],[i_0_823,c_0_599]),
[final] ).
cnf(i_0_1516,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(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_824]),
[final] ).
cnf(i_0_1517,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_825]),
[final] ).
cnf(i_0_1518,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_826]),
[final] ).
cnf(i_0_1519,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_827]),
[final] ).
cnf(i_0_1520,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_828]),
[final] ).
cnf(i_0_1521,plain,
( hBOOL(hAPP(hAPP(X3,esk60_2(X4,X3)),X4))
| ~ c_Predicate_ORangeP(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1522,plain,
( X2 = X3
| c_List_Onth(X1,X2,esk97_3(X1,X3,X2)) != c_List_Onth(X1,X3,esk97_3(X1,X3,X2))
| 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_830]),
[final] ).
cnf(i_0_1523,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1524,plain,
c_List_Olistsp(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(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_832]),
[final] ).
cnf(i_0_1525,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_833]),
[final] ).
cnf(i_0_1526,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_834]),
[final] ).
cnf(i_0_1527,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_825]),
[final] ).
cnf(i_0_1528,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_826]),
[final] ).
cnf(i_0_1529,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_835]),
[final] ).
cnf(i_0_1530,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_818]),
[final] ).
cnf(i_0_1531,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_835]),
[final] ).
cnf(i_0_1532,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_835]),
[final] ).
cnf(i_0_1533,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_836]),
[final] ).
cnf(i_0_1534,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_837]),
[final] ).
cnf(i_0_1535,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_837]),
[final] ).
cnf(i_0_1536,plain,
( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk81_3(X1,X3,X2)),esk82_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_838]),
[final] ).
cnf(i_0_1537,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_839]),
[final] ).
cnf(i_0_1538,plain,
c_Product__Type_Ocurry(X1,X2,X3,hAPP(c_Product__Type_Ointernal__split(X1,X2,X3),X4)) = X4,
inference(rw,[status(thm)],[i_0_840,c_0_599]),
[final] ).
cnf(i_0_1539,plain,
( X3 = X4
| ~ c_List_Odistinct(X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2))
| c_List_Onth(X1,X2,X3) != c_List_Onth(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1540,plain,
( X3 = X4
| c_List_Onth(X1,X2,X3) != c_List_Onth(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1541,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_836]),
[final] ).
cnf(i_0_1542,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_843]),
[final] ).
cnf(i_0_1543,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(rw,[status(thm)],[i_0_844,c_0_599]),
[final] ).
cnf(i_0_1544,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(rw,[status(thm)],[i_0_845,c_0_599]),
[final] ).
cnf(i_0_1545,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_846]),
[final] ).
cnf(i_0_1546,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_836]),
[final] ).
cnf(i_0_1547,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_847]),
[final] ).
cnf(i_0_1548,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,X1)),X3),X4),X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X3,X5)),hAPP(X4,X5))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_848]),
[final] ).
cnf(i_0_1549,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_849]),
[final] ).
cnf(i_0_1550,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4),hAPP(hAPP(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_850]),
[final] ).
cnf(i_0_1551,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_851]),
[final] ).
cnf(i_0_1552,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_852]),
[final] ).
cnf(i_0_1553,plain,
( hBOOL(hAPP(c_List_Olistsp(X1,X2),esk82_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_838]),
[final] ).
cnf(i_0_1554,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_853]),
[final] ).
cnf(i_0_1555,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_854]),
[final] ).
cnf(i_0_1556,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_855]),
[final] ).
cnf(i_0_1557,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_856]),
[final] ).
cnf(i_0_1558,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_857]),
[final] ).
cnf(i_0_1559,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_858]),
[final] ).
cnf(i_0_1560,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_859]),
[final] ).
cnf(i_0_1561,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_860]),
[final] ).
cnf(i_0_1562,plain,
c_List_Onth(X1,hAPP(hAPP(c_List_Oappend(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4)),c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1563,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_862]),
[final] ).
cnf(i_0_1564,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_863]),
[final] ).
cnf(i_0_1565,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_864]),
[final] ).
cnf(i_0_1566,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_865]),
[final] ).
cnf(i_0_1567,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_866]),
[final] ).
cnf(i_0_1568,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_867]),
[final] ).
cnf(i_0_1569,plain,
( hBOOL(hAPP(X1,esk81_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_838]),
[final] ).
cnf(i_0_1570,plain,
( c_Predicate_ODomainP(X4,X5,X1,X2)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1571,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1572,plain,
( c_Predicate_ORangeP(X4,X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_869]),
[final] ).
cnf(i_0_1573,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_870]),
[final] ).
cnf(i_0_1574,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_871]),
[final] ).
cnf(i_0_1575,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1576,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X3),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1577,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_874]),
[final] ).
cnf(i_0_1578,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_875]),
[final] ).
cnf(i_0_1579,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_876]),
[final] ).
cnf(i_0_1580,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_877]),
[final] ).
cnf(i_0_1581,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_838]),
[final] ).
cnf(i_0_1582,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_878]),
[final] ).
cnf(i_0_1583,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_879]),
[final] ).
cnf(i_0_1584,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_880]),
[final] ).
cnf(i_0_1585,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_825]),
[final] ).
cnf(i_0_1586,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_826]),
[final] ).
cnf(i_0_1587,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(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_881]),
[final] ).
cnf(i_0_1588,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(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_882]),
[final] ).
cnf(i_0_1589,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(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_883]),
[final] ).
cnf(i_0_1590,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_884]),
[final] ).
cnf(i_0_1591,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_885]),
[final] ).
cnf(i_0_1592,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_886]),
[final] ).
cnf(i_0_1593,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(tc_fun(X1,tc_HOL_Obool),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_1594,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_888]),
[final] ).
cnf(i_0_1595,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_889]),
[final] ).
cnf(i_0_1596,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_890]),
[final] ).
cnf(i_0_1597,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1598,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_892]),
[final] ).
cnf(i_0_1599,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_893]),
[final] ).
cnf(i_0_1600,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1601,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1602,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1603,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3))
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1604,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_895]),
[final] ).
cnf(i_0_1605,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_896]),
[final] ).
cnf(i_0_1606,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_897]),
[final] ).
cnf(i_0_1607,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_898]),
[final] ).
cnf(i_0_1608,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_897]),
[final] ).
cnf(i_0_1609,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_898]),
[final] ).
cnf(i_0_1610,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_899]),
[final] ).
cnf(i_0_1611,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1612,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_901]),
[final] ).
cnf(i_0_1613,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_902]),
[final] ).
cnf(i_0_1614,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_902]),
[final] ).
cnf(i_0_1615,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_643]),
[final] ).
cnf(i_0_1616,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_903]),
[final] ).
cnf(i_0_1617,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_1618,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_904]),
[final] ).
cnf(i_0_1619,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_643]),
[final] ).
cnf(i_0_1620,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_1621,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_902]),
[final] ).
cnf(i_0_1622,plain,
( hAPP(hAPP(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_905]),
[final] ).
cnf(i_0_1623,plain,
( hAPP(hAPP(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_906]),
[final] ).
cnf(i_0_1624,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk97_3(X1,X2,X3),c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3))
| X3 = X2
| c_Nat_Osize__class_Osize(tc_List_Olist(X1),X3) != c_Nat_Osize__class_Osize(tc_List_Olist(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1625,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_907]),
[final] ).
cnf(i_0_1626,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_908]),
[final] ).
cnf(i_0_1627,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_895]),
[final] ).
cnf(i_0_1628,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1629,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1630,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_911]),
[final] ).
cnf(i_0_1631,plain,
c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
inference(split_conjunct,[status(thm)],[i_0_912]),
[final] ).
cnf(i_0_1632,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1633,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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_914]),
[final] ).
cnf(i_0_1634,plain,
( c_Orderings_Oord__class_Oless(X1,hAPP(hAPP(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_915]),
[final] ).
cnf(i_0_1635,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_916]),
[final] ).
cnf(i_0_1636,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(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_917]),
[final] ).
cnf(i_0_1637,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_918]),
[final] ).
cnf(i_0_1638,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_919]),
[final] ).
cnf(i_0_1639,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_920]),
[final] ).
cnf(i_0_1640,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_921]),
[final] ).
cnf(i_0_1641,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_922]),
[final] ).
cnf(i_0_1642,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_704]),
[final] ).
cnf(i_0_1643,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_911]),
[final] ).
cnf(i_0_1644,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_923]),
[final] ).
cnf(i_0_1645,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_924]),
[final] ).
cnf(i_0_1646,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_925]),
[final] ).
cnf(i_0_1647,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_926]),
[final] ).
cnf(i_0_1648,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_927]),
[final] ).
cnf(i_0_1649,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_928]),
[final] ).
cnf(i_0_1650,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_929]),
[final] ).
cnf(i_0_1651,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_930]),
[final] ).
cnf(i_0_1652,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_931]),
[final] ).
cnf(i_0_1653,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk79_3(X1,X2,X3) != esk80_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_694]),
[final] ).
cnf(i_0_1654,plain,
( c_Relation_Osingle__valued(X3,X2,X1)
| esk51_3(X1,X2,X3) != esk52_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_695]),
[final] ).
cnf(i_0_1655,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1656,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_902]),
[final] ).
cnf(i_0_1657,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_933]),
[final] ).
cnf(i_0_1658,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_808]),
[final] ).
cnf(i_0_1659,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_818]),
[final] ).
cnf(i_0_1660,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_895]),
[final] ).
cnf(i_0_1661,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_934]),
[final] ).
cnf(i_0_1662,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_935]),
[final] ).
cnf(i_0_1663,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_936]),
[final] ).
cnf(i_0_1664,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1665,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_938]),
[final] ).
cnf(i_0_1666,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_939]),
[final] ).
cnf(i_0_1667,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_940]),
[final] ).
cnf(i_0_1668,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_941]),
[final] ).
cnf(i_0_1669,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_942]),
[final] ).
cnf(i_0_1670,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_939]),
[final] ).
cnf(i_0_1671,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1672,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_943]),
[final] ).
cnf(i_0_1673,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_944]),
[final] ).
cnf(i_0_1674,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_945]),
[final] ).
cnf(i_0_1675,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1676,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_1677,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_1678,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_947]),
[final] ).
cnf(i_0_1679,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_871]),
[final] ).
cnf(i_0_1680,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_948]),
[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_949]),
[final] ).
cnf(i_0_1682,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_1683,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_951]),
[final] ).
cnf(i_0_1684,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_952]),
[final] ).
cnf(i_0_1685,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_953]),
[final] ).
cnf(i_0_1686,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_954]),
[final] ).
cnf(i_0_1687,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_1688,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_1689,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_957]),
[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_958]),
[final] ).
cnf(i_0_1691,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_1692,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_1693,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_961]),
[final] ).
cnf(i_0_1694,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_938]),
[final] ).
cnf(i_0_1695,plain,
( c_List_Onth(X1,X2,esk98_2(X2,X1)) = c_List_Onth(X1,X2,esk99_2(X2,X1))
| c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1696,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1697,plain,
( X1 = X2
| hAPP(hAPP(c_List_Olist_OCons(X3),X1),X4) != hAPP(hAPP(c_List_Olist_OCons(X3),X2),X5) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1698,plain,
( X1 = X2
| hAPP(hAPP(c_List_Olist_OCons(X3),X4),X1) != hAPP(hAPP(c_List_Olist_OCons(X3),X5),X2) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1699,plain,
( X2 = X4
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X4),X3) ),
inference(split_conjunct,[status(thm)],[i_0_964]),
[final] ).
cnf(i_0_1700,plain,
( X3 = X4
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != hAPP(hAPP(c_List_Oappend(X1),X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_965]),
[final] ).
cnf(i_0_1701,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1702,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1703,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X3)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_968]),
[final] ).
cnf(i_0_1704,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1705,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_920]),
[final] ).
cnf(i_0_1706,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1707,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_970]),
[final] ).
cnf(i_0_1708,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_1709,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_1710,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_1711,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_974]),
[final] ).
cnf(i_0_1712,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_975]),
[final] ).
cnf(i_0_1713,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_948]),
[final] ).
cnf(i_0_1714,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_976]),
[final] ).
cnf(i_0_1715,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_977]),
[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_974]),
[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_975]),
[final] ).
cnf(i_0_1718,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_978]),
[final] ).
cnf(i_0_1719,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_938]),
[final] ).
cnf(i_0_1720,plain,
( hAPP(hAPP(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_979]),
[final] ).
cnf(i_0_1721,plain,
( hAPP(hAPP(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_980]),
[final] ).
cnf(i_0_1722,plain,
( hAPP(hAPP(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_981]),
[final] ).
cnf(i_0_1723,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) != X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1724,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1725,plain,
( c_List_Odistinct(X1,c_List_OdropWhile(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1726,plain,
( c_List_Odistinct(X1,c_List_OtakeWhile(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1727,plain,
( c_List_Odistinct(X1,c_List_Oinsert(X1,X3,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_985]),
[final] ).
cnf(i_0_1728,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk22_2(X2,X1)) != hAPP(esk22_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_755]),
[final] ).
cnf(i_0_1729,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1730,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1731,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1732,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_944]),
[final] ).
cnf(i_0_1733,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_989]),
[final] ).
cnf(i_0_1734,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_990]),
[final] ).
cnf(i_0_1735,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_1736,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_991]),
[final] ).
cnf(i_0_1737,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_992]),
[final] ).
cnf(i_0_1738,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_988]),
[final] ).
cnf(i_0_1739,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_993]),
[final] ).
cnf(i_0_1740,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_994]),
[final] ).
cnf(i_0_1741,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_990]),
[final] ).
cnf(i_0_1742,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_995]),
[final] ).
cnf(i_0_1743,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_996]),
[final] ).
cnf(i_0_1744,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk99_2(X1,X2),c_Nat_Osize__class_Osize(tc_List_Olist(X2),X1))
| c_List_Odistinct(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1745,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk98_2(X1,X2),c_Nat_Osize__class_Osize(tc_List_Olist(X2),X1))
| c_List_Odistinct(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1746,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_945]),
[final] ).
cnf(i_0_1747,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1748,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool),X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1749,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_998]),
[final] ).
cnf(i_0_1750,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_996]),
[final] ).
cnf(i_0_1751,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1752,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1753,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1001]),
[final] ).
cnf(i_0_1754,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1755,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_976]),
[final] ).
cnf(i_0_1756,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_1003]),
[final] ).
cnf(i_0_1757,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_1758,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_1005]),
[final] ).
cnf(i_0_1759,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_1006]),
[final] ).
cnf(i_0_1760,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_1007]),
[final] ).
cnf(i_0_1761,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_954]),
[final] ).
cnf(i_0_1762,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_1008]),
[final] ).
cnf(i_0_1763,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_1009]),
[final] ).
cnf(i_0_1764,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_1010]),
[final] ).
cnf(i_0_1765,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_957]),
[final] ).
cnf(i_0_1766,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_1011]),
[final] ).
cnf(i_0_1767,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_1768,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_1012]),
[final] ).
cnf(i_0_1769,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_1013]),
[final] ).
cnf(i_0_1770,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1771,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1772,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1773,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1774,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1775,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1019]),
[final] ).
cnf(i_0_1776,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1777,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1778,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1779,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1780,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1022]),
[final] ).
cnf(i_0_1781,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1782,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1783,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1784,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1785,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1786,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_1026]),
[final] ).
cnf(i_0_1787,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_1026]),
[final] ).
cnf(i_0_1788,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_1027]),
[final] ).
cnf(i_0_1789,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_1027]),
[final] ).
cnf(i_0_1790,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1791,plain,
( hBOOL(hAPP(c_List_Olistsp(X2,X3),X1))
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_838]),
[final] ).
cnf(i_0_1792,plain,
( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1793,plain,
( X2 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1794,plain,
( X3 = c_List_Olist_ONil(X1)
| hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1795,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1796,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1797,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1798,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1799,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1800,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1801,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1802,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1803,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1804,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_1038]),
[final] ).
cnf(i_0_1805,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1806,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1807,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1808,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1809,plain,
c_Relation_ORange(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1810,plain,
c_Relation_ODomain(X1,X1,c_Relation_OId__on(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1044]),
[final] ).
cnf(i_0_1811,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_918]),
[final] ).
cnf(i_0_1812,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_918]),
[final] ).
cnf(i_0_1813,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1814,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1815,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1816,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1817,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1818,plain,
c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1819,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1820,plain,
( c_List_Odistinct(X1,X2)
| ~ c_List_Odistinct(X1,c_List_Orotate1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1821,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1822,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_1026]),
[final] ).
cnf(i_0_1823,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_1027]),
[final] ).
cnf(i_0_1824,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_1052]),
[final] ).
cnf(i_0_1825,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_1053]),
[final] ).
cnf(i_0_1826,plain,
( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1827,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_1055]),
[final] ).
cnf(i_0_1828,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_1056]),
[final] ).
cnf(i_0_1829,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_949]),
[final] ).
cnf(i_0_1830,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_949]),
[final] ).
cnf(i_0_1831,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1832,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_974]),
[final] ).
cnf(i_0_1833,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1834,plain,
c_List_OdropWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1059]),
[final] ).
cnf(i_0_1835,plain,
c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1060]),
[final] ).
cnf(i_0_1836,plain,
( c_List_Odistinct(X1,c_List_Orotate1(X1,X2))
| ~ c_List_Odistinct(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1837,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1061]),
[final] ).
cnf(i_0_1838,plain,
( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1839,plain,
( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1840,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1841,plain,
( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1842,plain,
c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1062]),
[final] ).
cnf(i_0_1843,plain,
c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1063]),
[final] ).
cnf(i_0_1844,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1064]),
[final] ).
cnf(i_0_1845,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1065]),
[final] ).
cnf(i_0_1846,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1066]),
[final] ).
cnf(i_0_1847,plain,
( c_List_Odistinct(X2,X1)
| esk98_2(X1,X2) != esk99_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1848,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_1849,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1850,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1067]),
[final] ).
cnf(i_0_1851,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_1068]),
[final] ).
cnf(i_0_1852,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1069]),
[final] ).
cnf(i_0_1853,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1070]),
[final] ).
cnf(i_0_1854,plain,
c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1071]),
[final] ).
cnf(i_0_1855,plain,
c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1072]),
[final] ).
cnf(i_0_1856,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1073]),
[final] ).
cnf(i_0_1857,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1074]),
[final] ).
cnf(i_0_1858,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1075]),
[final] ).
cnf(i_0_1859,plain,
( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1076]),
[final] ).
cnf(i_0_1860,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1077]),
[final] ).
cnf(i_0_1861,plain,
( X2 = c_List_Olist_ONil(X1)
| c_List_Orotate1(X1,X2) != c_List_Olist_ONil(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1078]),
[final] ).
cnf(i_0_1862,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1079]),
[final] ).
cnf(i_0_1863,plain,
( c_List_Orotate1(X2,X1) = c_List_Olist_ONil(X2)
| X1 != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1078]),
[final] ).
cnf(i_0_1864,plain,
c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_1080]),
[final] ).
cnf(i_0_1865,plain,
c_List_Orotate1(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_901]),
[final] ).
cnf(i_0_1866,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1081]),
[final] ).
cnf(i_0_1867,plain,
c_List_Odistinct(X1,c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_1082]),
[final] ).
cnf(i_0_1868,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1869,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1870,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1871,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1872,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1873,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1874,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1875,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1876,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
[final] ).
cnf(i_0_1877,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
[final] ).
cnf(i_0_1878,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
[final] ).
cnf(i_0_1879,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1880,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1881,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1882,axiom,
X1 = X1 ).
cnf(i_0_1883,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1884,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| esk80_3(X1,X3,X4) = esk80_3(X2,X3,X4) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| esk80_3(X3,X1,X4) = esk80_3(X3,X2,X4) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| esk80_3(X3,X4,X1) = esk80_3(X3,X4,X2) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| esk79_3(X1,X3,X4) = esk79_3(X2,X3,X4) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| esk79_3(X3,X1,X4) = esk79_3(X3,X2,X4) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| esk79_3(X3,X4,X1) = esk79_3(X3,X4,X2) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| esk52_3(X1,X3,X4) = esk52_3(X2,X3,X4) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| esk52_3(X3,X1,X4) = esk52_3(X3,X2,X4) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| esk52_3(X3,X4,X1) = esk52_3(X3,X4,X2) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| esk51_3(X1,X3,X4) = esk51_3(X2,X3,X4) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| esk51_3(X3,X1,X4) = esk51_3(X3,X2,X4) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| esk51_3(X3,X4,X1) = esk51_3(X3,X4,X2) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).
cnf(i_0_1909,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_1910,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_1911,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_1912,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_1913,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_1914,axiom,
( X1 != X2
| c_List_OdropWhile(X1,X3,X4) = c_List_OdropWhile(X2,X3,X4) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| c_List_OdropWhile(X3,X1,X4) = c_List_OdropWhile(X3,X2,X4) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| c_List_OdropWhile(X3,X4,X1) = c_List_OdropWhile(X3,X4,X2) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| esk98_2(X1,X3) = esk98_2(X2,X3) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| esk98_2(X3,X1) = esk98_2(X3,X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| esk99_2(X1,X3) = esk99_2(X2,X3) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| esk99_2(X3,X1) = esk99_2(X3,X2) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_1941,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_1942,axiom,
( X1 != X2
| c_Relation_ORange(X1,X3,X4) = c_Relation_ORange(X2,X3,X4) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| c_Relation_ORange(X3,X1,X4) = c_Relation_ORange(X3,X2,X4) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| c_Relation_ORange(X3,X4,X1) = c_Relation_ORange(X3,X4,X2) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| c_FuncSet_Ocompose(X1,X3,X4,X5,X6,X7) = c_FuncSet_Ocompose(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| c_FuncSet_Ocompose(X3,X1,X4,X5,X6,X7) = c_FuncSet_Ocompose(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_1947,axiom,
( X1 != X2
| c_FuncSet_Ocompose(X3,X4,X1,X5,X6,X7) = c_FuncSet_Ocompose(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_1948,axiom,
( X1 != X2
| c_FuncSet_Ocompose(X3,X4,X5,X1,X6,X7) = c_FuncSet_Ocompose(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_1949,axiom,
( X1 != X2
| c_FuncSet_Ocompose(X3,X4,X5,X6,X1,X7) = c_FuncSet_Ocompose(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_1950,axiom,
( X1 != X2
| c_FuncSet_Ocompose(X3,X4,X5,X6,X7,X1) = c_FuncSet_Ocompose(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_1951,axiom,
( X1 != X2
| c_List_Onth(X1,X3,X4) = c_List_Onth(X2,X3,X4) ) ).
cnf(i_0_1952,axiom,
( X1 != X2
| c_List_Onth(X3,X1,X4) = c_List_Onth(X3,X2,X4) ) ).
cnf(i_0_1953,axiom,
( X1 != X2
| c_List_Onth(X3,X4,X1) = c_List_Onth(X3,X4,X2) ) ).
cnf(i_0_1954,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1955,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1956,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1957,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1958,axiom,
( X1 != X2
| esk29_4(X1,X3,X4,X5) = esk29_4(X2,X3,X4,X5) ) ).
cnf(i_0_1959,axiom,
( X1 != X2
| esk29_4(X3,X1,X4,X5) = esk29_4(X3,X2,X4,X5) ) ).
cnf(i_0_1960,axiom,
( X1 != X2
| esk29_4(X3,X4,X1,X5) = esk29_4(X3,X4,X2,X5) ) ).
cnf(i_0_1961,axiom,
( X1 != X2
| esk29_4(X3,X4,X5,X1) = esk29_4(X3,X4,X5,X2) ) ).
cnf(i_0_1962,axiom,
( X1 != X2
| esk28_4(X1,X3,X4,X5) = esk28_4(X2,X3,X4,X5) ) ).
cnf(i_0_1963,axiom,
( X1 != X2
| esk28_4(X3,X1,X4,X5) = esk28_4(X3,X2,X4,X5) ) ).
cnf(i_0_1964,axiom,
( X1 != X2
| esk28_4(X3,X4,X1,X5) = esk28_4(X3,X4,X2,X5) ) ).
cnf(i_0_1965,axiom,
( X1 != X2
| esk28_4(X3,X4,X5,X1) = esk28_4(X3,X4,X5,X2) ) ).
cnf(i_0_1966,axiom,
( X1 != X2
| c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).
cnf(i_0_1967,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).
cnf(i_0_1968,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).
cnf(i_0_1969,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).
cnf(i_0_1970,axiom,
( X1 != X2
| c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).
cnf(i_0_1971,axiom,
( X1 != X2
| c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).
cnf(i_0_1972,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_1973,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1974,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1975,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1976,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1977,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1978,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1979,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1980,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1981,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_1982,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_1983,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_1984,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_1985,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_1986,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_1987,axiom,
( X1 != X2
| c_List_Orotate1(X1,X3) = c_List_Orotate1(X2,X3) ) ).
cnf(i_0_1988,axiom,
( X1 != X2
| c_List_Orotate1(X3,X1) = c_List_Orotate1(X3,X2) ) ).
cnf(i_0_1989,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_1990,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_1991,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_1992,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_1993,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_1994,axiom,
( X1 != X2
| c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).
cnf(i_0_1995,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).
cnf(i_0_1996,axiom,
( X1 != X2
| c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).
cnf(i_0_1997,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1998,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X1,X3)
| c_Relation_Otrans(X2,X3) ) ).
cnf(i_0_1999,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X3,X1)
| c_Relation_Otrans(X3,X2) ) ).
cnf(i_0_2000,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_2001,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_2002,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_2003,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_2004,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_2005,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_2006,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_2007,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2008,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2009,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2010,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2011,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2012,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_2013,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_2014,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_2015,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_2016,axiom,
( X1 != X2
| ~ c_List_Odistinct(X1,X3)
| c_List_Odistinct(X2,X3) ) ).
cnf(i_0_2017,axiom,
( X1 != X2
| ~ c_List_Odistinct(X3,X1)
| c_List_Odistinct(X3,X2) ) ).
cnf(i_0_2018,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2019,axiom,
( X1 != X2
| ~ class_Lattices_Osemilattice__inf(X1)
| class_Lattices_Osemilattice__inf(X2) ) ).
cnf(i_0_2020,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_2021,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_2022,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_2023,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2024,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2025,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2026,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X1,X3,X4,X5)
| c_List_Olistrelp(X2,X3,X4,X5) ) ).
cnf(i_0_2027,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X1,X4,X5)
| c_List_Olistrelp(X3,X2,X4,X5) ) ).
cnf(i_0_2028,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X1,X5)
| c_List_Olistrelp(X3,X4,X2,X5) ) ).
cnf(i_0_2029,axiom,
( X1 != X2
| ~ c_List_Olistrelp(X3,X4,X5,X1)
| c_List_Olistrelp(X3,X4,X5,X2) ) ).
cnf(i_0_2030,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X1,X3,X4,X5)
| c_Predicate_ODomainP(X2,X3,X4,X5) ) ).
cnf(i_0_2031,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X1,X4,X5)
| c_Predicate_ODomainP(X3,X2,X4,X5) ) ).
cnf(i_0_2032,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X1,X5)
| c_Predicate_ODomainP(X3,X4,X2,X5) ) ).
cnf(i_0_2033,axiom,
( X1 != X2
| ~ c_Predicate_ODomainP(X3,X4,X5,X1)
| c_Predicate_ODomainP(X3,X4,X5,X2) ) ).
cnf(i_0_2034,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X1,X3,X4,X5)
| c_Predicate_ORangeP(X2,X3,X4,X5) ) ).
cnf(i_0_2035,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X1,X4,X5)
| c_Predicate_ORangeP(X3,X2,X4,X5) ) ).
cnf(i_0_2036,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X1,X5)
| c_Predicate_ORangeP(X3,X4,X2,X5) ) ).
cnf(i_0_2037,axiom,
( X1 != X2
| ~ c_Predicate_ORangeP(X3,X4,X5,X1)
| c_Predicate_ORangeP(X3,X4,X5,X2) ) ).
cnf(i_0_2038,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_2039,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_2040,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_2041,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_2042,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_2043,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_2044,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_2045,plain,
X1 = X1,
inference(equality_inference,[],[1112]) ).
cnf(i_0_2088,plain,
X1 = X1,
inference(equality_inference,[],[1468]) ).
cnf(i_0_2093,plain,
X1 = X1,
inference(equality_inference,[],[1534]) ).
cnf(i_0_2094,plain,
X1 = X1,
inference(equality_inference,[],[1535]) ).
cnf(i_0_2097,plain,
X1 = X1,
inference(equality_inference,[],[1607]) ).
cnf(i_0_2098,plain,
X1 = X1,
inference(equality_inference,[],[1609]) ).
cnf(i_0_2103,plain,
hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
inference(equality_inference,[],[1658]) ).
cnf(i_0_2104,plain,
X1 = X1,
inference(equality_inference,[],[1697]) ).
cnf(i_0_2105,plain,
X1 = X1,
inference(equality_inference,[],[1698]) ).
cnf(i_0_2106,plain,
X1 = X1,
inference(equality_inference,[],[1699]) ).
cnf(i_0_2107,plain,
X1 = X1,
inference(equality_inference,[],[1700]) ).
cnf(i_0_2108,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1705]) ).
cnf(i_0_2109,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,[],[1732]) ).
cnf(i_0_2110,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,[],[1734]) ).
cnf(i_0_2112,plain,
X1 = X1,
inference(equality_inference,[],[1747]) ).
cnf(i_0_2113,plain,
~ c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1748]) ).
cnf(i_0_2114,plain,
c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
inference(equality_inference,[],[1750]) ).
cnf(i_0_2120,plain,
hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
inference(equality_inference,[],[1791]) ).
cnf(i_0_2121,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1802]) ).
cnf(i_0_2122,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1803]) ).
cnf(i_0_2123,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1816]) ).
cnf(i_0_2124,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(equality_inference,[],[1817]) ).
cnf(i_0_2125,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1819]) ).
cnf(i_0_2126,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[1826]) ).
cnf(i_0_2130,plain,
hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
inference(equality_inference,[],[1838]) ).
cnf(i_0_2131,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(equality_inference,[],[1839]) ).
cnf(i_0_2132,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
inference(equality_inference,[],[1840]) ).
cnf(i_0_2133,plain,
X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
inference(equality_inference,[],[1841]) ).
cnf(i_0_2134,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[1850]) ).
cnf(i_0_2135,plain,
c_List_Orotate1(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
inference(equality_inference,[],[1863]) ).
cnf(i_0_2247,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2258,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,X2),
inference(rename_variables,[],[i_0_1821]) ).
cnf(i_0_2279,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1852]) ).
cnf(i_0_2307,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_1652]) ).
cnf(i_0_2310,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_2331,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2332,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1632]) ).
cnf(i_0_2339,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1797]) ).
cnf(i_0_2343,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(rename_variables,[],[i_0_1798]) ).
cnf(i_0_2344,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(rename_variables,[],[i_0_1846]) ).
cnf(i_0_2357,plain,
hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
inference(rename_variables,[],[i_0_1846]) ).
cnf(i_0_2373,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1797]) ).
cnf(i_0_2380,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2387,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2393,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2410,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2446,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1852]) ).
cnf(i_0_2452,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1852]) ).
cnf(i_0_2455,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1852]) ).
cnf(i_0_2458,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1808]) ).
cnf(i_0_2461,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1808]) ).
cnf(i_0_2492,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2495,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_1652]) ).
cnf(i_0_2741,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1632]) ).
cnf(i_0_2744,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2752,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2764,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2793,plain,
c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_2864,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_1652]) ).
cnf(i_0_2936,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_1652]) ).
cnf(i_0_3183,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_3192,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_1852]) ).
cnf(i_0_3260,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_1652]) ).
cnf(c_0_1870,plain,
X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
i_0_1806 ).
cnf(c_0_1871,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
i_0_1519 ).
cnf(c_0_1872,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_1870,c_0_1871]) ).
cnf(c_0_1873,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_1872,c_0_1871]) ).
cnf(c_0_1874,plain,
hAPP(c_COMBI(X1),X2) = X2,
i_0_1866 ).
cnf(c_0_1875,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_1873,c_0_1874]) ).
cnf(c_0_1876,plain,
$false,
inference(er,[status(thm)],[c_0_1875]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT141+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n006.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 01:58:16 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 108.13/96.37 % Version : CSE_E---1.7
% 108.13/96.37 % Problem : theBenchmark.p
% 108.13/96.37 % SZS status Theorem for theBenchmark.p
% 108.13/96.37 % SZS output start CNFRefutation
% See solution above
% 166.33/154.59 % Total time : 95.236s
%------------------------------------------------------------------------------